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I AO-AO8 729 ARMY ENGINEER TOPOGRAPHIC LABS PORT BELVOIR VA Pie I/5PROTOTYPE IMAGE SPECTRUM ANALYZER (PISA) FOR CARTOGRAPHIC PEATU-ETC(U)OCT 79 P CHIN F. B RONK. V 11 SEEMILLER

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ETL-0204 LEVEL,trototype image spectrum

Whalyzer (PISA) for

cortographic feature extraction

- -Fuay Chen

8redrick W. Rohde Q... i_ illiam W. Seemuller

OCTOBER 1979

U.S. ARMY CORPS OF ENGINEER

ENGINEER TOPOGRAPHIC LABORATORIES

FORT BELVOIR, VIRGINIA 22060

APPROVED FOR PUBLI( REIEASI,; DISTRIBUTION UNLIMITED

"80

.., .11

Destroy this report when no longer needed.Do not return it to the originator.

The findings in this report are not to be construed as an officialDepartment of the Army position unless so designated by otherauthorized documents.

The citation in this report of trade names of commercially availableproducts does not constitute official endorsement or approval of theuse of such products.

11,A

SECURITY CLASSIFICATION OF THIS PAGE (When Dote Entered)

REPOT DCUMNTATON AGEREAD INSTRUCTIONSREPOT DM AENTTIONPAGEBEFORE COMPLETING FORM

I.- REPORT *kMMER----- - 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

/(' ETL-02044. TITLE (Aomf biM - 5- TYPE OF REPORT & PERIOD COVERED

~ ~~TOTYE~A E SPECTRUM NALYZER (PJSA/ - Research Iote' RCARTORAHI FEA TEI E RACIN 6. PERFOOMMO CMO. A&ORT NUMBER

~.7- AUTHjOS(.) S. CONTRACT OR GRANT NUMBER(*)

Pi-Fuay/ChenFrederick W.jRohde

,,&la" kj Seemulier_______________9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

-AREA & WORK UNIT NUMBERS

U.S. Army Engineer Topographic Laboratories/ .Fort Belvoir, Virginia 22060 -4AI61121152C

11. CONTROLLING OFFICE NAME AND ADDRESS t RIDTM

U.S. Army Engineer Topographic Laboratories /-;&*= 7Fort Belvoir, Virginia 22060 4MUGOFPCS

14. MONITORING AGENCY NAME A ADDRESSI different from Controlling Office) IS. SECURITY CLASS. (of this report)

~ I15o~. DECL ASSI FICATION/ DOWN GRADING

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20. it different froomi Report)

1S. SUPPLEMENTARY NOTES

Plasma Discharge DevicesWalsh TransformsOrthogonal Functions

SAMTRAC? MAIN 0110" N If nnpoa id iefir by block nambw)

An elect ro-optical system for obtaining two-dimensional Walsh transforms of cartographic imageswas developed. The system uses a plasma discharge device to generate visible two-dimensionalWalsh function pattern masks. The cartographic imagery is placed in contact with the plasma tube,and the product of the mask and image is integrated with a single photodetector. The system iscapable of producing 5 12 by 512 (262, 144), two-dimensional Walsh functions, and the samenumber of associated Walsh transform coefficients in about 14 seconds. The quantitative measure-ment and display of the relative magnitude of the frs~t block of Walsh transforms (64 x 64) wasfacilitated with a system minicomputer and a CRT display. A set of selected cartographic images

00 , 'j=7 W3 com or t~ no oa01SLT UNCLASSIFIEDgCUIimTv CLAMSFCATION OF THIS PA69 (Mben Data DniteP.

SECURITY CLASSIFICATION OF THIS PAGE(Whn Daa Zatefre)

20. Continued"'-- and targets were used to evaluate the system. It was discovered that most of the signi-

ficant transform information appeared in the lower order Walsh transform coefficients,and further that each Walsh transform pattern is unique in itself and can be distinguishedfrom the others for a limited set of well defined inputs. The dynamic range, the temporalresponse, and the symmetry of responses of the Prototype Image Spectrum Analyzer(PISA) were found to be relatively poor.

SECURITY CLASSIFICATION OF THIS PAGIREha, DSI. ZEed-

PREFACE

This work was authorized by the U.S. Army Engineer Topographic Laboratories,Fort Belvoir, Virginia unde r DA Project-Task Area Work Unit No. 4A161 102B52Centitled "Electronic Image Analysis for Feature Extraction."

COL Daniel L. Lycan, CE, was Commander and Director of ETL during thereport preparation.

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Dis~ special

CONTENTS

TITLE PAGE

PREFACE I

ILLUSTRATIONS 3

INTRODUCTION 7

SYSTEM DESCRIPTION 7

PLASMA DISCHARGE DEVICE ASVISIBLE PATTERN GENERATOR 9

TWO-DIMENSIONAL WALSHFUNCTION GENERATOR 14

OPTICAL PATH AND LIGHT SENSINGAND LIGHT CONVERSION 19

ANALOG COEFFICIENT PROCESSOR 19

CONTROL PANEL 21

INTERFACE ELECTRONICS FORSYSTEM MINICOMPUTER 23

SYSTEM'S MINICOMPUTER ANDSOFTWARE FUNCTIONS 23

SYSTEM TEST RESULTS AND DISCUSSIONS 25

CONCLUSIONS 63

APPENDIX 64

2

I.

ILLUSTRATIONS

FIGURE TITLE PAGE

I System Block Diagram 8

2 Experimental Set-Up 10

3 Construction of the Plasma Tube II

4 First 8 by 8, Lower Order,Two--Dimensional Walsh Functions 12

5 A Walsh Pattern Generated by thePlasma Tube 13

6 Master Counter and Lower OrderWalsh-Function Generator 15

7 Higher Order Walsh--Function Generatorand Plasma Tube Drivers 17

8 Photomultiplier Tube and AnalogCoefficient Processor 20

9 Control Panel 22

10 Interface Electronics for System

Minicomputer 24

I1 Target Representing Road Intersection 26

12 Walsh Transform of Figure 11 26

13 Walsh Transform of Figure I I after Filtering 27

14 CRT Display of Figure 13 27

15 Target Representing Horizontal Line Road 28


17 Walsh Transform of Figure 15 after Filtering 29


19 Target Representing Square Building 30


3

ILLUSTRATIONS

FIGURE TITLE PAGE

21 Walsh Transform of Figure 19 After Filtering 31


23 Target Representing Vertical Line Road 32




27 Target Representing Diagonally OrientedRoad Intersection 34




31 Target Representing Diagonally OrientedLine Road (1) 36




35 Target Representing Diagonally OrientedLine Road (2) 38




39 Target Representing Diagonally OrientedSquare Building 40


4

ILLUSTRATIONS

FIGURE TITLE PAGE


42 Aerial Photo-Transparency (1) 43








50 Target Representing Wal (1, x) Wal (0, y) 47


52 Target Representing Complement ofWal (1, x) Wal (0, y) 48






58 Target Representing Wal (3. x) Wal (0, y) 51

59 Walsh Transform of Figure 58 5I


61 Walsh Transfer of Figure 60 52

4 i

ILLUSTRATIONS

FIGURE TITLE PAGE





66 Walsh Transform for Target RepresentingRoad Intersection 55

67 First Repetition of Walsh Transform forthe Same Target Produced figure 66 56

68 Second Repetition of Walsh Transform forthe Same Target Produced Figure 66 57

69 Third Repetition of Walsh Transform forthe Same Target Produced Figure 66 58

70 Walsh Transform for Target RepresentingVertical Line Road 59

71 First Repetition of Walsh Transform forthe Same Target Produced Figure 70 60

72 Second Repetition of Walsh Transform forthe Same Target Produced Figure 70 61

73 Third Repetition of Walsh Transform forthe Same Target Produced Figure 70 62

TABLE System-Operating mode as a function ofthe position of the control switches 21

6

PROTOTYPE IMAGE SPECTRUM ANALYZER (PISA)FOR CARTOGRAPHIC FEATURE EXTRACTION

INTRODUCTION

The transformation of complex signals into relatively simple and compact formshas been widely employed in such fields as communication, coding, etc. Normally, thewell-known Fourier technique is used with either digital computers or laser optics asthe means of transformation. In this report, a technique for obtaining transforms oftopographic images based on discrete function technology is presented. An electro-optical system capable of producing Walsh transforms of topographic images is described.The heart of the system is a plasma discharge device that generated visible Walsh functionpatterns as masks to be multiplied by the input imagery. The cartographic imagery isplaced in contact with the plasma tube, and the light energy transmitted through theimagery (transparency) is integrated with a single photo-detector and processed tobecome Walsh transforms. 'The generation of Walsh functions, the method of plasmatube-driving, the technique of signal processing, and the display of the quantitativetransform coefficients ar. addressed. The system test and evaluation results using aselected set of topographic feature images and targets are discussed. Finally, conclusionsare presented.

SYSTEM DESCRIPTION

The PISA system consists of a two-dimensional, digital, Walsh function generator:a plasma discharge device with drivers, a lens, and photomultiplier. an analog coefficientprocessor; a minicomputer with a CRT terminal; a CRT display unit: and a line printeras shown in figure 1.

The two-dimensional Walsh functions of order up to 5 12 by 5I12 were generatedby the Walsh function generator. The plasma tube is driven by the Walsh function gen-erator through the tube drivers to generate visible, two-dimensional Walsh functionpatterns as a light source. The plasma tube has a light-emitting surface of approximately8.5 by 8.5 inches. and 512 electrodes in both X, and Y directions. The topographic

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imagery was placed in direct contact with the light-emitting surface of the plasma tube,and the light energy transmitted through the imagery was collected by a lens and inte-grated by a photomultiplier. The output of the photomultiplier was processed by ananalog coefficient processor to become Walsh tansforms. The first 64 by 64 ordersof the Walsh transform coefficients were further processed and manipulated by a mini-computer to provide quantitative measurement and display of relative magnitude. Thequantitative measurement of transform coefficients was printed by a line printer and alsodisplayed by a CRT monitor unit. The experimental set-up is shown in figure 2.

PLASMA DISCHARGE DEVICE AS VISIBLE PATTERN GENERATOR

The heart of the system is the Digivue-51 2 plasma discharge tube. The construc-tion of the plasma tube is shown in figure 3. The tube consists of 512 X-directionalelectrodes and 512 Y-directional electrodes sandwiching a neon gas. The tube has a totallight-emitting surface of approximately 8.5 by 8.5 inches. When the proper voltage isapplied across an X electrode and a Y electrode by the plasma tube drivers, the neon gasdischarges producing a small light at the intersection of the electrodes. For our case,the minimum discharge voltage difference between two electrodes is 250 volts. By pro-perly addressing both X- and Y-directional electrodes with a two-dimensional Walshfunction generator, visible two-dimensional Walsh function patterns of order up to 512by 512 can be generated in any sequence. For our system, the Walsh function generatorwas designed to produce Walsh patterns of the following sequence: Wal(O, 0), Wal(0, 1),Wal(O, 2) ..... Wal(O, 511), Wal(l, 0), . . . , Wal(2, 0),..., Wal(511, 511). Themaximum switching rate of this plasma tube is 50 kHz (kilohertz); however, the tube isrefreshed every 33 ps (microseconds). In the automatic running mode, the tube at thepresent time is switched at a relatively slow rate because of the I/O (Input/Output)time restriction of the system's minicomputer. Repeated Walsh function patterns canalso be produced in a manual switching mode with a push button switch for inspectionand demonstration purposes. The first 8 by 8 lower order, two-dimensional Walshfunction patterns are shown in figure 4. The black areas represent that the plasma lightis on, and the white, is off. Figure 5 represents the plasma tube that is lighted with atwo-dimensional Walsh pattern.

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12

FIGURE 5. A Walsh Pattern Generated by the Plasma Tube.

13

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TWO--DIMENSIONAL WALSH FUNCTION GENERATOR

The Walsh Function Generator (WFG) consists of a master counter board andgroups of Walsh function generator logic, which are organized on 16 plasma tube driverboards for ease of accessing all the plasma tube electrodes. The master counter boardis shown in figure 6. The master counter is the system hardward controller. It containsmost of the control logic that the operator interfaces with when operating the system, aswell as containing the system clock, an 18-bit binary counter chain, and a small amountof Walsh function generator logic. The counter chain develops all of the strobes,IX . . .9X, and IY . . .9Y. The chain is made up of five(74193)synchronot.s 4-bit up/down binary counters wired in tandem. The first three strobes (I X, 2X and 3X) from thechain (chip S26) are decoded through exclusive or (7486) gates S17 and S18 to producea Walsh function code 3Xa . . . 3Xh. Each one orthese codes goes to a different plasmatube driver board. The next six strobes from the counter chain (4X . . . 9X) go to everyX-axis plasma tube driver board. These six strobes are purely binary in nature. Chips S3and SI0 are buffer chips to increase the line-driving capability. The same sequence ofstrobes are repeated for the Y-axis 3Ya . . . 3Yh, 4Y ... 9Y. The only difference is thatthe Y-strobes are higher up on the counter chain. They start with the 10th bit of thechain; therefore, for every time a Y-strobe changes, the X-strobes go through all 512possible combinations.

The counter chain is driven by the system clock. This circuitry consists of aMotorola, 256 kHz, crystal oscillator IC with a TTL compatible output. The output isfed into a binary counter (74193), S12, and divided by 16 to yield a 16 kHz signal. The16 kHz clock is connected to the 18-bit counter chain control logic through the auto--matic/manual mode switch on the control panel. The clock also directly drives the X-Walsh function generator logic (driven by the clock signal) and the Y-Walsh functiongenerator logic (driven by the complement of the clock signal). The control logic doesfour jobs. Through the control panel switches, the operator is able to (I) Start thecounter, (2) Reset the counter, (3) Put the counter in automatic (clock-driven) mode,or (4) Put the counter in manual (switch-driven) mode. The counter--enable switchon the control panel interfaces the master counter board at Pl. Grounding this switchfires the one-shot (74121) S23, the output, Q, goes low and sets the output of the RSflip-flop, S21, to a high at S21-6, enabling the strobe to appear at S21-2. This enablesthe Clock to pass through S21 at S21-3 and drive the counters through the S15 gates.When the counter chain ripples completely through, it resets itself through the inverter(7404) S22 by resetting the RS flip-flop at S21-10. This locks out the clock at S21-1.The RS flip-flop may also be reset by the counter reset switch on the control panelthrough chip S5 and pin P25. the manual counter switch on the control panel enablesthe operator to step the counter through its states (manually) one at a time. The con-nection is made at P27 and P28, and the SPST switch switches the states of the RS flip-flojp, S5. This toggles the counter when the correct paths in the intervening controllogic are opened.

14

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The X and Y scanning for the display of transform coefficients are provided bythe system computer at 30-frames-per-second rate to avoid the smear of the displayedpattern using a single frame storage display monitor.

As mentioned before, the high orders Walsh function generator logic circuits arephysically built on 16 plasma tube driver cards. They are shown in figure 7. Inputs tothese circuits are from the counter strobe lines through the distribution board socket.The distribution scheme is not included in this report.

PLASMA TUBE DRIVERS

The high--voltage plasma tube driver is a sourcing and sinking type switch circuit(see figure 7). Current is sourced through QI and Q2 and sunk through Q3 and Q4.The transistor used is an MPSA42, which is a high-voltage (300VDC), NPN switchingtype. It is also able to handle 1/2 W Power, The most critical requirement of this circuitis that both sourcing and sinking halves of the circuit must never be "on" at the sametime. If they should be "on" together for any amount of time, the circuit will over heat.The .0022pF (microfarad) capacitor in the emitter circuit of Q3 delays the base-to-emitter junction from reaching 0.7 VDC and thereby turning Q4 "on," this ensuresthat QI and Q2 will be "off" by the time Q4 does come"on." In the other direction,when Q3 is going "off" and the input drops to between 1.4 and 0.7 VDC, Q3 isstill "on" acting like an emitter-follower and Ql is still "off," but Q4 has gone"off"already, eliminating the problem associated with the two halves of the circuit being "on"at the same time. The rise and fall times of the circuit are adequate, 3 to 4 ps. TheDarlington configurations, Q3, Q4, QI, and Q2 are used for current gain. There isapproximately 0.6 VDC noise immunity between Q4 VBE + Q3 VCE and QIVBE + Q2 VBE. This level is adequate for system noise immunity. The output changesfrom 0 to +3.5 VDC.

The plasma display can be thought of as a tube containing 512 neon lights, oneat each X- and Y-electrode intersection. Electrically, the tube is a capacitor, ie. thereis a dielectric covering the X and Y electrodes. This means that the tube must be re-freshed, or run dynamically. The unit in this system is refreshed at a 33 kHz rate. Thefiring voltage on the tube is about 250 VDC. This is accomplished by switching theintersecting electrodes to opposite polarities by 125 VDC each. In other words, oneelectrode goes down 125 VDC while the other electrode goes up 125 VDC, therebycausing the capacitive plasma tube to see a 250 VDC change because of its capacitivecharacteristic.

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OPTICAL PATH AND LIGHT SENSING AND LIGHT CONVERSION

The optical path is straight forward. It consists of a lens mounted one focal-length away and centered over the plasma tube. The photomultiplier tube is positionedon the other side of the lens. This configuration enables the lens to diffuse the lightcollected from the plasma tube over the whole photosensitive area of the photomultipliertube anode, canceling out the effects of sensitivity variations across the surface of theanode. The photomultiplier tube (6199) integrates the light passing through the imagefrom the Walsh function mask, thus producing one Walsh coefficient for each mask. Thephotomultiplier tube's supply voltage is approximately 600 VDC. This voltage is gen-erated by a Venus C23 high--voltage converter powered on a 5 VDC primary, as shown infigure 8. The cathode is held at -600 VDC while the photon acceleration elements aresupplied through taps on a 1.5 meg E2 resistor chain (RI . .RI1). Capacitors C2through C4 are used to help hold constant voltage on the acceleration"-pins when apulsed light input is used.

ANALOG COEFFICIENT PROCESSOR

The analog coefficient processor circuit consists of a Walsh coefficient sample andhold, a difference amplifier, and a buffer amplifier, as shown in figure 8. The sample andhold, HI, holds the Walsh coefficient signal. The Walsh coefficient signals are narrow (3to 4 ps) negative pulses produced by each of the higher order Walsh functions. Specialsampling one-shot circuits, S2a and S2b, are used to form and position the Walshcoefficient sample-and-hold pulse so that it occurs exactly coincident with the max-imum Walsh coefficient signal. Circuit S2a is triggered by the positive edge of the systemclock, and R14 adjusts the width of its output pulse from 3 to 40 ps. The negative-going edge of the output of S2a triggers the pulse from S2h, thereby enabling one toadjust the position of this narrow (4 As) sampling pulse along the whole clock cycle byadjusting R14. The peak amplitude level of each Walsh coefficient signal is held in thesample and hold until the next sample. The droop is about 100 1jV (microvolts), Signallevels from the sample and hold is fed into the negative input of Al, the LM301 dif-ference amplifier. Originally, a normalization signal is fed to the positive input of thisdifference amplifier. However, because of poor performance of this circuitry, the norma-lization task was redesigned to be done by the system minicomputer, and the differenceamplifier is used as an ordinary amplifier. The LM318 buffer amplifier, A2, is used toenable some adjustment of the output voltage before it is fed into the interface elec-tronics of the system computer.

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CONTROL PANEL

The control panel itself consists of one push--button switch, three toggle switches,and five 2 K 2. 114 W, 5%r resistors, as shown in figure 9. The required position of eachof the four control panel switches as a function of the system operating mode is shownin table 1.

TABLE 1. SYSTEM--OPERATING MODE AS A FUNCTION OFTHE POSITION OF THE CONTROL SWITCHES

Name of Switch System Operating Mode

Automatic Running Reset Manual Step

Enable Counter On Off On

Manual Counter Off On OffReset

Manual/ Automatic N/A ManualAutomatic Mode

Manual Step N/A N/A Activated

Currently, the counter reset and counter enable in automatic mode are controlledby the system minicomputer. Two coxial cables are connected from these two switchesto the interface electronics, and then to the system's minicomputer as shown in figure 9.

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22

INTERFACE ELECTRONICS FOR SYSTEM MINICOMPUTER

To obtain quantitative measurement of the Walsh transform coefficients, onemust process the output of the Analog Coefficient Processor by the system mini-computer. The interface electronics was designed to convert the analog signalrepresenting the relative magnitude of the transform coefficients into a 6-bit digitalsignal for input to the HP 2108 minicomputer. The interface electronics is shown infigure 10. The square wave clock from PISA is shaped and delayed by two 74121monomultivibrators and used as the trigger input to the MP271 2C analog--to--digitalconverter. The output of the analog coefficient processor is amplified one to two timesby an pA7 15 operational amplifier before going to the analog input of the analog--to-digital converter. The converter has a I 2-bit capability, but only the most significant6 bits are used. These 6 bits are buffered by the quad NAND (7437) gates. The end-of-conversion signal from the analog-to-digital converter is also buffered and suppliedto the minicomputer.

SYSTEM'S MINICOMPUTER AND SOFTWARE FUNCTIONS

An HP 2108 minicomputer was used to provide quantitative measurement anddisplay of the relative magnitude of the Walsh transform ,oefficients. The computeris also used to control and initiate the system when it is operated in the automaticrunning mode. The following functions are performed by the system minicomputer:

I. Inputs first 64 by .64 lower order Walsh transform coefficients into memory.2. Computes the lowest coefficient A(0, 0) as twice the average of all coefficients.3. Scales coefficients into the range of 0 to 99.4. Computes actual coefficients by subtracting 1/2 A(0, 0) from each coefficient.5. Passes coefficients through a variable valued threshold gate.6. Provides repeated x, y scanning signals to a CRT monitor set and displays the

absolute value of the coefficients after threshold.7. Scales coefficients for display.

The software developed to execute the above tasks is shown in the appendix.

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SYSTEM TEST RESULTS AND DISCUSSIONS

A selected set of targets representing manmade topographic features. such as roadintersections, straight line roads and buildings, together with aerial photo--transparenciescontaininlui roads and farm lands, and four lower order Walsh function patterns wereused as input to test and evaluate the system performance. After each target or trans-parency was placed in direct contact with the light-emitting surface of the plasma tube,the corresponding Walsh transform was obtained. Although the PISA produces 512 by5 12 Walsh transform coefficients for each target or transparency, only the first 64 by 64lower order coefficients were transmitted to the system minicomputer for further pro--cessing to yield quantitative measurement and display of their relative magnitude, Itwas discovered that the significant spectral components are distributed among a fewlower order Walsh transform coefficients for all the cases examined. Therefore. the resultsincluded in this report are restricted to the first 32 by 32 lower order transformcoefficients, although it is possible to print out all 64 by 64 coefficients.

The less signmificant Walsh transform coefficients can be filtered out if so desired.Either filtered or unfiltered results can be displayed by a monitor set. Figures I11through 38 are arranged to show the original test target, the corresponding Walshtransform coefficients, the filtered coefficients, and the filtered coefficients that aredisplayed by a monitor set for these targets stated above. The shaded areas of the targetsare transparent and the unshaded one,opaque. In figures I I through 22, the results areshown for the targets representing a road intersection, a horizontal line road, and a squarebuilding, respectively. It is seen that the signal signature of the spectrally decomposedcomponents (or Walsh transform coefficients) is very simple for all cases. The significantspectral components are distributed among the very few lower order Walsh transformcoefficients.

Further, each transform is unique in itself and can be distinguished easily from therest. For example, the road intersection resulted in large first row and first columncoefficients (figures 12 & 13), the horizontal straight line road yielded large coefficientsin the first column (figures 16 & 17), and the square image was transformed into fourlarge coefficients (two in the first row and two in the third row) (figures 20 & 21 ). If nowthe straight line road is turned 90 degrees, then the corresponding significant spectralcomponents (or Walsh transform coefficients) will appear in the first row as shown infigures 24 and 25. In figures 27 to 4 1, the results are shown for the three types of targetsconsidered above after turning 45 degrees with respect to the x. y coordinates of theplasma tube. Again, very simple, yet unique, distributions of spectral decomposition wereobserved for all cases. It is evident that a simple decision procedure, either in hardware orsoftware, can be implemented to detect and recognize the above limited set of targetsautomatically. A figure for the CRT display of figure 39 is not included because of afailure in photographic work.

25

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FIGURE 11. Target Representing Road Intersection.

VAL$ COEFFICIENTS

1 2 3 4 5 6 7 8 9 10 V. 12 13 14 15 16 17 1o 19 20 2t 22 23 24 23 26 27 20 29 30 31 32

1 6a -a 52 4 32 0 20 -6 30 4 12 6 10 4 14 4 0 0 0 0 -6 0 -2 2 10 2 tO 6 14 4 12 2a t6 o a a -2 0 * * -2 -4 a -a . -a2 -4 0 0 -2 -a -4* -2 2-2 -2a -a 2 0 0 -23 44 4 0 I0 -9 o-22 -26 -2 -a 4-2 4 4 6 2 0 2 a 0 0 2 4 4 4 4416 4 a 0-2 6 2 4 2 6 4 4-2 4-2 4 4 4 2 0 4 2 0 0 2 2 2 a as 40 6 -2 1-10 0 -4 2 0 0 4 4 0 0 2 -2 4 a 4 0 0 a a 20 -2 0 a 4 4 0 26 14 a a 4 -a 4 -2 0 -2 -2 4 -2 0 . 2 -4 o -a * -4 -2 -2 -a -2 0 -2 0 -2 0 -2 -2 -27 42 4 -a s -8 6 -4 2 -a * 6 4 * * 4 -2 4 4 4 0 0 0 4 0 2 -4 a 0 2 0 * 21 16 4 2 6 -2 6 0 0 0 -2 4 0 2 0 4-2 2 a a - -2-2 o 0 0-2 0-2 0 0 2 0

9 16 a a 0 0 6 0 2 a a 6 0 0 0 a - a a a a -a 0 * a -a * 0 2 * a 0 0 616 0 2 4 2 2 4 2 0 2 0 4 -2 a 0 2 -a -2 0 a -a -a -a 1 -2 -a -4 2 -2 0 0 0 -a1 14 4 2 4 -2 2 * -2 0 4 -a 2 0 4 -2 0 4 0 -2 -2 0 *0 60 -2 2 0 2 2 0 0

It * -a 0 0 0 0 0 -4 -8 -4 2 -4 0 -2 0 -4 -2 -a -a -4 -6 -2 -8 -4 -2 -4 -2 -2 -2 -2 -2 -213 14 0 -2 4 -6 a -4 -a -a -4 a -4 -2 -4 0 -4 6 0 0 -4 -2 -2 0 0 -2 -2 0 0 0 0 0 014 -a -4 -2 0 -a -a -2 -6 -4 -6 -a -1 -2 -6 -a -1 -6 -6 -4 -6 -6 -6 -6 -6 -6 -6 -4 -' -4 -4 -0 -4I 12 0 -2 a -4 0 -4 -4 -2 -6 -2 -4 -2 -6 -a -I -a -4 -4 -I -6 -6 -4 -6 -6 -6 -4 -4 -2 -4 -4 -416 2 -4 0 -a -a -2 -2 -6 -4 -6 -4 -6 -4 -I -2 -a -6 -8 -6-10-t$ -I -0 -8 -1 -0 -I -I -' -I -6 -01? 6 0 2 4 0 2 0 0 -2 -2 0 -a 0 -a -a -6 -a -a -a -6 -4 -4 -4 -6 -4 -0 -4 -4 -4 -2 -4 -610 i -2 -a a -4 0 -2 -2 -4 -4 0 -4 -4 -4 -2 -6 -a -4 -2 -6 -4 -4 -4 -I -6 - -4 -6 -6 -6 -4 -6Is 6 -a 4 4 0 2 0 0 0 -a a -a 0 -a o -4 -2 -a 0 -4 -4 -2 -2 -4 -2 -4 -2 -4 -2 -2 -2 -420 10 -2 -2 2 -4 # -a -a -2 -4 0 -4 -2 -a -a -6 -a -4 -2 -' -4 -2 -4 -6 -4 -4 -2 -6 -4 -4 -4 -621 4 0 a a -a 0 0 -a -a -2 0 -4 0 -4 0 -6 -1 -a -a -4 -6 -4 -4 -6 -4 -4 -2 -4 0 -4 -4 -422 6 -2 -2 -2 -4 -2 -4 -4 -4 -6 -2 -6 -4 -4 -2 -6 -4 -4 -4 -g -0 -6 -6 -6 -6 -6 -6 -0 -4 -6 -4 -622 2 -222 0 40 -2 -2 -4 0-40*-4 0 -6 -2 -8-2-6-4 -4-4 -6-4 -4-4 -4-2 -2-2 -414 1 -4 -2 -4 -2 -4 -4 -6 -i -2 -6 -4 -i -2 -i -4 -0 -4 -6 -8 -0 -6 - -8 -i - -0 - -6 -6 -62S 14 4 4 6 0 6 2 2 8 2 4 4 2 -2 4 -a 2 2 2 -2 -2 -2 0 0 0 -2 0 0 0 0 4 026 68 2 802 * - -- a 2 -4 -2 -4 0 -6 -2 -4 -2 -6 - -6 -2 -4 -4 - 4 -2 -4-2 -4 -427 14 1 6 S8 1 2 4 4 2 0 8 4 8 6 0 4 4 4 0 0 0 8 0 2 0 2 0 1 0 0 020 1 4 4 6 0 4 4 0 0 -8 2 -8 2 0 1 -1 0 6 0 -4 - -a -2 -4 -2 -4 -8 -2 -2 -2 -2 -229 16 6 1 I 4 4 2 8 6 8 2 2 4 0 4 4 4 0 * 0 8-1 01-2 2 0 4 0 2 020 0 1 8 0 2 -a 0 0 8 -2 2 -8 8 -8 -8 0 0 -2 -2 -8 0 -8 -2 -2 0 -2 0 -4 -2 -43 12 4 4 6 8 6 2 4 4 t 6 0 4 8 G 0 4 4 4 1 2 8 4 1 2 0 6 2 4 4 4 222 6 0 2 2 0 2 0 -2 -8 -4 2 -1 0 0 8 -4 -a -2 0 -4 -4 -a -2 -2 -a -4 0 -2 -8 -2 o -4

FIGURE 12. Walsh Transform of Figure 11.

26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1? 10 19 20 21 It 23 24 25 26 2? 21 29 30 31 32

6.02 036 2: 36 0 0

3 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

4 0 *0 0 0 0 0 0 00 1000 0010 0S m 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0

23 000 0 0 0 0 0 0 0 0 0 0 0 0 0 001 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Is 0 010 0 0 0 00 0 0000 0 0 000000£0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 0? 0 0 0 0 0 0 0 0 0 0 0 0 0 0£3 0 0 0 0 0 0 0 0 $ 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 034 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

£0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0£7 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0£0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2£ 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0

22 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

247 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 02?0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 021 0f Of 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 0 0 0 0 0 0 0 # 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

FIGURE 13. Walsh Transform of Figure I1I after Filtering.

FIGURE 14. CRT Display of Figure 13.

27

FIGURE 15. Target Representing Horizontal Line Road.

NALS COEFFICIENTS

I a 3 4 s 6 7 1 9 10 11 12 1I 14 15 16 17 a1 It 20 21 23 23 24 2s 26 27 24 29 30 31 32

1 45 3 Is at -3 1 a -3 -1 a 5 1 -a a a -1 3 3 1 -a -3 -I -a a 5 -3 I 3 5 1 3 32 9 s a 3 -1 3 a -1 a a 3 a a a a -1 1 1 1 -3 -3 -a -a -1 -1 -1 -1 a -1 -a -a -a3 63 5 1 ? -a S 5 -a a 3 3 1 3 a 5 -1 3 3 3 -a -a -a -a a a -3 1 3 3 a a 1413 5 33 -1a3 1 53 a 1313 3 31 -i -a -1 -1 -a 1 -a -a

1 ?? 1 5 -11 3 3 5 1 5 3 -1 -1 1113 -3 3 5 1139 Ia SI! aI 3353 13 1a3 S31-1 11131313 111a

5 5 -1 13 -5 1 3 3 5 3 ! 1 3 1 -3 3 3 t-I I 1 3 1 3II 55 3 o S 1 13 513 313 1 - 1 3 5II1 3 53 11

8 a, 3 5 a t a a a 3 3 3 3 1 3 1 3 3 - 1- a 3 1 1 a 3 1 3 3 a a9 s 3 3 3 a s 3 a 3 3 9 3 3 3 3 1 3 3 3 a-a 3 3 3 3 t 3 3 S 5 3 5o -a -a a -I - -a -a -a -I - -3 a - -a -3 -3 -1 -I -a -3 - -I - - 1aa V 35 5 3 -is 3333 1 3 a1- a a 33 1 33333a 7 -I I -I I I - -a -a a -a -a -a a -a - Ia -3 -5 -a -3 -3 -3 -a - -a - -313 13 3 3 3 1 3 a. -1 1 3 3 a 3 a a 3 3 3 a -a a a a a -a 3 a 3 a a a14 s -a - -a -3 - -a -a - -I -3 -a -3 - I I -3 -S -m -3 -3 - -S - -I -a -3 -315 13 3 13 - 1 3 13 3-1 1 3 3 1 1 - I I -i 2 3 a 1 316 S -a -a a -3 - -3 -t - -I - -3 - -3 -I - t 1 -9 -- -3 -3 - $ -3 -5 - 1 -3 -3 -3 -aI ? -I -3 I -3I -I -2 -a -a -3 -I -3 - -3 -1 -I -1 -3 -S -a -3 -3 -3 -3 -a - -3 -1 -3 -aai -a -a -1 - -a -1 - - -I I -3 -a -a -a -3 - -I 3 -3 -3 -S -a -a -5 " - 1 -3 -3 -I19 3 -3 I - -3 1 -3 -S -3 -3 - -3 -3 -3 -3 -I -3 -3 -3 -5 -7 -3 -5 -3 -3 -S - -3 -a -3 -a -32o 1 -I I -a -3 -a -3 -S -3 -3 -a -a -3 -8 -I - - - -a -S -5 -3 -3 -3 -3 -5 -3 -3 - -1 -3 -321 a -3 -a -a -S -a -3 -5 -5 -3 -3 -3 -s -i -3 - -3 3 -3 -? -? - - -3 -3 7 - -5 -S - -s -322 3 -I -I -I -3 -1 -3 -3 -3 -3 -1 -3 - -3 -3 -$ -a -3 -3 -? -7 -s -5 -5 -5 -? -3 -5 -5 -3 -5 -323 a -a -a -1 -3 -a -3 -3 -3 -3 -a -3 -3 -3 -3 -$ -3 -3 -3 -? -s -3 -5 -5 -3 -3 -5 - - -5 -5 -524 5 -a -a a -3 -a -3 -5 -I\ -3 -I -3 -3 -3 -3 -3 -3 -3 -1 -5 -5 -3 -5 -s -- - -5 5 -s -S 3 -25 Ia 7 1 7 3 3 3 1 3 3 5 3 3 1 51S 5 S 3 3 -a a a 3 a 1 1 3 3 3 3 16 1 -S -1 -1 -u -3 -3 -1 -3 -3 -a -3 -3 -3 -3 -8 -3 -3 -3 -9 -? -5 -s -S -s -7 -3 -g -5 -s -$ -

27 1 5 5 1 5 3 3 2 3 S 3 3 1 3 1 1 3 J I 1 1 3 3 3 1 3 1 S 3 1 1

2i i -u -3 a -5 -1 -3 -1 -8 - -a -3 -5 -a -3 -5 -3 -3 -3 -I -? -3 -5 -s -$ -7 -3 -$ -5 -5 -5 -129 13 1 5 3 $ 3 a 3 3 5 3 a 3 3 -1 5 3 3 a -1 a a a 3 -a 3 3 1 1 t t30 5 -3 -3 -i -g -1 -3 -5 -3 -3'-i -3 -3 -3 -3 -? -3 -u -3 -s -5 -7 -5 -5 -3 -? -1 -3 -3 -3 -i -3I II S ? 3 1 3 1 3 3 9 3 3 3 3 I 3 13 1 a-1 a -a a a a 3 1 a 3 a I32 7 -1 -1 1 -3 -1 -3 -$ -3 -3 -1 -3 -3 -8 -3 -0 -3 -3 -3 -5 -Y -5 -7 -5 - - - 5 -3 -3 -3 -


28

S.

VAL$ COEFFICIENTS

1 2 3 4 3 4 7 6 9 10 11 12 13 14 13 16 1? 1S 19 20 21 22 23 24 23 26 2? 28 29 30 31 32

1 46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 00 00 0 000 0 00000 00 a0 0 060000 0 0 000 00 02 Go 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 004a0 000 0 000 0 0a0 0000 00a @0 00 0 080 003640 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0(A 0 0 0 0 0a00 0 00 00a0 0 00a0 000 000 000 00 00 07 58 : 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

*~~ 000 0 0 0 0 0 @0 00:000 0 0 000000 01 00000 0 00 00 0000 00 00 0000 0 00 0 0

10 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0II 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0!2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 # 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 S 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02? 0 0 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 029 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 030 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02£ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

FIGURE 17. Walsh Transform of Figure 15 after Filtering.


P 29

iJ

FIGURE 19. Target Representing Square Building.

VAL$ COEFFICIENTS

a 3 4 7 0 9 to i1 12 1 14 15 16 17 1 $1 20 21 22 23 24 25 26 2? 26 21 30 31 32

a I -1 35 3 9 3 11 I -? -1 -? I I 1 ii -a 1 a 3 1 -3 -3 -3 -a -a -a 1 -a 5 1 I as 1 3 1 a -1 1 -1 -1 -1 -l -1 1 -1 a -a 1 -aI1 -a -a -i -a -a -a -a -a -a 1 -' a -a

3 35 -a 31 1 9 a 9 -1 -7 -a -7 -1 9 -a 9 -a a 1 a a -3 -3 -3 -I -1 -3 -3 -a s a ? I4 3 a S 3 I 1 -a a t -a -1 -a a -a a -a a a a -a -a -a -a -3 -t -I -a -a a a a a3 1 a at 3 3 1 5 1 -a i-i-a s-a I- t a a a -a -a -a -1 -a a 1 1 3 3 3 a6 I a 1 1 1 1 1 -1 3 a a 1 3 - a a a-a a -a a a a a a a a a7 is a 13 a 5 a 3 1 -3 -a -a -a 3 1 $ -a a a 3 a -a -1 -a -a -a -a a -a 3 a 3 a

I -1a -a 3 -a a a -1 3 -a 1 a s -a a a a -a -a -a a -a a a a a a a a a-$ a -s 3 -a a -3 -a 3 -a 3 -a -a -a -a a a a 1 -a -a 1 -a -a a a a a a a a a

10 3 -: 3 1-1 -1 1 1 1 -t t -t t -t t -1 -1 -t -t -1 -t -1 -t -t -1 -1 -1 1 -1 1 -1

Ii -3 a- 3 -1 a -a a 3 1 3 a -a a 1 1 1 1 -a -a - - - - - -a - a -a12 3 a a I -a a a a a -a a -a a -a a -a a a a -a -a -a -a -3 -a -a -a -a a 1 -a -a%3 IS I I 1 a a a a -t -a -a -a 3 -a 3 -1 1 1 a -1 -3 -a -3 -3 -1 -1 -1 -3 1 -a a -a14 S a 3 a -a -1 -a -a -3 -a -a -3 -a -a a -a -a -a -a -a -I -3 -3 -3 -1 -3 -a -3 -a -a -a -aas aa I I 3 a a 3 1 -3 -I -3 -a 3 -1 3 -a a -a a -a -3 -1 -3 -a -i -a -a -a a a a a16 S -1 3 -a -a -1 -I -a -3 -a -3 1 -a a -a -a -3 -a -3 -3 -3 -s -3 -3 -3 -3 -3 -a -a -a -a17 ? a 3 a a a a A -a -a -1 -a a a a -a -a a a -a -a -a -a -1 I -I -a -a a -a a aao Ia -a 3 -a a -a a a -a 8 -a a -a a -a a -a 1 -a -a -a -a -a -a -a -a -I a a a -a1 s 3 1 a a a a a -a a -a A -a a -a a 1 -a -a -a -a -a -1 -a -a -a -a -a a a a20 3 a a a a a a a a -a a -a a a a a a a a -a -a -a -a -I -a -a -a -1 a -a a -aaa a a -a a -a -a - -a -a -a a -a a -a a - -a -a - -3 -3 - - - 1 - -3 -a -a -t -a22 5 1 I a -a a a 1 -a -3 -a -3 a -a a -I -a -a a -a -3 -3 -3 -3 -3 -3 -3 -3 -a -a -a -a23 3 1 3 3 a a a a a -a 1 -a 1 -1 3 -a -a -a -a -a -3 -a -3 -a -a -a -a -I -i -I -a -324 S -a 3 a -a a a a -a -a -a -a a -a t -I 1 -t I -a -a -a -a -a -a -a -a -3 -a -a 1 -1as S3-ala1 ss as a aa a1 a a1 s a1 1 a1 a1 1 a1 a 133326 P -a a -a -a -a -a -a -a -a -a a -a a -a -a -a a -a - -a - -a -a -a -a -a -aI -a -a

a? 1 1 a 3 I 3 1 a a a 3 1 a 1 3 a a a a 1 -a a a -a 1 1 a a a a 3 a2s S -a 3 a -s -a -a -a -a -3 -a -3 a -a a -I -a -a -a -I -a -3 -3 -s -a -a -1 -a -a -a -a -a29 s 1 ? 3 1 3 3 a a a 3 1 3 a 0 a a a 3 a -a -a a a a a a a 3 3 a 33 s a a a -a -a 1 a a -a .- -a -a -a a -a -a -a -a -a -3 -a -a -a -a -a -a -a a -a a -a

32 3 a a a -a -a a -a a -a a -a a -a A -a a -a a -a -I -a -3 -a -a -a -a -a -a -a -a -a IFIGURE 20. Walsh Transform of Figure 19.

30

4

0*3.3 COEFFICIENTS

1 2 3 4 3 G 7 S 9 10 ti 12 13 14 15 16 17 It 39 20 21 22 23 24 25 26 2? 26 29 30 31 32

1313 033 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 0 000 00 00 0 0 0000*0 00 0 00 0 00 0 00 000 00 03 3? 033 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 0 00 00 000 00 00 0 00 00 0 0 00 *00 00 0 00 00 05 00 00 00 00 00 00 00 0 000*0000 @ 40 a00 0 00006 0 000 000 0 0 0 0 0 0 04000 0 0 0060 0 00 0 0 0 0@0? 0 00 00 00 00 00 00 0 0 0*00 0 000040 00a00 00 00 0 0 000 00 00 00 00 0 0060 060 0 000400 0 00 00 09 0 00000* 0 00 0 0 900 00060 0 0040 0@0 0000a0 0

t0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 # 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 033 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 034 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0to 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 024 0 0 -) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 027 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 029 0 0 0 0 0 0 00 o0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 030 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0



31

FIGURE 23. Target Representing Vertical Line Road.

1 2 3 45 6 7 S 1 10 11 12 33 14 15 16 1? If 19 20 21 22 23 24 25 26 27 21 29 30 31 32

1 49 -3 57 3 43 3 45 1 1 -9 1 -3 3 -S 5 -5 -S -1 -3 -a -7 -1 -? -a 5 -3 7 -3 1 -3 9 -3a 3 -3 1 1 1 -1 1 1 1 -3 1 -3 1 -3 -a -3 -a -3 -s -'1 -5 -3 -3 -5 -1 -3 -a -3 1 -1 -3 -3

s ? a a 3 -a a -, a -13 a-1 a -a 3 -2 1 -1 1 -1 .1 -a -a -a 1 -2 1 21 1 3 21

6 3 -3 a a -a -a -a -1 -a -5 a 1 -a -1 -5 - - - -3 -3 -3 -3 -3 -3 -a -3 -1 -3 -1 -1 1 -3? 3 1 2 1 1 3 1 t1 I-3 1, -3 1 -3 a -3 -1 -t -a -3 -t -3 -1 -I -a -1 a -3 1 -i 1 -11 3 1 1 1 -a a a 1 1 -3 3 -3 1 -3 a -3 -a -3 -a -3 -1 -3 -3 -3 -1 -1 1 -t -t -a -1 -a9 1 1 A 3 -1 3 1 1 a -3 a -a 1 -1 a -3 -1 -3 -1 -5 -3 -3 -1 -3 -1 -3 -1 -3 -1 .1 -2 -31o4 3 531 ts 3 3 13-131 t3 -i a-ta a-1-a -i a-a a-a -1- 1 i -aaa 3 15 3 33 2 a 3 -1 3-i s-a -a a-a -a -a a-i a a a-a a-1 a-a22 ? 3 3 5 a 5 3 3 a -a a -a 3 -a 3 -3 1 -1 a -3 -a -3 2 -a a -a a -1 1 -1 1 -at31 331 3153 3 1 S-1 3-132 1 33-a -1-al- I- a - 3 - 121214 9 1 3 3 A 3 1 a a -3 1 -3 1 -1 1 -S -1 -a -1 -3 -3 -3 -a -3 a -a a -1 1 -a a -1as s -a 3 a a a 1 a -a -3 a -3 -1 -3 1 -1 -3 -3 -3 -3 -3 -3 -3 -3 -a -3 -1 -3 -1 -3 -a -316 5 -3 1 -1 1 -1 1 -1 -3 -1 -1 -7 -3 -5 -1 -$ -1 -1 -3 -5 -5 -5 -s -5 -s -5 -3 -5 -3 -5 -3 -51?7 1 3332133 3 A-1 3 -1 3-1 3 -S a a-a -i -a -a 1a-a a a a a 111

19 9 3 35 3 5 3 2 3 -i1 3-1 3 t 3 -1 1 -1 a -3 -i -a -a -a -1 a a a 1 i a 120 9 15 717 ?51 a 7217 il5l 3213 1211 1-113 a ai a 32122 7 3 2 5 3 9 3 3 3 -1 1 -a 3 -1 3 -a I 2 I 1 -3 -3 a 1i -3 -a 1 -1 -1 -1 -a 1 -122 7 3 1 1 1 1 3 3 3 -2 1 -2 3 -1 1 -3 1 1 a -1 -i a a -i a I a I a a I I-a23 7 3 1 1 3 1 1 3 3-1 3- 1 3-1 3 -3 2 -1 3- 1 1 2 1-3 1 1 1- 1 1 1 1 234 7 2 1 1 1 3 a 1 1 -3 1 -3 1 -3 1 -3 1 -3 1 -3 -3 -3 -t -3 -1 1, 1 1, -t -1 1 -321 S I 3 I 2 1 2 1 3 -a1 3 -i 1 a 5 - 1 3 1 1 -I A 1 3 1 3 3 a 1 3 3 3 126 7 -1 3 3 1 3 1 1 -1 -3 1 -3 3 -1 1 -3 1 -2 -1 -3 -1 -3 -a -3 a -1 1 -1 2 -1 a -127 1 3 3 1 1 0 3 1 3 1 3 1 3 -1, 3-1 1 1 3 -t1 -i I-i 3 1 3 1 3 3 126 ? 2 3 3 1 3 3 3 1 -2 1 -a 1 -1 3 -S 2 -1 -1 -3 1 -1 -1 -3 a -a 1 -3 2 -a a -a29 * a a 3 1 3 1 If a -3 3 -3 1 -2 1 -3 1 -2 a -a -a -a -a -3 1 -a a -3 1 -1 1 -130 5 -1 3 t 1 1 1 1 -1, -S -t -1 1 -3 -1 -11 -3 -3 -1 -11 -3 -3 -3 -S -1 -3 -I -11 -1 -3 -1 -3

3S 1 1 3 3 1 1 1 1 1 -3 1 -3 2 -3 a -S -2 -3 -a -3 -2 -3 -a -3 -a -a -1 -3 1 -1 1 -3


32

SOLS COEFFICIENTS

1 2 3 4 3 4 7 0 9 10 It 12 13 14 13 16 17 10 19 20 21 22 23 24 25 26 27 26 29 30 31 32

1 50 0 54 0 40 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 a000 0 00 0 00 0 0 00a 0 0 0 00 0 0 0 0 0 0 0 00 0 0 03 0000 0 000 *0 0 0 0 0 0 00 0000 0 0a0 0 0 0 0 0 0 0 04 0a0 0 0 00 0 00 00 00 0 000 000 0 0 0 0 0 0 0 0 0 0 0 0 05 00 00 0 0000 0 00 400*40 00 00 0*0 0 000 00 00 04 00 000a0 000 0 00)1 @00 00 00 00 000 a0 @000 07 0 000 0 00 000 0 00 00 00 0 0000 00a0 00 00 0 00

9 00 00 00 00 0 00 0 0000a0 00 00 0 00 000 000 0a

10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0it 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 029 0 0 0 0 $ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 030 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

FIK-,URE 25. Walsh Transform of Figure 23 after Filtering.


* 33

FIGURE 27. Target Representing DiagonallyOriented Road Intersection

DOLS COKPICtINTS

1 2 3 4 5 6 6 9 10 It 12 13 14 1516 1? 13 19 20 21 22 23 24 25 26 27 29 29 30 31 32

3 04 6 2 2-24 6 0-10 - -4 2 -4-10 0 2 -4 4 0 0 -4-12 -4 -4 -2 -4-1 t -2 0 0 0 22 64 4 S -2 0 -2 0 5 4 0 0 -2 0 -4 2 -2 -2 -6 -0 -4 -6 -4 -4 -s -4 -4 -4 -2 -4 -43 22 0 76 12 4 16 20 2 0 2-16 2 G 4 12 * 2 2 2 -2 -4 -2 -2 6 -2 -2 -4 -4 0 6 10 64 20 8 14 25 6 20 10 5 12 t1 12 10 15 10 t2 6 12 10 12 2 6 6 A 62 4 310 6 65 -2 6 4 6 34 0 4 6 0 6 10 6 22 6 2 9 4 4 2 0 2 2 2 2 0 4 4 10 4 0 26 20 & 6 2 2 G 2 2 6 4 6 6 4 4 6 0 4 4 6 0-2 2 0 2 2 2 4 2 2 6 2 a? 14 0 22 1 I 2 6 6 0 4 0 10 4 6 0 10 2 6 6 6 2 6 4 4 4 2 5 4 2 4 3 1 2* 1 4 612 0 6 6-4 4 2 6 4 2 4 6 2 6 4 0-2 2 2 2 0 0 4 4 6 6 6 &9 12 4 4 3 -6 4 4 0 -2 4 4 2 4 2 4 0 4 4 2 * -2 $ 0 0 -2 0 2 2 2 6 4 a0 19 6 1 4 32 610 & 4 8 6 10 4 6 6 1 6 1 6 2 0 4 6 4 4 2 4 2 6 0 4 A1 146-I 10 12 6 4 0 2 & 4 4 2 0 2 0 4 6 0 -2 -2 # 0 0 -2 4 4 2 2 2 2

12 14 9 641 4 # * 0 4 6 2 4 -2 4 0 4 0 2 -4 -2 0 0 -2 0 2 0 2 2 0 11 146 16 4 2 4G 62 1 -422 0-o 2 2 a 002 4 220114 34 1 4 4 -4 4 2 -4 0 -2 0 0 0 -2 2 -45 0 0 -4 -6 -4 -4 -2 -4 -6 -2 -4 -4 0 -2 -S15 it 0 4 4 -2 2 4 -6 -2 -2 0 -2 -2 -2 4 -4 0 0 0 -4 -0 -6 -6 -4 -6 -4 -2 -4 -2 -2 -2 -0II 10 -4 -2 -2-10 -4 -6 -0 -6 -6 -2 -4 -4 -4 -0 -u -4 -2 -6-10-12-30 -8 -0 -8-10 -6 -I -I -6 -8 -0IT 10 0 4 6 0 4 2 -4 2 2 4 4 2 2 2 -4 4 4 2 0 -4 0 0 0 0 -2 2 0 0 2 0 1

10 15 1 0 & -2 0 -2 -4 0 0 # 1 2 -2 2 -4 2 0 2 -2 -4 -2 -2 -2 -2 -4 5 -2 2 2 2 019 O0 0 0 2 -4 0 -4 -6 -4 -4 2 0 -2 -4 -2 -4 0 -4 -2 -6 -1 -4 -4 -4 -4 -4 -2 -2 -2 2 -2 020 10 2 2 4 0 4 4 -4 2 0 2 2 0 -1 4 -4 2 -2 0 -2 -6 0 -2 -2 -2 -2 0 0 0 2 0 0I 12 -2 2 4 -0 -2 -4 -g -I -4 -2 -2-10 -6 -1 -S -4 -4 -4-tO-Ul -%-%4 -9 -9-14 -I -6 -I -4 -6 -422 10 0 0 4 -6 0 * -I -a -4 -2 -2 -4 -6 -2 -4 -4 -4 -4 -6-10 -0-10 -1 -l-10 -I -6 -1 -6 -6 -023 I0 0 24 -4 04 -6 - 5 0 -2 -2 -4 -4 -4 -6 -4 -4 -4 -8-10 -6-10 -s-16 -8 -4 -0 -6 -6 -1 -0

24 12 0 -2 1 -I * -4 -6 -4 -4 -2 -4 -4 -4 -2 -4 -4 -4 -4 -6-12 -I -4 -0 -$-1$ -6 -I -I -6 -I -S23 12 4 4 1 0 6 4 0 - 2 4 2 1 0 4 -2 1 2 2 -2 -4 0 6 -2 -2 -4 0 0 0 40 -124 It 0 2 4 -4 0 0 -4 -2 -2 J 4 -2 -2 0 -4 -2 -2 -2 -6 -8 -4 -6 -4 -2 -6 -4 -4 -6 0 -4 -42? 10 6-2 2 6 4 -2 4 6 6 4 * 0 2 -2 4 4 4 -2 -4 5 5 2 0 -2 0 2 -2 2 0 920 32 1 G 4 2 2 -4 0 011 0 0 -2 0 -2 0 0 0 -4 -4 -4 -6 -4 -6 -6 -2 -2 -2 0 0 -429 S11 0 1 4 2 0 -4 0 -2 1 0 0 -2 0 -4 -2 5 -1 -4-30 -4 -4 -4 -4 -4 -2 -2 -2 -2 -4 -43* 15 0 4 4 -2 2 0 -4 -2 -4 0 5 -1 -1 -4 -4 -2 -2 -1 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -2 -4 -031 32 6 10 If0 4 4 0 0 0 4 2 0 0 4 5 2 0 2 -2 -4 -9 -2 -4 -2 -4 0 -2 -2 2 0 -2

32 16 4 4 ,-2 4 0 -2 0 0 2 0 0 0 0 -4 0 5 -2 -4 -1 -6 -4 -4 -9 -1 -a -6 -4 -2 -4 -4

FIGURE 28. Walsh Transfori of Figure 27.

34

MORNH

MALS COEFFICIENTS

I 2 3 4 3 6 7 S 9 10 1 1 12 3 14 13 16 17 1S 19 20 21 22 23 24 25 26 27 28 29 30 31 32

1 as 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 02 0000000000 0000 000 00 0 0 0 00 0 0 000 0 03 0 073 00 0 00 00 0 00 0000 0 00 0 0 0 0 0 0 0 0 0 0 0 0 04 0 0 0 00a0 0 0 0 0 0 00080 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 05 0 000330 0 000 0 4 000 0 0 0 0 0 0 000 0 0 0 a0 0 0 0? 00 0000 0 00 0 0 0000 00 @0 0000 0 0 0 0 00 0 0 0

00000000000000O000000000000000

8 00000000000000000000000000000000

4 0000000000000000000000000000000£0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0£1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

£2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0I3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 a 0 0 0 014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0£4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0is 0 0 0 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02£ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 021 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0



35

14 G O- -O O G O *OO O'-40 0 0 0 0

FIGURE 31. Target Representing DiagonallyOriented Line Road (I ).

GALS COEFFICIEMYS

1 2 3 4 5 6 7 1 9 10 1 112 1 14 1S 16 17 16 19 20 21 22 23 24 25 26 2? 28 29 30 31 32

1 0 2 0 0-12 0 6 1 0 -2 2 -2 -4 -2 4 -6 ' 0 -2 0 -6 - -4 4 0 0 -0 0 0 0 0 0 02 4-56 -' 0 -4 16 4-2 -4 0 -6 -2 0 0 -0 -4 -6 -2-10 -6 -6 -6 -6 -4 -0 -6 -6 -4 4 -6 -63 26 240 4 4 0 0-2-4 0 2-2 0 2 0 -2-4 0-2-4-2-2-2-4 2 2 6 04 12 0 4-16 412 2 0 6 6 4.* 4 4 2 0 4 4 2 2-2 0 0 0 0 2 2 4 0 4 0 05 4 012 422 4 6 2 2 0 4 4 12 0 6 2 2 2 -2 -4 0 -2 -2 -2 0 0 2 0 0 0

122 10 2 - 4 2 4 -4 0 0 2 0 0 -2 -2*2 -2 04 0 0 -2 27 422 0 2 4 6 4 2 4 22 4 0-2 2 2 0 0 -2 2 2 2 0

2 12 2 2 10 01 2 S 4 4 4 6 $ 6 2 0 0 0 2-2 0-2 4 2 2 4 0 012 8 4 6 2 2 2 4-6 4 4 4 4 2 4 0 4 4 2 0 4 0 0-4 2 0 4 2 6 2 4

10 10 6 0 6 6 4 0 4 2 0 6 0 2 2 60 2 4 4 2-2 2 4 2 2 4 4 2 4 4 4 40 012 0 2 4 2 2 2 2 4 2 2 0 2 0 4 2 2 2 4 4

12 10 10 2- 0 4 4 4 0 2 04 4 0 0 0 0 2 4 4 0 4J26462 4 0432 42400 20-24400 00 224

4 0 4 2 0 -4 -2 -4 2 0-2 0 0 2 -4 -2-4-4 2 -2 -4 -4 -2-4 0 0 -2 -2i3 30 -2 0 2 -2 2 2 -4 -4 -2 -4 0 -2 2-4 -2 -2 0 -4 - -2 -4 -4 - -4 -4 0 -2 -21 -4 0 0-2 - -2 -4 -4 - -4 - -2-14 -4 -4 -2 - -0 -6 - 6 - - 6 - -6 - -4 -0 -?210 4 4 4 2 -2 2 0 4 2 0 4 0 4 0 2 0 2 0 02 0 0 -2 0 2 0

10 0_2 4 0 2 -2 2 2 0 2 -2 -2 2 -2_ 0 -2 -2 -2 -2 -2 -2 0 0 -2 0 0 02 0 2 0 4 -4 -2 0 2 0 2 -2 2 -2 0 -2 0 -2 4 -2 2 0 -2

20 6 4 4 -2 0 0 2 0 2 0 0 0 2 -2 0 0 0 0 40 0 2 0 221 6 -2 2 -4 - -4 -2 -- 4-4 -4- -4 -4 -4 -2 -6 -4 -4 -4 -0 - _4 -2 -4 -0 -4-4 - -2 -2 -422 0 -4 -4 -2 -6 -4 -4 -0 -4 -4 -0 -6 -4 - -4 -4 -0 - - 0 - -4" -- 0 -4 - -4 -4 -4 -423 4 -4 -2 -2 -6 -2 -4 - -6 -0 -4 -4 -4 -4 -2 -0 -4 -6 -4-16 - I - -0 -0 - -6 -4 :6 -4 -1 -024 0 -4 -2 - -4-1: -4 -0 - -0 -6 -- -4 - : -6 -4 -1 -0 - -6 -0 , -0 -0 - -06 - -0

21 0 22 2 0 0-2 -4 0 2 -2 2-2 0 0-4-4-4-4-2-4-2 2-2 -2 I -4-22 0 2 2- - -4- 4 4 -2 -4 -2 -4 -2 -4 -2-2 - -4-0 -2 0 - -6- -4 -4 -4 -4 -227 4 0 4 2 4 2 -2 0 0 2 4 0 2 -2 1 0 -2 -4 4 -2 * -2 0 0 -2 4 0 -22 2 - 0 - 0-2 0 0 -2 0 -2 0 -2 -4-4-2 -4 -4-4 -2 -4-2 0-4-2

a0 2 4 2 2 2 0-| 0 0 0 -2 0- -2 0 0-2 -4 -4 - -2 -4 0 -2 0-2 -2 2

0 2 -2 -2 -2 -4 -2 -2 0 -2 0 -4 - -4 0 -2 -2 -4 - -4 -4 -4 - - -4-4 -4 -2I0 2-2 2 0 2-2 -4 -4 -2 -2 -2 0 -2 4 2 0 0

32 10 4 2 0 -2 0 4 -0 -a -2 0 -2 -2 -4 -2 -4 -2 -1 -4 -4 -0 -4 -4 -6 -4 -4 -2 -2 -4 0 -2 -4

FIGURE 32. Walsh Transform of Figure 31. *

36

__4.

VAL , COEFFICIENTS

1 2 3 4 5 6 7 0 1 10 1 1 12 13 14 13 16 17 10 19 20 21 22 23 24 25 26 27 20 29 30 31 32

1 60 0 0 0 0 0 0 0 0 0 0 0 0 & 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 0-54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 03 0 03 0 00 00 0 0 0 0 0 0 0 00000 00 0 0 00 0 0 0 0 0 04 0 00 0 000 0 000 00 00 00 00 00 00 0 000 00 00 03 00440000 0 0 0 00 0 0 0000 0 00 000 0000 0 000 0' 0 00 0 000 00 00 00 0 00 0 0@0 0 00 00 00000 007 @ 000 0 00 0 0 0 0 00 0 000a0 0 0 0 00 0 0@0 00 000S 0 0 00 00 0 0 00040 00 40 0 0000 00 0 000 0 00 009 0 00 0 000 000 00 0 00 00 00 000*0 0 00 0000a0 0

t0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0It 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 0 0 0 0 0 0 0 0 0 0 0 0 ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 025 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 0 00 00 000 00 0 00 0 0 : : 0 : 0 : : 0 : o 0 0 0 0 0 0 027 0 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

20 00a0000a000000000000 0 0 0 0 0 0 0 0 0 0 0 029 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 030 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 031 0 0 0 0 0 0 C0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

32 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0



37

%JI

FIGURE 35. Target Representing DiagonallyOriented Line Road (2)

04 LS COEFICIENTS

1 2 3 4 5 0 ? 1 9 20 1 1 2 13 14 1 S6 ? I0 19 20 21 22 23 24 25 26 2? 20 29 30 32 32

6 0 0 22 12-12_00: -6 2 -2 2 , -2 -2 4- 2 0 2 -4 -6 -2 -2 0 - 0 0 2 2 02 28 4 2 34 2- 0 - 2 _ 2 2 - 2 2 4 0 - - 0 - -2 0 0 0 2 0 02 2 4 -3 4 0 06 -a 10 42 -2 2 2 0 -4 4- -2 0 0 0 0 0 0 0 0

s a. , a. 0044 2202 *-a a .a 0 -0-a 0000002000. .

S22-2 0 2 2 1 2 - 2 * . a 4 2 - 0 _ 04 -1 2 :- -a_2-7 20 -222 1 4 4 02 6 -2 4 0 0 26 4 4200 -2 0 -2 0 0 0 2 2 0

1:-4 0 4 -2 - 4 0 4 4 4 4 2 4 2 2 -2 0 2 2 2 2 292 04 0 020 2 4-, 2 4 2 0 2 4 2 0 2 2 0 2 4 06 4 2

22 22 -a 24-o -a 4 4 0 2 4 4 2222040- 2 4 0 4 42023 1 0 6 0 4 2 4 2 2 2 2 4 0 2 4 2 0 - 4 0 2 2 2 4 0 4 2 46 _2 , , . , -4 2 2 6 a , , 4 2 ,- _4 4 _2 ._-2+. .

24 0 004 -2 0 2 -2 -2 -2 2 -2 0 2 -4 2 -4 -6 -6 -4 -4 -2 -4 -4 -4 0 4 -4 0 -- 4IS 1:2 2 0 02 -2 0 -2 -2 -2 0 -0 2 -0 0 -2 * -2 -6 -4 -4 -4 -2 -4 -4 -2 -2 -a -a2 1 -6. -6 -22 -- -4 -2 -4 -6 4 4 -2 -0 - -4 0 -- -0 -6 -0 -0 -4 -6 -4 -0 -4 -0 -4 -41? 2 2 0 0 2 _ 04 6 - 222-a -a 1 4 -a 2 0020 1 2 4 0 -2 4 2 0 0 0# 0 2 0 :20- - - 2 2 -2 2 0 0 * 0 029 0 0 0 2 0 4 0 -2 2 6 2 -2 2 -4 2 - 2 2 01 - -4 0 4 -2 a- 0 -2 -2 0 0

22 0 -4 . 2 2 6 0 -2 0. 4- 2 -0 -2 0 -4 24_ 4 -4 -0_4 0 -I -4- 4-4- - -2 -4 -4 - -2 -22 4 0 2 -0 -4 -0_2 -0 -2 0 _4 -4 -0 -4 -0 -2 -4 -2 -4 -0I -04 -4 -0-4 -' -4 -4-4 -2 -4 -223 2 -2_ 2 -2 2 - 4 0- 4- 4 4- -4 -4 -2 -- 0 -0 -0 -04 -0 -0 -0 -4 :4 -0 -424 0 0 -2 a -0 - 6 -0 2' - &- 4- - -4 -0 -0-:4 -:- 0 ,- - g- -6 -0 ' -4 -021 10 0 2 0 2 2 2 0 4 a 2 : -2 0 -2 0 2 -4 _4 _4 -2 -0 -4-_- a -2 -220 0 -2 0 0 -4 0 -2 -4 -- -4 0 -4 -2 -2 -0 -2 4 -2 -0 -6 -0 -0 -0 -4-10 -4-10 4- -427 0 _4 A 2 0 0 2 2 a 0 0 4 .0I 2 -:4 0 1 -2 :2 :2 2 - :-2- 0 -4 020 0 2 2 -4 0 -2 -4 -2 0 2 4 0 -2 0 2- 4 -4 4 4 4 - 4 -2 -2 -2 - 429: 2 2 2 2 2 -11 0 0 0 0 2 0 0 -2 0 0 -4 -4 -4 -2 -2 .I-_4 -2 _4 -2 -2 -2 -4

0 0-00a- 0-4--20 - -2 0 0 :4 -2 -2 6 0 :04 -4 -4 -4 :4 -0 -4 -4 -4 -2 -4 -22 040004 4 04 0 0 41 2 -2 2 02--2 0 0 0 -2 -4 0 0 -2 0

22 0 -2 2 0 -2 0 6 -2 -1 -4 0 -4 -2 -2 6 -4 -2 0 0 -0 -0 -2 -4 -4 -4 -6 -4 -4 -4 0 -4 -2


38

OIL$ COEFFICI~ENTS

1 2 3 4 3 0 7 0 9 10 2t 12 23 14 15 16 1? 16 19 20 21 22 23 24 25 26 2? 28 29 30 31 32

1 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0a #50 000 0 a009000 0000 0 0000 0 0 0 0 0 0 0 0 0 0 003 0 036 0 0 0 0 00 00 0000 00 00 00a0 00 00 00 00 04 0 000 a0000 0 0a0 0 0 0 0@0 0 000 a0 00 00000 00 03 0 00 0 000 0 000a0 0 00 00a00 0000 00 00 00 00 00 0 0 0 000 00 00 000 00 00 00 00a0 000 00 0 00 00? 0 00 00 0 000 a0000 00 00 0 00 00 00 0 00 0a00 0a 0 000 0 000 0 00 00 00 000 00 0 00 00 000 0 00 09 000 0 00 060 0 00000 0 000 0 00 00 00 00 00 00 0

10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 024 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 # 0 0 # 0 420 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 029 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 030 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 0 0 0 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0



39

FIGURE 39. Target Representing Diagonally

Oriented 5amli n R,,..

MALI COEFFICENITS I

1 2 56 7 1 10 11 12 13 14 15 16 171 S19 20 21 22 23 24 25 26 2? 28 29 30 31 32

1 29 1 39 5 15 3 15 1 I 1 1 1 9 1 9 1 3 3 1 1 -t I -1 I I I I 1 9 1 9 123 1 -1 - -I 1 1 1 -1 1 -I 1 -Il -1 -I -I-I -I -3 1 1 1 -ia 2? -1 at 1 13 1 13 -3 - -I 1 -1 ? -I 9 -1 1 1 I -1 -1 -1 -1 1 1 -I 1 -1 9 1 9 34 3 33 1 -1 1 -1 1 - -- -1 1 -t I I 1 -1 1 - 1 -11 -1 3 1 3 15 1? 3 15 3 -3 I 1 i -5 -I - 1 3 1 3 1 1 1 1 1 -2 1 I 1 -1 -1 -1 -1 5 1 5 1S 5 13 3 1 1 1 1 1 I -t I 1 1 -1 1 1 1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 1 1Y I? 1 15 3 -1 1 1 3 -5 -I -$ -1 3 -1 3 -1 3 1 1 -1 I -1 -1 -1 1 - -1 3 3 3 1

5 3 3 3 1 1 1 I 1 -1 1 -1 3 1 1 -1 1 1 1 1 -1 1 1 -1 1 -1 1 -1 1 I 1 -19 1 3 2 -5 1 -3 1 1 1 3 -1 1 1 1 1 1 3 2 1 1 1 3 1 1 -1 1 1 1 1 1 130 -33 1-3 13- 31-1 31-I111- -3 - - -1113-1111

It 3 1 3 3 -I 1 -5 1 1 -1 3 -1 3 1 3 - 1 1 1 1 1 1 1 -1 1 I 1 -1 1 1 1 112 -32 13-22 32 31 3-3-11 11 l 3 - 2 - --II -3IIII112 5 1 3I -1 1I -1 1 -1 1 -1 1 -1 -1 1 1 -1 -3 -1 -1 1 -1 1 -3 1 1 1 1

13 9 1 7 1 -1 1 -1 I -I -1 1 -I -1 -1 1 -1 -1 -1 -3 -1 -I -3 -1 1 -t -1 -1 -3 1 1 1 114 1 -1 1 -1 -3 -3 -1 -3 -1 -3 -1 -3 -1 -3 - -3 - -3 -1 -3 -3 -3 -3 -3 -3 -3 -1 -1 -I -t -1is -1 7 1 I -1 -1 -1 -1 -3 -1 -1 -1 -1 -3 -1 -3 - -3 -1 -1 -1 -1 -1 -I 1 -3 1 1 1 116 2 -1 1 3 -3 -1 -1 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -S -3 -3 -J -3 -3 -3 -3 -3 -I -3 -1 -337 3 -3 1 1 -1 -1 -1 -3 -I -1 -1 -3 -3 -3 -3 -3 -1 -3 -3 -2 -3 -2 -2 -1 -1 -1 -3 -2 -I -1 -1 -1

Is 3 1 1 1 -1 -1 -1 -1 -1 -3 -1 -3 -1 -t -t -3 1 -I -1 -1 -2 -3 -2 -3 -1 -3 -1 -3 -1 -3 -1 -3II 3 -I 3 1 -1 I 1 -1 -I -1 -1 -1 -3 -1 -1 -1 1 -1 -1 -2 -3 -1 -3 -3 -I -3 -1 -1 -1 -1 -1 -320 3 -1 1 1 -3 1 -1 -1 -1 -1 -1 -1 -1 -3 I -3 -1 -1 -1 -1 -3 -3 -3 -3 -3 -3 -t -3 -1 -3 -1 -1213 -1 1 -1 -I -3 -1 -2 1 -3 1 -1 -1 -1 -1 -3 -1 -3 -2 -2 -5 -3 -3 -3 -2 -3 -1 -s -1 -3 -1 -222 3 -2 I -1 -3 -1 -1 -I -3 -2 -3 -3 -3 -3 -1 -2 -3 -2 -3 -3 -2 -5 -S -5 -3 -3 -1 -3 -1 -3 -1 -33 3 -1 I 1 - -I -1 -1 I -3 1 -1 -1 -3 1 -3 -1 -3 -i -3 -3 -3 -3 -2 -1 -3 -1 -3 -1 -1 -1 -3

24 2 -1 1 -1 -1 - -3 - -3 - -3 -3 -3 - - -3 -3 -I -3 -3 - 3 - -2 -3 - -3 -1 -3 - -3 - -3a5 1 3 3 -1 1 -3 11 I 3 I 3 I A I I 1 I I 1 -1 -11 -1 I 1 3 3 2 126 3 -I I I -1 -1 -1 -1 -1 -2 -1 -3 -I -3 -1 -3 -2 -3 -1 -3 -2 -3 -3 -3 -1 -3 -3 -i -I -2 -1 -337 3 3 3 S -3 3 -1 1 1 1 1 -3 I 1 1 1 1 11 1 -3 1 -3 1 1 1 1 -3 1 1 1 I36 1 -13 1 -1 -1 1 -1 -1 -1 -1 -3 -3 -3 - -3 -1 -1 -3 -3 -3 -3 - -3 - -3 - -3 - -3 - -3I 9171 3 3 1 1 3 1 1 1 -1 1 1 1 1 1-111 1 130 S 1 3 1 1 1 1 3--1 - -3 I -1 - -I - -- -1 -i - -3 -3 - -3 -1 -2 -1 -31 9 3 9 3 1 1 3 1 3 1 3 1 3 3 3 1 3 1 3 11 1 11 3 1 3 3-1 3 3 3 132 3 1 3 I -I 1 1 I -1 -I -1 -1 1 -I I -1 -1 -1 I -1 -1 -2 -1 -3 -1 -I -1 -8 -1 1 1 -1


40

1 a 3 4 3 & 7 1 9 10 11 12 13 14 13 t6 17 IS It 20 21 22 22 24 23 26 27 26 29 30 31 32

3 24 0 30 0 12 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a #4 0 0 0 0 00 a Cee e * *ese000 0 0.. 6C 0 0 0 05 S e is 0 0 0 0 0 C 0 0 * 0 0 4 4 0 0 0 0 0 C 0 t 0 0 0 67 to0 6 0 0 0CC 0 06e *0 0 5 o e ee 0 e e. 00 ,.,, 00

s 4* *i 0 0 0 0 0 C e * * e * 0 0 0 4 e 0 4 C 0 0 6 C 0 0 *

19 0 0 0 0 0 0 0 0 0 0 0 * 0 * 6 4 * 4 0 4 0 0 0 0 0 0 5 0 * 4 0as * 0 0 0 0 e 0 6 * e e 0 * 0 s * 0 * 4 0 0 0 4 1 , . 4 . , * 4

32 0 s o e 0 S 0 e s e * * e~ e e 0 C 0 0 4 0 0 0 5 0 0 0 0 4023 0 6 0 * 0 0 * 0 0 * * 0 e 9 * 0 0 C 6 0 6 9 0 0 * * * 0 024 e a C 0 C0 6 0 0 0 0 * 0 * 0 6 6 * & 0 C 4 6 0 0 0 0 0 C 5 0 025 0 0 4 0 0 S 0 0 0 6 0 0 0 50 C 6 0 0 4 C S 0 * 0 0 4 0 6 *

IS 0 0 S 0 0 0 0 6 0 0 0 0 C 0 0 0 e 0 4 0 0 0 0 0 0 0 C 0 0 0 0 629 0 * 4 0 e 0 0 0 4 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 03. 6 4 C 0 0 6 0 0 e 6 o o e e o 0 0 4 6 0 C 0 S C * 0 0 0 * 0 0 0

22 C 0 0 6 0 0 0 6 0 C 0 * * 4 0 * 6 0 0 0 40 0 0 0 0 0 0 0 4 0

2 0 4 0 0 0 0 0 0 0 5 0 0 0 S C C 0 0 4 0 0 4 0 0 4 S 0 0 C


41

The dynamic range of the PISA was tested by using aerial photo--transparencies(size expanded to cover the entire light-emitting surface of the plasma tube) containingmanmade topographic features, plus background terrain. The dynamic range of the PISAwas defined to be the saturated signal voltage divided by the RMS (root mean square)value of noise voltage appearing at the output of the PISA. The test results are shown infigures 42 through 49. Only figure 43 shows a marginally recognizable result, that is amarginally large decomposed coefficient of -37 compared tc other coefficients owingto background terrain and system noises (largest 19). The result thus may be identifiedas a piece of farmland resembling the Walsh function pattern; Wal (0, x) Wal ( 8, y). Inthe rest of the figures, no significant coefficients can be recognized. This indicates thatthe dynamic range of the PISA is poor. Two factors that caused the poor dynamic rangeof the PISA were identified. They are ( I) the high-switching voltage (250 volts) of thePlasma tube resulting in high-switching noise and (2) the inability to isolate unwantedbackground scenes that indirectly contribute noise. The symmetry of the PISA responseswas evaluated with four simple targets representing lower order Walsh functions;Wal (1, x) W(0, y), Wal (0, x) W( 1, y), Wal (3, x)W (0, y), and Wal (0, x) W(3, y).Since Walsh functions are two valued functions of +1 and --I, any input pattern andits complement shall ideally yield responses of same magnitude, but opposite in sign. Thesymmetry test results are shown in figures 50 through 65. The shaded area of targets aretransparent and the unshaded, opaque. It was discovered that the PISA gives largerpositive outputs than negative ones for all four cases. This implies that either the analogcoefficient processing circuitry is nonlinear or the normalization of the coefficientsis not properly performed.

The time dependency, or temporal response, of the PISA is very important andwas evaluated by repeatedly running the system for a fixed input pattern. In figures66 through 73, the temporal responses are shown for targets representing a road inter--section and a vertical line road, respectively. More than 10 percent variation in one ormore of the significant spectral coefficients was obse rved for both cases. The causes ofpoor temporal responses can be traced to the variation in switching noise, which in-directly results from the change of plasma lights intensity with time and the possiblevariation of stray light.

42

FIGURE 42. Aerial Photo-Transparency (I).

MAL$ COEFFICIENIS

1 2 3 4 S 6 ? S 9 10 It 12 13 14 15 16 1? 16 19 20 21 22 23 24 25 26 27 26 29 30 31 32

1 $1 9 1S 13-11 3 7 -9-3? -1 7 3 3 1 5 1 S 7 3 -5 -5 1 -1 3 -? -7 3 3 9 5 ? 3

2 13 1 -3 5 -1 3 -3 1 -1 1 5 1 1 -1 1 -3 3 1 1 -$ -3 -I I -3 -I -3 1 1 1 1 -1 -13 19 5 9 9 1 7 5 1 3 3 7 5 ? 3 5 5 9 ? 5-11 3 3 3 11 3 55 9 9 7 7

4 17 71111 311 7 3 9 7 9 7 ? 5 ? ? ? 9 ? 3 3 5 75 3 5 7 9311 9 9 95 13 3 3 9 -1 7 1 1 3 1 5 5 31 3 1 3 3 3 -I -3 -I I -I -1 -3 3 3 3 3 3 3

6 13 3 1 5 -3 3 -I -I I -3 3 -1 3 -3 1 -1 3 I 1 -S -5 -5 - -3 -3 -5 -3 -I -I I -I -I7 IS 5 3 ? 1 5 3 -1 I -1 5 3 3 1 5 -I t 1 -3 -3 -3 - -1 1 -I3 -I 1 1 3 1 1I 1? 7 7 9 1 7 3 1 1 1 5 3 5 3 5 3 3 5 3-I-1-I -I1 1-3 1 1 3 5 1 3

9 IS 3 3 7 -3 1 3 -1 3 1 5 3 5 -1 3 1 3 3 3 -3 -3 -3 1 1 -1 -3 1 1 3 3 -1 1

80 15 7 5 13 3 7 3 3 3 3 9 3 7 3 5 3 S 7 3 -I -I 1 I 1 -1 -1 1 5 5 7 5 513 15 5 11 1 F 3 1 1 1 ? 3 3 1 3 1 3 53 -I -I I 1 -I 1 3 5 1 3 1

12 13 3 7 -I 3 I -I I I 1 3 1 3 -I 3 1 1 -5 -3 -1 -1 -1 -1 -3 -I 1 1 3 -I I13 9 3 3 -1 1 I 3 -1 5 3 3 - 3 1 3 5 3 1 -3 -1 3 3 1 -1 1 3 1 5 3 314 9 -3 -3 -1 -5 -3 -3 -3 -5 -3 -3 -1 -3 -1 -s -3 -1 -3 -, -7 -S -s -s -3 -7 -3 -3 -I -3 -3 -3

is 9 -I -3 1 -? -3 -5 -, -9 -5 -3 -3 -5 -7 -3 -9 -s -3 -5 -9 -9 -? -5 -F -7-Il -s -$ -3 -3 -5 -316 13 -S -5 -I -9 -s -?-II -9 -9 -5 -7 -7-11 -?-If -? -? -9-13-13-13 -9 -9-13-13 -9 -9 -9 -S -9 -?

17 13 3 3 5 -3 1 -1 -3 -1 -3 3 -1 I -3 -1 -3 -1 -1 -1 -5 -? -5 -5 -3 -5 -7 -5 -3 -3 -3 -3 -31 13 1 3 ? -1 5 -1 -1 1 -3 1 -1 3 -3 -1 -3 -1 -1 -3 -5 -? -S -5 -3 -5 -7 -3 -3 -3 -1 -3 -519 9 1 1 5 -3 3 -3 -1 -1 -1 3 -1 1 -3 -1 -3 -1 3 -3 -7 -3 -5 -S -5 -5 -? -3 -3 -3 -1 -3 -3

20 13 5 9 9 -I 5 3 1 3 -1 5 1 3 -1 3 -1 3 3 1 -3 -3 -3 -1 -3 -3 -3 -3 -1 -1 1 -1 -121 11 I 1 3 -5 -1 -t -3 -s -3 -1 -3 -3 -5 -1 -5 -i -1 -3 -7 -9 -7 -3 -$ -7 -9 -5 -3 -5 -3 -3 -722 I1 1 1 3 -3 1 -1 -3 -3 -1 -1 -3 -1 -3 -1 -3 -1 -1 -3 -? -9 - - -7 -7 -9 -3 -5 -3 -I -3 -3

23 9 1 -1 3 -5 1 -1 -3 -S -3 1 -3 -1 -3 -1 -? -3 -3 -3 -9 -7 -7 -S -3 -7 -9 -? -3 -3 -3 -5 -324 15 -1 -3 1 -S -1 -3 -? -3 -5 -1 -3 -1 -S -3 -5 -3 -1 -s -9-1 -? -? -? -9 -9 -3 -9 -3 -3 -3 -323 13 3 3 7 -I 5 1 3 3 -1 5 I 3 1 I 1 3 S 3 -3 -3 -3 -1 -I -I -3 -1 -1 1 3 1 -t

26 13 3 1 5 -3 3 -I -3 -3 -3 1 -1 1 -3 I -3 -1 -I -3 -? -? -? -3 -3 -5 -? -S -3 -1 -1 -$ -327 13 9 9 9 5 9 5 15 3 7 3 1 5 3 4 5 3 -3 -1 -1 1 -1 -3 -3 1 3 1 5 3 320 19 ? $ ? I ? 3 1 3 13 J 3 -1 1 -I 1 1 1 -3 -5 -3 -t -3 -3 -5 -1 -1 -1 1 -1 -3

29 13 ? 5 9 1 ? 3 3 1 3 7 3 1 3 1 3 3 3 -2 -3 -3 -1 -3 -3 -S -1 -1 -t 1 -1 130 13 S 5 7 -3 5 3 -1 I 1 3 I 3 -1 3 1 3 1 -1 -3 -5 -1 -1 -3 -5 -3 -3 -3 -3 -1 -3 -331 13 7 ? 13 3 S 3 5 9 ? 7 1 S 3 ? ? 5 1-1 1 3 1 3 1 3 5 5 5 3 332 13 3 3 5 -3 5 1-1 1 1 3 A 3 1 3 1 3 3 3 -3 -3 -1 -1 -1 -1 -3 1 11 1 I 1


43

I I I I 1 l-

FIGURE 44. Aerial Photo-Transparency (2).

VALs COEFFICIENTS Ii1 2 3 4 5 6 7 3 9 10 11 12 13 14 13 16 17 10 19 20 21 22 23 24 25 26 27 28 21 30 It 32

1 410 6 0 -6 -2 -2 -0 -4 -4 2 -2 -2 -4 0 -4 0 2 0 -2 -0 -4 -2 2 0 -4 2 2 6 0 2 02 -2 2 -2 2 -4 -4 -4 -0 -2 -4 -2 -4 -2 -4 -2 -4 -2 -2 -4 -4 -4 -2 -4 -4 -4 -4 -2 -4 -2 0 -2 -23 12 2 2 4 -2 -2 0 -4 -2 0 2 -2 0 -4 2 -4 -2 0 0 -4 -4 -4 -2 -2 -2 -4 0 -2 4 0 -2 04 0 2 4 4 2 a 2 2 4 2 4 22 0 2 4 2 22 -2 0 0 a -2 0 -22 0 2 2 05 102 a a 0 2 -4 2 2 a o a a a -a a * 0 aa-2 -2 -2 2-2 -2 -4 0 -2 o -2 0 -20 6 0 a a 0 22 -20 0 2 a 0 -2 0 -2 0 0 -2 -2 -4 -4 -4 -2 -4 -4 -2 -4 -2 -2 -2 -4

? I 0 0 4 0 2 2 -2 2 0 o 0 0 0 -4 22 0 -2 -2 -2 -2 -2 -2 o -2 0 0 0 -2S14 42 042-202 a0 204-22 2 2000200-22020009 1 2 2 2 0 2 2 06 0 1 2 2 2 2 2 0 2 2 2 0 0-2 0-2 0-4 0 0 2 2 0 0

10 10 2 4 4 2 4 2 0 2 2 4 2 2 0 2-2 2 2 2 0-2 0 2 2 0-2 2 0 2 0 2 0it 6 2 44 2 4 2-2 2 2 4 0 2 2 2 0 2 2 2 0-2-2 0 0 2 0 2 22 2 0012 0 2 2 4 2 2 2 0 2 2 2 0 2 0 2 -2 2 4 2 -2 -2 -20 -2 -2 -2 0 0 0 2 2 013 10 4 4 4 0 2 2 0 2 2 0 2 2 2 2 0 2 2 2 0-2 0 2 2 0-2 2 2 2 2 0 014 10 2 2 4 0 2 0 -2 0 0 2 0 0 0 0 -2 2 0 0 -4 -4 -4 -2 -4 -2 -4 0 -2 0 0 -2 -215 10 2 2 2 2 2 2 -2 2 2 2 0 0 0 2 -2a 2 0 -4 -2 -2 0 -2 -2 -4 0 -2 0 0 0 -21612 2 2 2 0 2 2 -4 0 -2 2 0 0 -2 0 -2 0 -2 -2 -4 -4 -2 -2 -2 -4 -6 -2 -4 -2 -4 -4 -4I7 0 4 0 0 4 4 4 2 6 2 0 2 4 2 4 2 6 4 4 0 0 2 2 0 0 0 2 2 2 2 2 01 110 4 40 2 4 222 2 62 42.62 4 24 0 0 2 22 202 22 2 0 219 1 2 2 4 2 2 2 0 2 2 4 4 2 2 4 0 4 2 2 0 0 0 2 0 2 2 4 2 2 2 2 220 12 2 4 4 2 4 2 0 2 2 4 2 2 4 4 0 4 4 6 2 0 2 4 2 2 0 4 2 4 4 4 421 6 2 2 2 0 00 -20 -2 2 0 2 0 0 -2 22 -2 -2 -2 -20 -20 -4 2 0 2 0 2 -222 6 2 0 2 0 0 0 -2 0 -2 2 -2 0 -2 0 -2 0 2 0 -4 -4 -2 -2 -2 -2 -2 0 0 0 0 0 -223 6 2 0 2 0 2 0 -2 -2 0 2 0 0 -2 0 -4 0 0 0 -4 -4 -4 -2 -2 -2 -2 -2 -2 0 0 -2 024 1 2 0 2 -2 0 -2 -4 -2 -2 0 -2 -2 -2 0 -4 0 -2 -2 -4 -4 -4 -2 -4 -4 -4 -2 -2 -2 -2 -2 -225 10 2 4 2 0 4 2 0 2 4 4 2 2 2 2 0 2 2 2 0 0 0 0 0 2-2 2 2 2 2 2 226 6 -2 2 2 0 0 0 -2 t 0 2 0 -2 -2 0 -2 0 0 0 -4 -4 -2 -2 -2 -2 -4 0 -2 0 -2 0 -22? 6 4 24 2 2 4 04 2 4 2 22 2 2 2 2 2 0-2 0 2 0 0-2 4 2 2 2 2 021 0 2 2 2 0 0 2 -2 0 0 2 0 0 -2 0 -4 2 0 0 -2 -2 -2 2 -2 -2 4 -2 0 0 0 0 -229 0 0 2 2-2 2 0-2 0 0 2 0 2-2 2-2 2 0 2-2-4-2 2-2 0-2 0 0 0 0-2-230 6 -2 0 2 -4 0 -2 -4 -2 -2 0 -2 -2 -2 -2 -4 -2 -2 0 -4 -4 -4 -2 -4 -4 -4 0 -2 0 -2 -2 -231 4 0 2 2 0 2 0 -2 0 0 2 0 2 0 0 0 2 0 0 -2 -2 -2 * 0 0 -22 0 2 2 2 022 0 0 0 -2 -2 -2 -0 -4 -4 0 -2 -2 -4 -2 -4 -2 -2 -2 -4 -4 -4 -2 -4 -4 -4 0 -2 -2 -4 -2 -2


44


NiLS COEFFICIENTS

I 2 3 4 3 6 7 9 9 10 Ii 12 13 14 15 16 17 18 19 24 21 22 23 24 25 26 2? 20 21 30 31 32

199 7 -5 15-23 -1 -5-1 -I -3 9 -3-11 -1 -3 -7 1 -3 1 -9 -9 -5 -3 1 -1-131 I 1 -IS -Ia21 t 1 3 -3 I -1 -9 -3 -3 -1 -1 -5 -3 -5 -9 -3 -1 -3 -9-.I -5 -7 -9 -7 -9 -7 -? -3 -3 -? -33 -1 5-11 13 -? 7 -1 -3 9 5 13 5 -1 5 -1 3 3 3 3 -3 1 3 3 3 3 t 3 I 3 -1 -14 23 13 13 15 9 13 13 7 9 II 13 II It 9 9 5 9 11 9 3 3 ? 7 ? ? 7 9 7 ? It ? 7

9 9 -1 11 1 9 3 -3 ? i1 3 1 5 3 -1 5 3 -1 -I 1 1 3 -1 -1 3 3 1 3 -i 121 7 3 It I ? 3 -3 3 3 5 1 3 1 I -3 1 1 -1 -5 -5 -1 -3 -3 -5 -5 -3 -3 -5 -1 -1 -3

713 I 3 15 3 13 3 3 It 915 7 3 ? 7 1 ? 7 5 I -1 3 3 3 1 -1 3 3 -1 3 -1 3S19 11 757 1 13 9 S It 9 1511 t 7 9 S 11 9 ? 3 3 5 5 5 1 5 5 3 7 1 39 25 ? 11 13 It It 5 7 I1 13 9 9 7 It 3 9 9 9 3 1 3 ? 5 5 3 7 7 5 9 S S

t0 1911 t Is 5 13 9 5 I1 1113 11 I 9 It ? 11 11 9 ? 5 7 9 9 9 ? 1111 t13 ?II 23 9 91 S 11 5 -1 5 7 T 5 5 9 I 9 9 r I -1 S 3 3 I ? 5 5 9 7 712 1? 5 ? 11 1 ? 3 -1 3 5 7 5 1 3 3 I 5 3 3 -1 1 I 3 3 1 -1 5 3 3 5 1 313 95 3 1 II I 1 3 1 7 7 9 5 3 5 3 1 5 ? 1 1 3 3 3 3 7 S 3 7 3 314 1? 3 3 3 -3 5 1 -5 1 1 5 I I -1 -1 -3 I -1 -1 -5 -7 -3 -3 -t -3 -3 -1 -1 -1 -1 -3 -3Is 9 -I -5 3 -? -1 -3 -9 -1 -1 3 -I -3 -3 -s -s -I -1 -5 -9-11 - -7 -s -5 -7 -3 -5 -5 -3 -? -514 57 -I -3 -I -9 -t -3-13 - -5 -3 -5 -? -? -S -9 -s -s -?-13-13-11 -9 -9-11-13 -7 -7 -9 -9-11 -917 IS ? 5 13 3 9 3 -I ? 3 9 5 5 1 -1 ? 7 3 -1 -1 1 1 1 I -I I 3 1 5 I 1I0 13 3 3 ? I 7 5 -I 5 5 9 3 3 3 3 -I 5 3 3 -3 -3 -I 3 1 -I -3 1 I -1 1 -1 I19 II 5 I ? -I 2 3 -3 3 3 9 5 I 3 3 -I 5 3 I -3 -3 1 I -3 -1 -3 1I I 3 -3 I20 II 3 1 9 -I 7 I -I 5 7 9 1 3 S 5 1 5 3 3-3 -1 3 3 3 1 I 5 5 3 5 1 321 9 -I -3 I -? I -3 -9 -3 -1 -I -3 -3 -5 -3 -s -1 -3 -1 -? -9 -? -? -5 -5 -7 -3 -3 -3 -1 -5 -522 II -I -1 -I -? -I -3 -9 -5 -5 -3 -3 -5 -5 -3 -9 -3 -3 -5 -9 -9 -s -3 -? -? -9 -3 -5 -3 -1 -5 -523 7 -3 -3 -I-I -3 -3-11 -7 -5 -5 -7 -9 -9 -9-It -7 -7 -?-It-1t -9 -7 -9 -9-13 -7 -9 -7 -s -9 -?24 13 -3 -3 -3 -9 -3 -7-13 -7 -9 -5 -9 -9 -9 -9-13 -9 -? -9-13-S-It -1-13-13-13-11-11-11 -?-11-Il23 13 i 3 3 -3 I I -7 -1 -1 I -3 -3 -5 -1 -? -3 -1 -5 -7-11 -7 -7 -7 -7-It -? -7 -7 -5 -3 -726 13 -1 -3 I -7 -1 -3 -9 -3 -3 -1 -3 -5 -? -3 -9 -3 -3 -9-13-13 -9-1-II-Il -9-It -9 -7-IIl2? 13 5 7 F 1 5 3 -5 1 I 5 1 -3 -I I -5 1 I 1 -5 -7 -3 -3 -5 -5 -7 -3 -3 -5 -1 -? --25 IS 3 1 5 -3 3 -I -5 -1 -3 3 -3 -3 -3 -3 -5 -1 -1 -3 -7 -9 -5 -3 -3 -5 -9 -? -3 -7 -3 -? -529 S -I -3 I -? 3 -3 -? -3 -3 1 -3 -5 -3 -3 -9 -3 -5 -5 -?-It -7 -Y -7 -7 -9 -3 -7-li -5 -9 -730 9 -3 -5 1 -9 -1 -3 -9 -3 -3 -t -3 -5 -5 -5 -9 -s -3 -?-11-1I -7 -? -7 -?-I1 -7 -? -9 -5-11 -931 3 5 -1 5 -3 5 -1 -S I 3 ? I -I -1 -1 -3 3 1 1 -5 -5 -3 -1 -3 -3 -5 -I -1 -3 -1 -5 -332 13 1 -1 3 -1 I -3 -7 -3 -3 I -I -3 -5 -3 -? -3 -3 -5 -9 -9 -? -1 -3 -7 -9 -3 -3 -7 -3 -9 -5


45

-7 Aow


WALS COEFFICIENTS

1 2 3 4 3 6 7 S 9 10 11 12 13 14 15 16 1 18 19 20 21 22 23 24 25 26 2? 20 29 30 31 32

1 52 -4-10 -6 -2 6 4 0 2 6 6 6 0 2 2 0 2 4 0 0-4 0 0 4 2 - 2 4 4 -2 -2 02 6-2040 220220 *0 0 0 -2-2-2-2-2 -4-2-222-2-23 1 4 2 6 0 6 6 2 2 4 6 2 2 6 4 2 4 4 4-2-2 2 4 2 2 0 4 2 0 4 2 24 16 6 8 4 9 4 4 6 8 6 4 6 14 6 1 8 2 2 4 6 4 4 4 6 6 4 6 6 6S62262 620024422404240022420242222S 6 0 0 2 -2 4 0 -2 2 0 2 0 -2 0 2 2 -4 2 -2 0 2 0

7 42240 44002400 20 222-2-4000-20 202005 .224062020422220242-2-2202-2-22200200 .2240 2002 220220 2200-20000-222000-2

10 64262 42244424402420-202200222202

II 62240422244202202420-22000-220222012 2240 42002222240242-2-2020-2-222020013 6 2 2 6 2 0 0 2 2 4 2 2 4 0 4 4 2 0 2 02 2 2 0 0 2 2 0 2 0 01 4 -2 -2 0 -4 0-2 -2 -2 2 -2 -2 -2 2-2 0 4-2 0-4-4-2 0-2 -2 -2-2 - 2 -2 -2-21 2 -2 -4 0 -4 -2 -2 -2-2 0-2 -2 -2 0 -2 -20 -2 -4 4 2 -2 2 4 -4 -2 2 -2 0-2 216 -4 -4 4 - 6 -2 -4 -6 -6 -6 -2 -4 -6 -4 -2 -6 -4 -4 4 -6 - 2 -6 -6 -4 -6 -6 -6 -2 -4 -4 -6 -61? 4 -2 2 0 -4 -2 -2 2 -2 0 -2 2 2 0 -4 -2 2 0 -2 -2 0 -2 0 0 0 -2is 0 -2 0 -2 0 -2 -2 0 0 -2 -2 2 -2 -2 * -2 -4 -6 -2 -2 -2 -4 -4 -2 -2 -2 -2 -2 -21 4 0 -2 -2 2 0 -2 -2 0 0 -2 -2 -2 -2 -4 -2 -2 -2-4 -6 -2 -2 -4 -4 -6 -2 -2 -4 -2 -2 -220 2 4 -2 2 2 0 -2 0 2 0-2 0 2 -2 0 -2 -4 -4 -2 -2 -2 4 -2 -2 -2 -2 -22 0 -2 0-4 -2 -4-4-2 0 -2 2-2 -2 - 2 2 0 4 --6 -4 -2-6 -6 -4 -4 -6 -4 -6 -422 4 -2 0-4 2 0 -2 -2 -2 2-2 -2 -2 -4 -2 0 -2 -4 6-2 -2 -4 -4 -4 -2 -4 -2 -4 -223 -2 -2 0-4 2 0 -4-2 - 2 0 -2 -2 -4 -2 -4 -2-2-2-4-6-2 -4 -2 6 -6 -4 -2 -2 -2 4 -224 4-2 -2 0 -2 -2 -4 -2 -2 0 -2 -4 -4 -2 -4 -4 -2 -2 -6 - -2 -4 -4 -4 -4 -2 -4 -4 -4 -4 -623 6 2 2 4 04 4 -2 0 2 2 0 0 2 0 2 2 0 -2 -2 40 0 0 -2 0 0 2 0 026 -2 -2 0 -2 0 -2 -2 0 2 -2 -2 -2 -2 -2 -2 0 -2 -4 -6 -2 -2 -2 -4 -4 -2 -2 -2 -2 -2 -2

27 2 2 4 04 2 2 2 2 2 2 0 0 2 2 2 4 2-2 -4 0 40 0-2 40 2 -2 2-2 028 2 0 2 0 4 2 -2 -2 2 0 -2 0 0 -2 0 2 -2 -4 -4 0 -2 -2 -4 -2 -2 - 2 0 4 -223 5 2 2 4 4 -2 0 0 0 2 0 0 2 0 - 2 0 0 0 - -4-2 -2 -2 -2 -230 S 2 40 2 -2 4 2 -2 0 0 4 -2 -2 0 -4 -2 -2 -2 -4 -6-2-2-2- -4 -4 -2 -4 -2 -4 -2

3 6 6 4 0 4 4 2 4 4 4 2 4 2 4 2 4 4 4 0 -2 2 0 0-2-2 2 2 0 2 0 032 30 2 4 4 2 4 0 2 2 4 2 2 2 2 0 0 2 0 -2 -4 -2 0 0 -2 -2 0 0 -2 0 -2 -2


46

FIGURE 50. Target Representing Wal (1, x) Wal (0. y).

VAL% COEFFICIEI'fs

t 2 3 4 3 6 1 0 9 t0 It 12 33 14 1S 16 1? IS 19 20 21 22 23 24 25 26 2? 26 29 30 31 32

1 04 -4-16-36--40-32-34-26-24-16-14-20-22-16-10 -S -- 4-14-18-20-10-la-14-16 2 -2 0 2 2 0Sis 1to a 4 0 -6 -a -s a -4 4 0 -2 -6 0 -6 4 -4 -2 -1 -4-10 -2 -6 -4-10 0 -4 0 -2 -2 -4

3 2i 12 14 10 6 0 4 -4 6 2 10 2 4 0 4 -a 10 6 4 -4 -2 -4 a -2 0 -6 0 * 6 0 8 04 24 10 16 16 12 2 8 2 12 1 16 10 8 6 10 4 14 6 1 0 6 -2 S 2 4 -2 10 4 10 6 3 45 22 10 12 0 0 4 6 -2 0 4 14 48 0 0 12 4 4 -4 0 -4 4 -2 0 -6 6 a 4 2 4 06 26 12 10 I0 4 2 2 -2 6 2 10 4 4 2 6 0 S 4 2 -4 -2 -4 a -4 0 -' 0 0 2 0 4 -27 aa 12 12 12 10 4 4 0 8 4 12 8 10 6 8 a 14 8 1 0 4 -2 4 0 4 -4 10 2 6 6 S 26 22 t0 12 10 6 4 6 -2 6 4 14 6 * a 6 0 12 6 1 2 4 -2 S 2 4 -2 10 4 S 6 10 49 22 6 10 6 4 2 2 -2 6 4 12 6 6 2 I 6 4 2 0 6 2 2 -4 12 4 S 6 12 410 22 10 12 12 10 4 4 -2 8 2 12 6 10 4 6 2 14 4 6 0 4 -2 4 -2 6 -2 32 6 12 3 12 4It 20 If 10 6 6 0 4 -4 6 6 30 4 6 -a 6 -2 6 4 4 0 0 -6 4 -2 0 -4 2 6 4 0 012 22 4 10 4 4 4 2 -6 4 0 3 2 4 0 4 -2 6 a -2 0 -6 4 -4 4 -4 1 0 4 0 6 -213 1O I I 10 G 4 2 -2 8 2 12 4 6 2 6 0 If 4 6 -2 2 -6 4 -a a -4 6 2 6 4 8 214 a. 1 6 a -a 0 -6 2 -a 0 0 2 -4 a -a 4 0 0 -4 -2 -6 0 -6 -4 -6 2 -a a * a -aIS 13 6 4 2 a -2 -2 -5 a -a 6 0 0 -4 0 -6 4 4 6 -6 -6-10 4 -6 -4-10 a -4 0 -2 a -416 2, 4 a 0 -4 -6 -0-10 -4 -s a -4 6 -I -2-10 2 -6 -4-12 -8-12 -4-12 -s-t0 -2 -8 -2 -4 0 -g1? 346 14 6 6 -2 0 -6 4 -2 t0 0 a -a 4 -2 1 2 2 -4 4 -6 2 -4 0 -0 4 -2 2 2 6 -21 16 4 6 4 a 4 4 -6 4 0 6 4 2 -2 2 -2 6 2 2 -4 -2 -8 a -4 -2 -6 6 6 4 0 4 -219 14 4 2 2 0 -4 -4 -0 a -2 6 -2 2 -4 a - 6 0 -6 -4 -6 4 -2 6 4 -2 2 2 2 -220 14 2 6 4 0 -4 -2 -1 2 -6 6 0 2 -4 2 -4 4 4 2 -6 -2 -6 A -4 -2 -8 & -1 6 2 4 -221 34 2 2 0 -4 -8 -6-12 -4 -, 0 -4 -4 -0 -2-14 # -4 -4-10 -6-12 -4-10 -6-12a -6 -2 -4 -2 -622 12 a -2 -a -6 -6-12 -6 4 -6 -4 -8 -4-12 0 -6 -4-12 -- 12 -4-16 -- 12 -2 -8 -4 -4 -2 -523 12 2 4 0 -2 -8 -6-12 -4 -5 a -4 -4 -0 -4-10 0 -6-12-10-14 -6-12 -6-14 -2 -0 -4 -4 -2-1024 16 & 4 -2 -4 -6 -6-10 -6 -8 -2 -6 -6 -1 -2-10 -6 -4-12-10-16 -6-14 -0-16 -4-14 -6 -$ -4-10IS 14 4 6 6 4 -2 4 -4 4 -2 1 0 4 -4 I -4 4 0 2 -4 -4 -g 6 -6 -4 -s a -4 -2 -2 4 -626 10 4 4 6 2 -6 -2 -0 0 -4 4 -1 * -6 -2 -6 2 -4 -4-10 -6-12 -2-10 -4-10 2 -6 0 -4 -2-102? 1 6 I 6 & 2 -4 4 4 14 2 4 4 6 -2 4 2 4 -6 -2 -s 2 -4 0 -4 6 4 4 0 4 020 16 6 6 4 2 -2 -2 -6 2 -2 6 -2 2 -4 2 -4 4 0 0 -6 -4 -8 4 -6 -4-10 1 -4 0 -2 2 -419 16 i 4 1 0 -4 -2 -8 * -5 6 0 2 -4 -2 -4 2 -2 2 -4 -4 -1 0 -6 -4-14 5 -4 4 -4 6 -4S0 16 4 2 0 -4 -4 -0 0 -6 4 4-4 -2 - 0 -6 2 -4 0-6-12-4-6-1a 0-4-2 -4 -2 -6

It 16 6 6 0 0 -4 4 -2 6 0 2 0 4 -4 6 2 4 -4 -4 -6 2 -2 -a -0 4 0 A 1 4 -22 316 4 6 4 0 - -4-62-4 4 -2 -2 -6 2 -6 - - -4-10 - -6 -4-13 5 -6 4 -4 0 -6 4


47

FIGURE 52. Target Representing Complement ofWal (I, x) Wal (0, y).

SILO COIFFIC3INTS

3 2 3 4 5 6 7 8 9 16 I1 12 13 14 13 16 1? 1619 20 21 22 23 24 2 26 27? 28 29 30 31 32

1 $1-71 3 24 312 34 30 to 14 16 146 0 0 12 16 4 6 4 12 4 0 6 -2 6 12 -6 -4 0 4 -4 -4 -2a 4 -1 -4 a -8 6 -4 -4 -6 -2 -6 -6 -8 -2 -6 -4-t0 -4 -6 -0-12 -4-10 -6 -S -6-14 -6-10 -4-14 -42 S -6 0 6 -4 t0 4 a * a 0 0 -2 0 -2 -4 2 -2 -4 -e a -6 -2 -2 -2 -8 -2 -6 0 -S -44 012 410 0146 0 666 4 44 a 460-26 0 2 6-2 *04-4 23 4 2 0 0 -4 12 4 2 0 4 a 4 a 4 2 0 -a 4 2 0 -6 4 -4 a -4 2 -6 2 -4 2 -6 06 * -4 -2 4 -6 10 2 . -2 a -2 0 -4 2 -a -4 -4 * 0 -4 -o6 -6 -4 -2 -2 -8 -2 -4 -2 -0 -27 4 -2 -2 4 -4 10 4 a 6 1 0 4 0 0 2 -2 -2 0 2 -2 -6 4 -4 2 -2 0 -4 -2 -4 2 -6 009 0 2 0 510 -4 It 4 2 4 4 4 0 4 2 0 -2 4 2 0 -6 4 -2 4 0 2 -4 2 -2 4 -4 29, 10 0 0 -2 12 4 4 0 4 0 4 0 4 2 0 -2 4 2 0 -4 4 -2 0 0 0 -4 2 -4 4 -4 2

t0 0 6 2 12 -2 84 0 6 4 4 4 6 4 4 6 0 40 4 4 -4 0 -2 6 2 4 -4 4 -2 6 -4 433 1 2 2 It -2 12 6 4 2 6 2 4 0 6 2 2 -2 4 2 2 -4 6 -2 4 2 2 -4 2 -2 2 -4 212 10 4 2 0 -4 14 4 4 0 6 2 2 0 4 4 -2 -2 4 0 2 -6 4 -2 2 0 2 -4 0 -2 2 -4 013 O 10 4 14 2 16 0 646 0 6 6 4 4 4 0 46 4 4 -2 0 -2 6 0 4 -4 4 -2 6 -4 44 14 0 2 -4 12 6 4 S 4 2 4 0 4 2 # -2 Sa2 -a -6 2 -2 2 -2 -2 -6 -2 -4 0 -8 -2

IS 10 -2 -2 6 -6 10 4 2 0 4 0 2 0 2 2 -2 -2 2 0 -2 -6 2 4 0 -2 0 -6 -2 -6 0 -6 S64 30 -6 -4 2 -8 4 0 -2 -2 0 -2 -2 -4 0 -2 -4 -4 0 -4 -4-10 4 -8 -2 -6 -4 -8 -2 -6 -2-10 -4

17 0 4 2 0-214 6 6 2 S 4 4 4 6 4 4 2 66 4 0 0 6 4 4 4 4 2 0 06If S 2 2 0-212 6 4 2 4 2 4 2 4 4 0 2 4 4 2-4 0 6 2 4-2 4 0 46-2 419 6 0 -2 0 -4 12 4 2 0 4 0 2 0 4 2 -2 -2 4 0 0 -6 6 -2 4 0 4 -4 4 -2 4 -4 120 6 # 2 12 -2 12 4 4 2 6 2 6 2 6 4 4 0 6 4 2 -4 6 -2 4 4 4 -2 4 -2 0 -2 6as 6 -a 4 4 -S 1 0 -2 -4 0 -2 -2 -4 0 -2 -2 -6 0 0 -4-10 0 -6 -2 -4 -2 -6 -2 -6 -2 -8 022 6 -2 -4 4 -6 1 0 # -2 2 -4 -2 -4 0 -4 -2 -6 0 -2 -4 -S 2 -6 -2 -4 -2 -0 -4 -0 -2 -4 -a13 4 -4 -64 4 -0 00 -2 -4 2 -2 -2 -4 -2 -2 -4 -6 -2 -2 -4 -9 0 -8 0 -4 -2-Is -4 -1 0-15 -424 6 -6-6 4 -0 4 0 -4 -4 -2--4 -4 -6-2-4 -4 - -40-4 -6-12 - -4 -6-4411 -6 -8 -2-10 -41 0 4 2 1 -0 12 4 4 0 4 2 4 0 4 6 2 -2 4 2 0 -4 4 -4 4 0 2 -4 2 -2 4 -4 2

24 6 -4 -4 4 -6 0 2 0 -4 0 -2 -2 -4 -2 -a -4 -' 0 0 -4 -8 2 -0 0 -4 -2-10 -4 -4 0 -8 -22? 4 4 0 4 -4 0 4 4 0 4 4 4 0 4 4 4 2 6 2 2 -4 4 -2 4 0 4 -2 2 -a 4 -4 220 6 -2 -4 4 -0 8 -2 -2 -4 0 -2 -2 -2 2 -2 -4 -4 2 0 -4 -6 2 -4 2 -2 0 -4 -2 -4 2 -6 209 1 -2 -4 2 -0 4 -2 -4 -6 -4 -4 -2 -4 -2 -4 -4 -6 -2 -4 -4 -0 # -6 -2 -4 0-10 -4 -4 2 -4 -230 a -6 -4 0-10 2 -4 -4 -9 -4 -6 -4 -s -4 -6 -0-10 -6 -6 -4-12 -2-10 -4 -0 -4-10 -0 -0 -2-1 -423 0 4 -2 4 -6 0 2 0 -4 2 -2 -2 -2 0 -2 -4 -6 -2 -2 -4-14 0 -64 -4 -2 -4 -2 -8 0 -8 -232 4 -4 -4 2-10 4 4 -2 -6 -2 -a -4 -4 -2 -6 -6 -0 -4 -6 -1-12 -2-10 -4 -S -4-10 -64-3 -4-32 -6


48

70'W,

FIGURE 54. Target Representing Wal (0, x) Wal (1, y).

N*LS COEFFICIENTS

1 2 3 4 5 6 ? I I t, It 12 13 14 i 1, 17 1, 19 20 21 22 23 2' 25 26 27 2, 29 30 3z 32

1 57 3 -3 -1-15 -3 -3-IS ? -5 -1 -7 -7 -? -3-1 -1 -3 -1 -9-13 -7 -7 -7 -3-13 -3 -3 1 - 1-3 -3a 109 a 31 ?-It -I I-1l -3 -s 3 -5 -5 -5 - 1 -9 1 -3 -3 -9 -9 -9 -7T -5 -5-11 -5 -3 - 1 -3 -5 -33 9 9 I 711 3 9 1 a 3 9 1 9 1? 7 9 51 11 3 5 7 ? 5 9 5 7 9 7 54 5 91aa3 ? 11w 9 9 ? 9 9 ? 9 9 11 11 9 $ 3 9 7 7 3 9 7 711 ?

3 1 1 3-1 -1 31 1 13 1 1 -1 3 ! 3 -3 -a -I I -I - I I I I1-Ia6 -5 -I -1 1 -3 i - -1 - 1 - I I -I - I 1I -3 a 1 1 -5 -5 -3 -3 -a -3 -3 1 -i -i I 1 -a

3 1

1 5 1 3 1 -3 1 1 3 1 1 1 1 1 3 3 -I-Ia 11 I I 11 1 3 1 3-I 3 l 1 3 3 - I 1 I 3 I -I a 1 l 3 I I -3 -3 1 - - I -I I I 1 3 -1 3

9 3 9 1 5 55 -1 3 3 5 1 3 3 1 1 3 3--31-111 1 3 11 3 1 3I 1 35917 5 1533 333-a 1 3 3--11-I-I-11-3-I-I-11 -11A1 7 3 5 9 1 ? 1 -a 3 3 5 1 3 1 1 1 3 1 I -5 -s -3 -3 - 1 -5 - -3 I -i -a12 1191 73-1 I33 1 3 J *1 1 1 -3- -a-I-3 I-3- - -1 1 -I-I131 ? 3 3 ? 3 ? 3 1I 9 a 5 3 a 1 3 -a 1 3 -a -3 -3 - I 1-3 1I -3 1i -3 1i I -3 -314 -1 3 1 3 1 I I 1 1 3 1 1 1 a I I I 1 1 -3 -3 -3 1 -3 1-I 3 - -3 -1 1 -I-Is 3 -? -5 -3-It -$ -7-il -? -9 -3 -9 -Y -9 -7-11 -7 9 -7-ia"a3-i1-ii--13-11-i1-1i -7-i-ia16 -i -7 -3 -3-i -7 -?-it -? -? - -7 -7 -9 -9-i -9 -? -I3"- -ti -9-13 -7-i-l -9 -9-ilI?

7 ? 1 7

-1 3 3 3 3 3 1 5 1 5 1 3 - -3 l l I a a 1 3 1 1Is a S 7 I 7 3 -i 3 3 5 I 3 I 3 -3 3 3 3 -1 -1 1 a -1 -I -I I t -3 3 -1 I19 777 9 3? 3 3 3? S351 3?31-13111 11 331124 l 11 9 13 3 11 3 $ 7 9 5 5 5 5 3 3 1 -t 1 1 1 -1 3 3 335 1 32i 7 3 1 5 -3 3 I -3 -i -1 o1 -3 -3 -5 -3 -7 -3 -3 -3 -?-It -7 -? -7 -? -9 -5 -7 -7 -3 -? -733 1 3 3 5 -3 3 -i -S -a -3 1 -1 -1 -1 -1 -3 -3 -1 -3 -9 - *? -? -s -? -? -s - -5 -s -? -23 ? 1a 3 - 3 -3 -3 -3 -1 -1 -3 -5 -3 -3 -5 -3 -3 -3 -? 9 -7 -s -*?-i -s -1 -? -5 -7 -724 i I -3 a -7 1 -3 -S -i -3 -1 -3 -j -5 -3 -7 -3 -S -3 -9 -7 -7 -7 -? -5 -5 -5 -5 -? -725 935 a ? 5-13 1 3 ? a 35a1i -1311113 1333326 I 3 3 9 -1 3 -I I I 3 1 a -a I -I I 3 a -3 -3 -a a -a -I -3 3 1 3 3 1 127 7 9373a?37p573 a1 513-11131i13 37 328 3 F ? 7 I 9 1 1 3 3 ? 3 1 3 5 1 3 3 3 1 I I -1 1 3 I 3 7 3 1t9 7 -I 13 -S I 1 -s -1 -I 1 -I -a -3 -3 -s -i -3 -a -F -7 -s -s -$ -7 -s -3 -- -I -3 -33 -3 I -a I -s -I -S -? -3 -3 I -3 - -s - -7 -1 -3 -i -9 -9 -7 -5 - -S -s - -? -i -7 -531 3 3 3 ? 1 3 I -3 I - * 1 -I i -a 1 -i I I I -3 -5 -3 -i -3 -3 -3 -3 -I -1 I -I -132 I 3 3 9 -I 1 I -I -I 3 S I I I 3 -I I i i -3 -5 -3 1 -3 -3 -I -1 -3 -i I -1 -3


49

11-• '-..... . .. I U I I -

FIGURE 56. Target Representing Complement ofWal (0, x) Wal (1, y).

SOLO COEFFICZItI

1 2 2 4 3 6 7 1 9 30 11 2 13 14 15 16 17 if 19 20 21 22 23 24 25 26 27 28 29 30 31 32

t I S -1 -9 3 3 -9 -1 -1 1 1 1 1 3 -3 S 1 1 -1 -7 -1 -1 5 3 -5 3 3 9 3 32 -1 -3 -S 1 1 -1 1 -1 -1 -1 1 -1 -1 -I -1 -3 -1 -I -3 -5 -3 - -35 -5 -1 -3 -S -? -3 -3 -s2 at I 1 -7 -3 -S -3 -3 -I -3 -3 -S -1 -9 -1 -3 -3 -9 -1 -s -s -7 -? -, -S -3 -S -3 -3 -S4 23 9 1 7 9 5 I ? S 9 S5 3 a7 3 7 ? 5 3-1 3 3 31 1 3 3 3 7 353 IS 5 5 7 1 7 5 3 3 S 7 3 3 5 1 S 3 3-t-I I 1 1-1 5 3 3 3 116 29 -11 5 -3 3 -1 -5 -I -1 3 - I -1 1 -5 1 -I -3 - 7 -3 -3 -3 -3 -S -I -I -I -I -I -I7 11 1 1 2 -23 11 -3 - -I 3 - I1 -3 1 - 1 I -1 -S -3 -3 -1 1 -3 - - -1 -3 -31 23 1 1 2 -2 3 -1 -5 1 -15 3 -3 -1 -3 1 1 1 -3 -7 -3 -1 - -3 1 I 1 3 1 1S13 - 1 -5 -3 -3 -7 -2 -7 -1 -$ -5? -3 -7 -3 -11 - -,I -I - ? ?-? -5 -? -3 -1 -3 -3 -S

10 21 5 I F -3 3 1 -3 1 1 5 1 -3 -3 I -3 1 - I -S -3 -1 -I -3 -3 -5 -1 - 3 3 -I -31 17 3 3 -3 3 -S -1 -3 1 - -I -3 -I -s -I - -3 -S -9 -s -s -3 -5 -7 -3 - -3 -1 -3 -3

32 33 3 3S -3 ;- -3 -t -3 1 - -3 -3 -3 -7 -3 -3 -3 -7 -9 - -s -7 -7 -s -S -s -s -- -7

II 5 ? 3 I S 7 S S 3 5 3 - - I -- t -I-I I t 1 3 1 114 25 -1 1 -7 -3 -7 -3 -3 I -S -3 -5 -3 -7 -3 -" -3 -9 -9 -7 -3 P -9 -9 -9 -7 -7 -1 -7 -7IS is 5 ? S 3 2 3 S 3 -I 3 11 -I I I I *II -I I1 3 1 "16 23 3 1 1 -s 1 -3 -7 -3 -3 I -3 -3 -S -3 -S -I -1 -3 -7 -9 -7 - -7 -? -9 -3 -3 -3 -3 -7 -317 17 3 13 -1 3 1 -3 1 5 - -I -S 1 1 I -3 -S -3 -3 -3 -S -S -3 -I I -I -I13 23 3 3 5-1 3 1 -I 1 3 I I1 - - -3 I -I -I -3 -7 -3 -3 -3 -3 -S3 -3 -II -I -339 13 3 3 3 -S 3 -1 -S -3 -1 1 -3 - -3 -1 -S -1 -3 I -7 -? -S -3 -3 -5 -9 -3 -3 -3 -3 -$ -320 23 3 3 1 1 7 5 -1 3 3 S 3 3 1 3 -1 3 1 3 -3 - -3 I I -I -I I I -I 3 -I Ii3 23 ? I 9 3 3 3 -3 1-1 3 1 1 1 3 -3 3 -1 -3 -S -3 -3 -3 -3 -3 - I - I -I -I -122 27 ? 7 9 1 7 1 -l - 35 3 1 3 3 -a 3 I -3 -3 -3 1 - - 1 -3 - - - - -33323 11 1 33 3 11 5 t ? 3 7 3 3 3 S - S 3 3 1- - I -I II - I - 1-1 31 -3 -134 29 7 1 9 3 3 3 1 1 3 9 3 3 1 3 3 3 3 1 - -I - -3 -1 -3 -3 -1 -1 -3 1 1 -I21 21 91313 531 7 21 ? 7 II I7? 7 3 ? 7 ? 1 3 1 7 5 1 37 5 5 33 326 25 3 1 ? -3 3 -IS 3I - 3 -3 -I -3 3 -3 3 1 1 - - - -3 -3 - -I - 1 - I 1 1 -32? 19 9 9 ) 3 7 7 1 1 1 9 3 ? 71 7 3 ? I 3 2 3 1 5 3 S 7 S20 23 I 3 3 - I I - -l 1 3 -I -I - I - S - 3 -1 -S -5 -5 -3 -3 -3 -3 -II -l 1-1 -3 -129 135 1 9 1 1 3 -m I 3 5 3 3 3 3 13 U5 J I -3 -I - I -I I -I S 3 3 1 3 130 23 1 1 "-33 I -3 -I 3 -I -1 -3 -S - -1 - - -S -3 -3 -3 -3 -S -3 -1 -3 -1 -3 -531 3 ? ? 7 V 3 5 3 1 5 5 7 5 3 1 5 13 1 -- 3 I I 3 1-1 3 3 3 3 132 23 3 3 -S 1 -3 -P -3 - -3 -3 -3 -I -I -7 -- -3 -3 - -7 -7 - ? -? -8 - ?--s -3 -3 -S -3


so

-saw- x MISS a -

//-


SALS COEFFICIETS

1 2 3 4 5 6 ? 1 9 10 It 12 13 14 is 16 171 s 19 20 21 22 23 24 25 26 2 5 2s 29 30 31 32

I 55 35 21313-15 3 9-13 - 3 9 -? -3 3 7 -1 3 3 7 1 -3 -5 - ? 7 -! - : -I ? 7 132 39 i 5 s -I S -I -3 -l 5 2 3 -3 1 -1 1 1 -1 -5 -3 -t -7 - 5 3 -53 23 7 3 -3 9 3 5 9 5 9 5 33 5-1 3 5 3-1 7 7 9 3 94 9 13 9 3 2 13 5 9 33 7 3 9 3 ; 7 31 7 3 5 9 5 : 11 9 9 13 13

9 75 1-3? 1 3 ? 1 3 -15 3 7 13 -31 3 -35 9 76 ~ 9 33 t-$ 5 -l -3 1 3 1 3-t - I-3 t 1 - 33-3 I -3 -t -,-5 -1-3 -,-l 3 5 - 3

7 15 3 13 - -1 1 1 3 3 3 -3 1 -7 -1 3 9 -7 1 5 -35 39 7 13 -3 31 3 - 3 7 1 3 S 1 3 3 5 3 5 -3 I -3 1 3 I3 - 1 5 7 79 39 7 1 3 -3 7 I -3 3 5 1 3 9 -3 3 3 -I 3 -3 - -: I 3 5 ? -: 5

30 17 9 -I 9 3 5 9 9 3 3 9 ; 3 3 -- 5 5 7 7-I 39 1 5 t3 -3 7 - I -3 3 5 3 3 5 -3 3 1 5 3 1 3 -3 1 3 _ 5 1 5 5 3 _1 312 t17 5 5 13 -3 5 1 -3: 3 3 -31 3 3 1 -3 3 1 3 - 3 1 -5 -3 1 -1 -7 1 3 7 -31 5Ii ii i I- - 3 5 - 3 3 - -3-33- -- l li--l- 5 -I-1 1- 1 5 - 3 5

34 3--3 -3 3 - 5 - -3 -3 -51 -3 -53 -7 -3 - , - -5 _3 -- ; -7 s- 531 -3, -1 -?15 9 -3 -7 1 - 311 - 13 - 1 -3 -, - ? -7 -9 -9 - - -9 - -i- -I - -3 -3 -9 ?114 13 -5 -9 3-1 3 -?-13-2-13 -7-13 -9-13 -- -i- ------- -- I- - - --

7 1 - - -1- -1 - 1 - 3 -33 -9 :-3- 1 - 3 -- - 9 -1 -- 3-:- 3 -- 3 - 7

1 11 1 1 5 -7 1 - -S*3 - *I -:?-:-1- - - S -5 -7 -S - 11 - -5 -5- I 3- 7-5 - 1- 9 - 3

1: 13 3 1 9 -? 3 -3 - -3 1 -5 1 -3 -1 -- 3 -5 -I - - -7 -- 11-7 1 -7-1: - -3 -1- -9 -1

20 37? 7 31 9 -3 ? : 31 : 3 5 1 1 3 :3 :3 :3 3 -33 - .- 9 :3 :; -3 -9 1 -? I21 3 3 3-?-9 1 57 33735197?-3-?5--7 11 97?7-3 7-- 13 S22 1 3 1- I- -7 - - -3 1 -5 -1 -5 -3 -? -5 -s -1 -5 -5 - -5-11 - -3 -5-11 -? -5 -1 -9 -133 It -1 -3 ? -9 -: -?-9 -3 --1.:5 - -- 7.-- -13 -7 5-7-13-: -3 :3-9 :314 13 - -3 7l I- -3 ?-3 -3 - :3 -5 3 -: 7 -7 :-5 -? -3 ,-3-5 --7?3:- -3 -5 3 -

25 13 3 9 -5 3 -3 :3 1 -3 3 -1 1 -1 -3 -3 3 3 -1 -7 -5 -1 -3 1 133 3- 1

27 1: 9 3 1 -a 7 1 1l 1 5 -3 3 . 3 3 3- --3 t - 3 S 3 3I5 '9 57 3 -1 -3 -5 3 - 3 -5 -7 3 -3 -3 - - -3 - 9 -1 - -5 -313 -5 -1 -1 -7 -12 9 3 9 1- -1 -3 3 3 - 1 -1 1 - 1 - 1 - - -1 3 - 3 -- - -5 -3-1 -3 - I -3 371 9 1 - 1 - -31 3 -1 3 1 - -1 -- 1 - - 3 -1 - - -9 -3 -5-13 -5 -1 -1 -7 -131 39 7 7 3 13 3 7 7 3 1 3 9 1 5 3 3 3 3 -t 3 -3 1 1 3 -7 35 3 -? S3 It S 311-3 S -1--3 3 3 -1 1 3 S-3 1 a 5 1 -- 3 -F-3-1 -9 1 1 5-3 1


51

-~ - *.19 I

FIGURE 60. Target Representing Complement ofWaI (3, x) Wal (0, y).

NILS COEFFICIENTS

A 1 2 4 5 6 7 a 9 tO 11 12 23 14 15 16 17 to 29 20 21 22 23 24 22 26 27 26 29 30 32 32

2 9 -2 -3 -5 I -2 2--3 -S -3 -1 5 53 -7 so -: 1 -9 - -S 1 -3- - -31 -23 -s1 -3 7 - 3 5 :1 3 2 1 1 1 -3 9 -1 a -3 ? -?3 1 2 :S -, -I S 1 -t -1 1 -, 1 -1 5 -34 9 S 7 7 S S ? 1 S -1 11 -1 3 1 It 2 9 3 7 -5 -3 1 3 S -1 22 3 1 3 7 a

S S 2 2 3 15 3 3 -2 2-3 I 2- s a- -9 - -s 3 a s - I - 2 2-33 3 -3232--I- 5 -3 -3 -s3 3 3 12- ,- S- ,3 - 5- 31 -7 9 1 2 -l 3 3 3 -3 -1 -2 7 -I1 -3 1 -1 a :52- ,-7- 3- -7 s s- - l-. 7 3 3 3 a 5 5 1 3 -1 1 -1 3 -3 9 -8 3 1 3 -a -3 -3 3 -1 -3 -7 7 -1 - -1 -1 -3

9 9233335- -l93 3 -3 7 -3 1 3 -7 :-* -23 1-31 -1 -7 7 -3 1s- -3293 22 1 1 521 1 22- 3 -5 - 72-l- 9 22-3

I2 7: t2 3 -2 9 -3 1 i- -3 -1 1 1 -3 - 9 2-3 -1 3 -312 9 S 7 3 3 9 _: -I : -It -1 1 -3 9 -3 1 1 ? -5 -3 S - -1 -7 9 2-1 t3-

t3 17 3 1 r I I I7 1 31 1 12 2 S 1 It -1 1 3 S -11 -3 -t 1 : 1 -2 It 2- 2 5

1 4 22 : -3 :1 :2 : 51 S5 -3 :-I :1 3 :1 :3 2-9 -? -5 -t - 9 -9 3 -3 -1 -s -51-15 7 I2- s-5 _: -5 -3 -I _I7- 3--2 9- 2- -9 - 3 -s -? -3 -3 -?1: 23-31-?7-1 1 1-5 -3 -? 3-3 -3 -9 2--3 -3-1 -2-7-1 -5-9-13 1-7-9-9 -3-11

27 3 2 9 9223 5 3 3 5 it2 -1 9 3 7 -5 -: 3- 125-2N 23 7 91 9 9 9: 7 : 5 3 7 : 12 -1 7 3 9 -5 2- 7 3;- 3 9 : 3 3 -1229 1: 5 7 9 7 3 1 3 13 1 IS 1 11 1 ? 3 7 -3 -1 1 7 3 -1 -3 9 I 1 -1 1 -120 23 ?I 7? 9 9 21 3 7 3 17 1 9 3 89 3 123 71 lot -, 3 9 7 I 1 25 5 $ 3 21 222 9 3 _I I 1 51 -I2- 9 -I 3 3 .3 :; -? _ -? -7 .I72- 3 9 2 -3 25-

22 9 2 3 -1 3 3 3 1 1 - r -1 f -3 ? -5 S - 3 -7 -5 -; 3 -: -3 -5 7 -1 -1 -1 3 -3

33 'T: -3 - 3 -' 1 -1 3 -2? -s 3 -1 3 -2 1 1-7 -7 -S :3 - 32 -s - 3 9 3 -3 -1 -I724 7 II -a- -3 -r2 9 -3 1 -1 -2 -7 3 -9 -1 1s 1-2-9- -3 -7 -9 -3-7--2-as _ 2 5 1 1 1 7 2 1 9a3- - i7--3-2S22-,92--213

27 99 7 S 7 1 1 -1 It -1 0 -3 9 -3 8 1 It -s -I -1 ? 1 -1 -3 9 -1 -1 3 5 -329 7 1 3 1 3 -8 1 -3 7-1 1 -3 1 -3 3 -1 1 -9 -1 -3 3 -3 -8 -7 7 -3 -3 -3 1 -u

29 9 -1 3 -1 3 1 3 -3 1 -3 7-1 -1 -11 1 -8 3 -1 1 -9 -7 -2 1 -3 -1 -11 6 -3 -1 -5 -1, -230 5 -: 1 -11 -: -31 : :.- 79 u- 7g 7*- -l' -7 -1 -3 -7 -9 3 -s -7 -3 -3 -7

2 22 232-I--3 2* -22- 3 11 a 1 -7 -3 -3 5 -1 -3 -1 7 1 -1 -1 3 -332 U -7 -3 -5 -8 -3 -1 -1 -3 -7 1 -8 -1 -1 a 7- 3-2- 9- -3 -? -7 1 -8 -1 -g -1 -7

FIGURE 61. Walsh Transform' of Figure 60.

52


@ALI COWCF1CIENTS,

1 2 3 4 3 6 7 S 9 20 11 12 13 14 15 16 1? 11 19 a0 21 22 22 24 23 26 27 as 2 30 N 32

1 77 9 7 3 -$ 5 7 -3 1 I 1 3 -1 3 S -I 2 5 1 -2 -$ -2 3 a -s 5 S 1 a a2 to 1 1 3 -s I -1 -I -1 -1 1 -3 -1 -2 -3 -7 1 -a -2 -? -? -1 -3 -$ -3 -7 -s -2 -1 -2 -4 -s3 13 1 I -s -3 -1 -s-1 -31 -1 - - -3 - -a -3- -7 -? -i - -- 3 -5 -3 -5 -3s - ----4 121 12 13 13 -s 7 7 -3 3 I 3 3 3 9 -1 9 3 s -I -3 -1 1 I a -3 S S 7 S a S3 19 7 7 I 9 9 7 1 S ? 7 7 3 a 7 1 1 7 1 - 1 3 a I -I a a 3 a 3 16 a1 7 1 7 -1 7 3 -1 a 3 5 3 3 3 -1 a 1 1 -a -a -3 -a -1 -3 -3 -1 -1 -1 1-1 -17 1? 1 7 7 1 3 3-1 3 3 S 3 3 -1 3 2 I -3 -S -I -1 -1 -1 -2 -1 -1 I I -k-3l at It 9 13 2 It 7 2 3 1 I1 7 7 57 1 7 7 I I I 1 5 S I 1 5 2 a a a9 23 9 9311 9 ? 3 7 1 9 7 7 5 9 9 ? 3 1 5 1 1 1 3 7 7 3 1 1 S

10 23 9 7 13 3 9 ? S 9 7 It 9 7 9 9 5 9 It 1 2 3 5 ? ? 7 7 ? 7 7 9 P 731 22 9 ? 9 2 ? ?7 2 It51 7 S 7 7 5 ? 7 7 5 3 5 2 5 1 7 1 9 9 1 ?12 13 2 -11 3 1 3 5 3 3 -1 3 3 2 -1-1 -1 1 -1 1-1 3 3 1 3 3l3 17 2 1 2 -1 1 -1 -3 -3 -1 3 -1 -3 -2 -3 -2 - I - - -3 5 -a - - - - 1 - -114 1 -1 -1 1 -5 -1 -2 - -1 -5 -1 -3 -3 -2 -3 -5 -3 -3 -3 -7 -7 -7 -S -7 -s -9 -5 -S -3 -1- -913 11 -1 -1 1 -7 -1 -2 -7 -3 -5 -1 -3 -S -3 -2 -9 -3 -2 -S -7 - -9 - -5 -7 -? -8 -$ -5 ---16 17 1 1 3 -S 1 -3 - - - 1 -3 - - - -3 - - - - 5 -s -7 -? -3 -? -s -9 -8 -3 -3 -2 -1 -3

17 17 1 7 9 3 9 5 1 1 5 9 3 52 7 1 5 3 3-I-1 3 1 3 1 1 32 3 8 30 17 2 S S -1 5 1 -a 3 1 3 A A 3 -2 2 3 1- -3 -1 - -3 -1 -1 -1 -1 -1 3-- -1

19 I 2 3 3 -1 a 1 -I 1 -1 1 a 1 1 a -3 3 1 1 -3 -s -a -1 - -I1 -3 -1 -1 1 1 1 -120 It 2 2 7 -I 3 1 -1 I 3 3 3 2 3 1 3 2 3 -1 -a -1 1 -I -1 -3 1 1 a a 9 a21 13 -S -1 -2-11 -U -7-11 -9 -9 -$ -9 -9 -7 -5-11 -7 -7 -1-3-ll-ll -9 -9 -9-l1 -7 -7 -9 -1 - -722 3 -s -3 -2-13 -1 -7-II -7 -9 -1 -9 -9 -9 -7-113 -7 -7 -7-12-3l -, -1-1I -9-1 -7-9I -9 -I -4 -924 1 -3 -9 -3-i -u -9-11 -9-11 -7-11 -9-31 -7-11 -9 -7 -9-13-12-33-13 -9-32-1I 9 -9 -9 -? --24 12 -2 -u -a-II -u -1-II -9-la -7 -l-l a-la -in-aa -9 -7 -7-ll-32-ll-3ll-ll-12-l2-33-ll -s +-usIIIt to a I 1 -3 a - a - a 3i -I -a -1 -g -1 -a -3 -s -P -7 -g -u -8 -1 -3 -3 -S -1-g -I16 A? 1 I 1 -2 1 - - - -I I -I -3 - -a s -a -a -I - - - -1 -S -I -, -a -a -s -- -I27 9 1 1 1 -2 a a -a -a -a a -1 -a -a a -S -a -I -a -5 -s-- -a -a - -3 -3 -I - - -a26 II 3 3 7 -3 i -3 a a 1 a -1 -a a -a 1 -1 1 -1 -s -a -a -3 -5 -3 -3 -5 -3 -a -I -29 Is I 3 1 - -I - - 1 - 3 -2 -I -g -3 -I -2 -I -I - - -I - -1 - 1 -- -a -I - - -a. 13 -1 a 3 -a 1 -1 -a -a -a a -1 -a -2 -3 -5 a -1 -a -$ -? -g -I -1 -- -1 - -3 -a - -33 9 I 3 S -a a 1 -a -1 -1 a -1 -1 -2 -1 -1 -a -a a -8 -1 -1 -a -a - -8 -3 -1 -3 -2 -1 -aat I? a a -8 a -a -0 -1 -1 1 -a -1 -2 -a -1 -3 -2 -3 -F -9 -1 -s -s -? -1 -a - -5.44-3


53

FIGURE 64. Target Representing Complement ofWal (0, x) Wal (3, y).

SAL$ COIFFICICNTS

1 a 3 4 5 6 7 0 1 3At 12 1314 3 1 617 Is I 920 21 22 23 24 25 26 27 26 29 3 It 312

-07 o3 7 2-15 -s -3-13 -? -? -1 -5 -? -S -S .9 -3 -2 -5 -9-11 -9 -5 -3-13 -3 -3 1 -3 -3 -5S 5- -' -1 -? -* -? -9 -* -5 -3 -5 -3 -7 -3 -9 -3 -5 -3 -9-11 -7 -? -7 -? -9 -5 -7 -7 -S -? -7

a 1 ? 9 5 5 3 ? 7 9 5 5 7 ? 3 7 7 3 31 5 3 5 3 1 5 1 S4-S I ?9? 3 797 77 5 355 7 5 39?3 3 ?S1 93 3S 13 -5 -3 I -S 1 -3 - -3 -3 1 -3 -3 -s -3 -5 -3 -3 -3 -? -7 -5 -5 -5 -5 -? -3 -s -3 -1 -3 -36 ? -a -3 t -s 1 -3 -9 -3 -3 1 -2 -3 -7 -3 -9 -3 -g -3 -9 -, -7 -7 -? -5 -7 -5 -5 -5 -3 -? -s7 13 -1 3 5 -1 I -2 1 1 -I -3 -I 1 -5I - -I -5 -? -3 -3 -3 -5 -5 -3 -I - -3 -3 -36 F 3 3 5 -2 5 3 - 12 -3 I -I 1 -5 I -1 -3 -3 - -3 -2 -3 -S -s -3 -2 - -1 -3 -39 ? - 3 3 - 3 I -3 3 I 1 -1 1 -3 -3 1 *1 -1 -3 -s -3 -1 -S -$ -5 -3 -S -3 -2 -5 -?

10 9 32 -15 -31-1 3 1 I- I -I a I 1- -5 -3 -3 -3 -3 -? - -3 -3 -I -$ -3I 13 - 3 5 -3 3 1 -I I -1 3 I - - 3I - 1 - -I I - 7 -3 -2 - -3 -s 1 -3 -2 - -512 21 3 a 5 -I - - -3 - 3 -3 a -3 1 -s -A I - -S -3 -3 -s -S -s - -3 I -3 -3II Is ? 13 13 9 13 II 7 9 9 13 9 9 7 9 5 9 1 9 1 1 5 1 7 3 9 5 9 1 ?714. II 3 1 9 I 3 3 -1 3 1 1 1, -1 3 -3 a I -3 -" l -1 -t -I - I - I - -1 3 -I -1IS 13 1 I 5 -3 3 -i "I -3 1 1 -1 -3 -1 -3 - - -I I -7 -3 - -3 FS 1s -3 -s -3 -3 -3 -334 7 -3 -5 -3 -9 -1 -?-11 -? -? -? -9 -? -9 -7-11 -9 -7 ---- 1--I3'1-II-113- I3'II -9-13-31I? ? 3 5 7 I S 1 -1 1 1 1 -1 -1 -I -1 -1 1 1 I -5 -s -3 -i -S -5 -5 -3 -3 -3 -1 -s -3I It 3 7 1 I 1 5 -3 a I 5 3 3 -1 3 -1 3 3 1 -3 -5 -3 -3 -3 -3 -2 -2 -1 -1 1 -3 -311 19 9 9 ItI S 1 I 5 $ 5 S 3 3 5 -I S I1 -3 -3 -3 -1 -3 -1 -3 -1 - -1 1 -3 -1to as 9 9 9 3 9 7 3 1 9 9 5 5 S 1 T 7 3 -I -3 1 -1 1 -1 -1 32 I 3 1 i21 I9 ? tit 1 9 8 3 7 1 9 7 ? S ? 3 9 7S 3 I 1 5 3 1 1I 3 3 37 3 322 13 F F 9 1 P I I 31 3 ? 5 S 3 5 3 F 1 I-I 3 1 3 1 1 3 3 3 3 323 13 S 8 1 -1 ? 3 -I 1 3 S 1 3 1 I 1 3 3 31 -3 - - I - -1 - -1 3 I 3 1 324 9 S 3 a 1 3 -1 -5 I 1 3 I 1 -1 3 -3 1 1 -1 -3 -? -1 -3 -" -3 -s -1 - 1 3 3 125 ? 1 1 -I 1 1 I 1 I3 3 3 3 1-1 S 3 3 -1 -3 I I 1 -I -1 3 3 I I a24 9 - 1 -3 -I -2 -3 -F -3 -9 -3 -0 -5 -? -8 -7 -g -I -5 -9-1l -7 -" -* -? -" -1 -" -5 -" -Y -T

I7 331 11 3 9 1 1 ? ? 9 ? ? I ? 3 9 1 5 1 1 3 3 3 5 3 3 1 3 7 5 526It 1 1 I 3 -3 - I -7 -I -? - -3 -3 -3 -5 - 1 -1 1 -Y -9 -8 -3 -$ -5 -S 1 1 -3 - 1 3 -t 13 1 3 1 -1 -1 -3 1 -I S I I I 1 - 3 3 1 -5 -5 -" -" - - -1 -3 -3 - 3 I3 - -Iis 1 -1 -I I -5 -3 -3 - -1 -5 -1 -3 -5 -5 -3 -? -3 -3 -5 -, -9 -? - -F -? -9 -1 -? -P -? -7 ?33 I I ? 9 3 ? 3 3 S 3 7 3 a SI "1 3 3 - -1 a1 1 I -t 3 1 1, 3 -t 132 1 -3 1 3 -2 1 1 -3 -1 1 3 -1 -1 1 1 -3 - -3 -s -5 -3 -1 - -3 -8 -3 -3 -3 -3 -3 -3


54

DAL$ COEFFICIENTS

1 2 3 4 5 6 7 6 9 10 11 12 13 4 IS 106 7? 19 It20 21 22 23 24 25 26 27 28 29 30 A 32

13 5 -3 42 3 39 -3 31 3-9 -S 31 7 -I 7 -3 -$ -3 -3 -3-11 -5 -9 -3 7 -S 1 1 it I 5I3a 1 -3 I 1 -a 1 -a -S -3 -3 -1 -I -i -5 -S -S -3 -3 -3 -5 -? -3 -3 -? -3 -i -3 -3 -3 -3 -a--x 4s 1 -a 5-11 3 -3 -1 -3 -3 I -3 -3 -2 -I -1 1 -t 1 - -5 -3 -t -3 -3 -s -3 -3 1 -3 --4 3 5 7 7 3 3 3 1 3 1 5 1 3 -I 3 -I I I I -3 -I -I 1 -3 -1 -I 1 -I I -1 -1-33 453 -3 $-I 3 -3 a -1 -3 3 -3 -1 -t 1 -3 3 I 3 -3 -3 -1 1 -3 -3 -5 -I -1 -I -1 -5-3

6 5 -1 7 3 3 3 a 1 -1 3 - 3 -3 3 -3 -I -: -1 -3 -a -a -3 -8 -3 -S -1 -3 -1 -1 -2 -37 43 3 -3 7-11 5 -5 -1 - l -3 3I I I I - -I - - 3 -1 -5 3 3 -1 -1 -- -1a 5 3 ? ? 3 1 5 -I-1 3 I a -1 3--3 11 1 --3-11--1-3 I-I 1 1 1 1 -9 t5 3 3 5 -1 7 1 1 1 1 5 -1 1 1 1 -3 13 3 3-1-I -a 1a-a 3-1 1 1 1 1 -6-1I* IS 3 1 3 -1 3 -1 1 -1 -1 1 -3 1 -a 8 -9 -1 -1 1 -5 -9 -3 -a -3 -1 -5 1 -1 a -1 -a -aIt 17 5 -a 7 3 3 3 1 5 a1 -1 3 -3 3 1a -1 1 -1 1 -1 1 -3 11 1 -1 1 132 15 3 1 3 -1 5 -1 -a -1 -a 3 -3 -a -3 1 -- -3 -1 -1 - -5 -3 -1 -3 -3 -S -1 -3 -3 -3 - -313 as 7 3 ? a 7 3 3 3 3 7 a 3 1 3 -3 a 3 1 1 -a a 3 -1 a -1 3 1 3 1 3 -1t4 a? 3 a 3 a a 1 -a 1 -3 1 -3 -1 -3 a -u -3 -1 -3 -3 -F --5 -2 -5 -5 -1 - -3 -3 -3 -5as 21 3 7 9 5 7 5 3 3 1 ? 1 33 1 -1 3 3 3 -1 -1 -1 -1 -a -1 -3 -1 -1 1 1 -116a 1 1a 3 3 a 3 a -a a -3 a -3 1 -3 1 -7 -3 -3 -1 -3 -3 -3 -3 -9 -3 -5 -2 - ' -3 -l -4 -3a? S 3 S 5 a 3 5 3 5 3 1 a 1 a -3 3 1 V -3 -1 1 1 -1 1 -t a I a a 2 aI ?1 3 131 1 1 -1 -1 3 15-1 1 -3 111 -111 3311111It 3 1 3 3 I1 3 1 1 - -1 3 -3 3 -3 3 -3 3 1 1 -3 -a - 1 -3 1-1 1 1 1 1 a2 1-1 -1 33 1 a1 -a 3-1 -1 3-a a a 1-1 1 a -la-a 3-1 1 3 123 3 -1 3 3 -a a a -a -3 -3 1 -3 1 -3 -1 -5 -a -a -1 - -3 -5 -3 -I -3 -5 -1 -5 -3 -3 - -322 5 -a 3 a -a 1 1 -a - -I -3 -a -3 -1 - -3 -S -S -5 -3 -1 -5 -3 -5 -3 -3 -1 -3 -9-123 -1 3 1 -1 1 a -3 -1 -5 1 -3 -1 -u -1 -5 -3 - - -5 -? -1 -5 -2 -3 -1 -3 -3 -1 -3 -0 -24 5 -1 3 a -a a a -3 -a -3 a -3 -3 -5 -1 -5 -3 -3 -l -5 -7 -5 -5 -3 -S -5 -3 -3 -3 -34- -525 1 1 ? 1 l 3 3 3 1 a -1 5 -1 5 -1 3 3 3 1 -1 1 3 1 1a1 1 1 3 3 3 130 a1 -3- 1 -u -1 -3 -3 -5 -5 -1 -7 -3 -7 -1 -9 -3 -1 -S -5 -Y -9 -5 -? -5 -7 -s -5 -s -3 4 -52713-373371?3-1 33? 1 1-1" 11 S15 -ala 313"111 3a 33 32-3t3 I 3 I9126 9 -1 -3 -a -S a -5 -3 -3 -S -1 - -3 -7 -1 -? -3 -0 -3 -7 -s -I -5 - - -7 -3 -3 -5 -3 -9 -529 It 3 1 0 1 5 1 -a -a -1 3 -1 a -1 3 -3 1 1 1 -1 -1 -1 3 -1 -a -1 3 1 1 1 3 134 7 -7-3-1 -Y-3 -5-7 -? -9 -5-9-5 -Y-3-11 -7 -7-3 -?-7 -9 -3-9-7 -7 -3-? -5 -F -531 I I I 3 -3 3 1 -1 -a -3 3 -3 1 -1 1 -3 1 1 3 -3 -t - -3 -1 -3 I -I 1 -1 t a22 9 -3 -3 -3 -3 -3 -3 -7 -? -9 -3 -, -7 -9 -3-a -7 -7 -?-It -9 -9 -? -9 -7-11 -5 -, -7 - -4 -1

FIGURE 66. Walsh Transform for Target Representing Road Intersection.

55

VAL$ COEFFICIENTS

1 2 3 4 S 6 7 S 9 10 It 12 12314 1 16 1? 18 19 20 21 22 23 24 21 26 27 2S 29 30 3 32

1 65 1 45 1 31 -3 37 -7 ? -1 Is 3 7 1 I 1 -3 -1 -5 -5-11 -3 -9 -1 9 -3 I1 3 21 2 a 12 3 1 5 3 1 1 3 -1 I -3 3 -I 1 -3 1 -3 1 -1 -t -3-5 -1 -3-3 -t -1 -1 -3 -I -3 -- 13 i ? 3 I11 -? 9 -1 3 11 t I I 1 5 -1 3 t I -1 -1 1 1 -1 -3 1 -I 3 1 4 -14 9It12 911 9??393 ?37 1 ?I1113 1311 45 7 1 13 -? 11 -1 3 3 3 ? 3 5 1 -I 7 ? 3 3 3 3 3 -1 3 1 3 3 £ 1

? ?73 77 77 55 1735 1 1 333 11111 11313 1-17 45 7 -I I1 -9 9 -1 3 1 1 7 9 I 1 5 -3 7 1 ? 1 3 3 5 1 3 - 1 3 3 3 51 3

? 3 ?;_57 7 5 ?3 51 ?33 1213333 3 1 11 1117 11 - ?1 3 3 3I71 1 -I 2133132; 11 3 11

10 151 1 3 -3 3 1 1 1 - 1 5 A -1 5 -3 3 3 -1 - I - I A I I -I 1 3 1I 1 1II I ? ? 5 9 3 1 I ? S 5 3 3 -I 3 3 3 - I 1 1 1 3 1 5 1 3

12 13 3 1 a -1 I a -1 -1 -1 3-3 -1 -1 3 -1 - a -I -1 -3 -3 -3 -1 -3 -1 -1 -1 -3 -I -3 a-I131 ? 3 9 1 ? I 3 1 1Y I 1 1I S -I 1 3 I I 1 3 -I 1 -1 3 1 3 3 9

14 13 1 1 3 -1 3 -I -3 -1 -3 1 -3 -3 -3 -1 -S -1 -3 - 1 - -3 -3 -1 -3 -3 -3 -I -I -S -t -3II IS 3 3 S 1 1 -1 3 - I -1 I -3 1 1 -3 -3 -2 I -I -1 -I 1 -3 -3 -2 -120 13 -3 I -1 -3 -1 -3 -3 -3 -5 -1 -S -5 -5 -3 -? - -3 -3 -? -? -? -3 -9 -5 -? -3 -1 -3 -? 4-T1? 3 -1 1 1 1 1 1 -1 -t -1 3 -3 1 -1 1 -S -1 1 -1 -3 -3 -I -1 -3 -3 -S 2 -3 -1 -3 -9 -3I3 3 -3 -1 -1 -3 -I -1 -3 -2 -3 1 -3 1 -3 1 -3 -1 1 -1 -3 -1 -3 -1 -3 -3 -3 I -3 -3 -3 -1 -319 1 -3 -1 1 -1 -1 -I -3 -3 -3 1 -5 -1 -3 -1 -7 -3 -3 -3 -2 -1 -5 -3 -2 3 -1 -2 -3 - -3 -1 -Ss0 3 -1 -1 2 -5 -1 -3 -3 -3 -5 -1 -3 -1 -3 -1 -7 -3 -3 -3 -3 -5 -3 -3 -1 -3 -3 -2 -3 -1 -1 - -321 1 -3 -1 -3 -3 - -1 - - - -1 -1 -7 -3 -, -1 - - -9 -9 -5 -7 - -- -3*- -1 - "22 3 -3 -1 -1 -3 1 -3 -3 -- - -7 -3 -7 -3 -7 -1 -3 -5 -7 -9 -7 -7 -? -? - 7 -? -1 -5 -723 3 -1 I -I -2 -2 -1 -5 -3 -5 -1 -3 -3 -5 -1 -? -3 -1 - 9 -9 - - -9 -7 -9 -S -, -? S -6-?24 3 -1 -1 1 -1 - A 1 -3 -1 - - --6 -i -1 -1 -7 -1 -1 -1 -7 -7 -1 -5 - -7 .7 -7 -1 -S -21 5 3 5 3 ? -I3 I3 3 3 -1 5 1 3 -1 3 -3 1 3 3 - I I 1 -1 -1 - I -I -I -126 9 -3 -3 -3 1 - -3 - -3 -5 -I -5 -3 -9 -3 -9 -1 -I -1 -7 - - F -? -7 3 -7 - ? " -7 4-T3? 13 U 5 7 I ? 3 3 5 I ? 1 3 1 5 -1 3 1 3 -1 1 I 3 1 -1 1 1 3 1 1 I -29 11 -3 -3 3 -3 2 -g -1 -3 -5 - 1 -- S -2 -9 -1 -3 -3 -9 -5 -2 - -?- -? - 1 - -1 4--29 III 3 3 I 2 I - 1 -1 5 -1 3 -3 3 1 3 -3 1 1 -I -1 -1 1 1 1 1 3 2 130 II - -- -1 -2 -1 -3 3 -1 -5 -3 -3 -? -1 -9 -3 - 3 -9 -? -7 -1 -F -? -F -I 1 -3 -5 4 -31 15 7 1 9 1 1 3 3 3 1 ? I S 1 5 - 1 5 3 -1 1 1 3 1 1 - 1 3 1 3 3 I

32 13 -I -S 1 -3 2 -A -I -3 -5 -1 -5 -3 -1 -9 -3 -3 -3 -9 -- 8-5 - - - -1--3 - 4-7

FIGURE 67. First Repetition of Walsh Transform for the

Same Target Used to Produce Figure 66.

56

. ......| ... . . ..... ....

@ALI COEFFICIENTS

1 2 3 4 3 6 7 1 9 i1 Ii 13 14 15 16 1? 19 19 20 21 22 23 24 25 262? as a9 20 31 32

1 66 -a 46 4 20 -4 34 -86s -2 S 1 8 6 1 -2 -s -4 -s -6-12 -6 -s -a 6 -6 s -2 11 -4 1 -2a a -a * a * * s -a * -a a -4 * -6 2 -6 -a -a -a -4 -6 -4 -4 -6 -6 -6 -2 -6 -6 -6 -4 -63 4 4 -2 -I1 6 -6 a - - a - a -2 4 -6 1 a4 -4 -2 -4 -2 -2 -4 1 - -2 -2 -s-a

4 15 11111811 6 441 6 242466 444w 464k 4q446

34610 1s 2-81a-a 6 4. a 0144 61 1 9 6 5 a 4. 2 4 a s a a 4 A a 46 6 a 6 4 a a 2 s 0s 4 -a s -a 4 -4 0 -2 0 -4 -a - -a -4 -2 -a 0 s s s 1 -a7 46 4 -2 6 -8 4 -4 6 * -2 4 -a s -2 2 -4 2 a a -a -a-1 0 -2 -4 5 -2 0 0 0 4

8 6 2 4 6 4 4 6 2 4 5 4 4 4 0 4 -2 4 0 0 -a * * -a -a -2 0 5 * . . a 492Is 66 62 24 2 6 40 6-2 2 22- 2 6 2-2 4 5 2 42 2 2 55 £14 4 6 0 6 2 2 * 5 4 0 1 5 -a a a-a-a-a-a 2-4 -2 -4 *-2 5-2 -I

I3 £ * a 1 0 -4 2 4 5 6 a 2 2 2 512 206 4 6 6 2 2 2 5 4 -a a 0 4 -a a 4 a -a . -a s -2 -2 -4 0 -a 0 -a -a -4

£2320 6 430 0 1 6 4 6 4 0 4 6 4 0 * 6 6 6 4 a 4 6 2 4 5 4 2 4 a 4 a14 14 a a 4 1 4 2 5 5 -2 4 6 5 -2 4 -4 0 a s -a -a 0 0 -a -a -2 0 -2 -2 -4 -a -a1 1 6 1 4 2 5 2 0 4 5 2 0 4 -2 4 2 4 5 2 * 2 0 2 5 4 2 4 4 4 a16 14 -a 0 5 -2 -2 5 -4 -4 -6 2 -2 0 -4 5 -6 -4 -2 -2 -6 -6 -4 -4 -4 -4 -4 -2 -4 -a -4 -a -4£7 2 5 5 2 0 4 4 -2 2 -4 2 -2 5 -4 2 -4 5 0 5 -4 -2 -2 -2 -2 -2 -2 5 0 2 5 0 4is 4 2 2 4 5 4 0 -2 6 -a a -a * -2 a -4 5 5 2 -4 -4 -4 -2 -2 -2 -4 5 -2 5 -2 0 5is 4 5 2 2 2 5 0 -2 0 -2 a -2 0 -2 0 -6 -I -a -4 -4 -4 -4 -2 -4 -4 -4 5 -4 -2 -4 -a -425 4 0 2 4 5 2 2 5 2 -2 2 -2 a -a 2 -4 0 0 5 -4 -2 -2 -a -a -a -a 4 0 5 5 -221 2 5 2 2 5 5 5 -2 -2 -4 5 -4 5 -4 5 -6 -4 -4 -4 -0 -6 -6 -6 -6 -4 -6 -2 -4 -4 -4 -4 -422 4 -2 5 2 5 5 -2 -4 -2 -4 5 -4 5 -6 5 -6 -4 -2 -4 -4 -6 -4 -4 -4 -4 -6 -2 -4 -2 -4 -a -423 5 2 1 4 0 5 -4 -2 -4 0 -4 5 -6 5 -4 -4 -4 -2 -6 -6 -4 -4 -6 -6 -6 -4 -4 -4 -4 -4 -624 4 -2 5 5 -2 5 5 -4 -2 -4 2 -4 -2 -4 -2 -6 -4 -4 -4 -6 -6 -6 -4 -6 -6 -6 -4 -4 -4 -4 -4 -6231£2 2 2 4 0 2 2 0 2 5 6 0 2 4 2-2 2 2 2 5 5 5 2 6 2 0 2 5 2 2 2 426 6 -6 -6 -4 -6 -4 -6 -6 -6 - -4 -8 -6-10 -4-11 -6 - -6 -8 -0 - -6 -4 - 8 .-6-4 -8 5- -6 - 4 - 62? 1 2 4 4 - 2 -2 0 -2 -2 2 -2 2 -2 2 -4 5 5 0 -4 6 -4 -2 -2-2 2 5 2 2 2 021 1 -4 -4 -4 -6 -4 -6 -4 -6 -1 -4 -I -6-10 -6-10 -8 -6 -6 -8 -8 -I -6 -8 -0-10 - -0 -6 -8 -6 -829 £2 2 2 4 -2 0 0 5 -2 -4 4 -4 0 -6 * -6 -a -a -2 -4 -4 -4 -4 -4 -4 -4 -4 -a -2 -236 I -4 -2 -2 -6 -4 -6 -6 -6 -8 -6 -8 -6 -I -4-16 -6 -I -I-32-14-I2 -I2 -11 -I'11 -I --- I-3£ I 4 4 4 5 2 0 42 0 4 5 0 -2 2 -4 5 5 0 -4 -2 -2 5 -2 -2 -2 -2 -4 -a -2 -2 -432 11 -2 -2 * -4 -a -4 -6 -4 -8 -2 -8 -4 -8 -2-I -6 -6 -6-Is -I -8 -I -8 -0 -g -6 -0 -6 -8 -6 -

FIGURE 68. Second Repetition of Walsh Transform for the

Same Turget Used to Produce Figure 66.

57wi I

VALS COEFFICIENTS

1 2 3 4 5 6 7 8 9 10 i1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

I 65 -3 51 5 31 -327 -? 1 -1 9 3 9 9 -I -3 -1 -5 -5-11 -3 -9 -1 9 -3 9 1 13 1 II 12 1 -33 3 £ I 2 -3 °1 2 -2 I - I -2 -t -t -3 -2 -s - °3 -2 -5 -! 3 -3 1 -2 49 5 3 9-9 7o5 15 152 - -3- 1 1 - -3 1 2 1 1497 913 7977 2$ 1 1 5 3 :: ! : :5 49 7 -7 -3 3 I 7 I -

6 9 5 $ 7 ? ? ? 5 7 1I 5 1 1 1 3 3 -1t -I -I -1 I I I7 47 ? 13 -? 9 -2 3 1 1 ? 3 5 3 7 -: ? I 7 1 3 1 3 I -1 I 3 3

* 8 9 29 7 7 7 7 7 5 27 5 7 23 5 5 5 3 2I S 1 317 1 5 5 5 29 9 5 7 9 1 7 ? 5 3 7 2 7 2 ? 2 1 3 3 5 5 2 5 3 3

S 3 5 75 1 3 I 7 7 3 5 3 3 3 3 3 1 7 3 2 2 3

33 37 5 3 7 2 3 : ? a -3 35 2 3 5 2 5 1 2

12 35 3 2 -2 2 I - - 2- 3 -l 2 1 l3 -3 - l - 3 - -2 I - 3 3 13 -IOIS755-9171217132 7-3555ill31111153312 1 - 1 3 - 7 15 1 - -1 3-2; 3 - 5 1 -3 1 3

3512 1 3 53 3 32 -3 3 - 1 -3 13 3 1 - 3 1l -3 1 3 2 1 -I3 1 - 3 - 113 -I 3 3 -2 3 - - -5 -. 3 -s - -5 - -- - -7 3 -. - -5 -5 -7 5 -? - -5 -3 -14 13 1 2 3 - I 1 - 3 -5 - - 3 -2 3 -3 ; - -2 -2 -; -; -2 -2 -: - 3 -3 -Ia 3 -2

1 51 I 2 I 1 2 - 1 2 2 - 3 - 1 3 -3 - 1 -3 -1 - - -1 -2 -3 1 1 - -1

1 6 13 -l I 1 - 3 21 - - 2 - - 2 - 3 - 5 3 -S : - : -- ? - 7 - - -5 - - - : - : - : : - 3 7I0 2 1 I 3 1 - 3 -3 -3 - I - -4 -3 -3 -3 - -2 - -2 -I I 3 -321 3 1 1 3 _ - - - - -3 3 -3 :- - -I -g - - - - - -I -g -g -2 - -2 -22 2 2 - 2 - - I 5 -1 - s - - 3 - - - 2 - , 1 - 5 - 2 - 9 - ? - 7 - - - 5 - - - - - -

2 3 3 -I -3 - -: - - 2 - - 1 - 5 - , - 5 - 5 - 7 - 9 - 7 - 7 -1 - - - - 5 - - - - -

24 5I -3 - -1 -3 -2 -l -s -3 -s -3 -2 -2 -7 -2 -7 -5 -7 -? -, -7 -7 -7 -9 -7 -9 -i -7. - 7 " -s -v25 13 S 7 I 2 2 - 1-3 2 l - 3 3 - - - 3 3 3 - 3 -3 -3 -3

32 33 -3 -3 -3 -5 -I -2 -3 -$ -u -I -u -i -7 -3 -7 -$ -5 -u -7 -7 - -7 - -9 -g -g -7 -5 -7 -7 -, -26 2 -I -3 1 - 3 - -$ -2 - -7 -3 - ? - 3 -7 -3 - 5 - 3 - 9 -7 - ? - 3 - 3 -s -7 - 5 - 3 - 3 -5 -5 -7

9 32 2 2 7 1 7 2 I 2 3 -1 2 I 3 -3 2 3 2 -I -I " -3 " -: -I I -:3 -: -

30 9I -I -1 - - I - - - s - - - s - - s - 3 -I - - - - - - - s - - - - " -7 -: :7 :7 :1

2 3 5 7 7 1 7 3 $ 3 I 5 I 3 1 - i 3 3 S I I 3 1 3 3 - I

32 9I -3 -3 I -8 I -3 -u - -3u - -7 -2 -3 .-3 -i -? -3 -3 -: : 7 - - -7 -7 -7 - Y - - 3 - -2 -3t1 11 2 7 1 a a 1 I I a a :9 1 : 7I t 1

32 II -3 -I 1 -I -1 -I -I -3 -5 -I -t -3 - 1 -I - 8 -I .3 .5 - ? " ."I" -7 - 3" -3 .3 .5 .3 "S

FIGURE 69. Third Repeition of Walsh Tranform for theSame Targt Usd to Produce Figure 66.

~58

NALS COEFFICIENTS

1 a 3 4 5 6 7 9 10 11 32 13 14 15 36 171 9 3 20 21 22 23 24 as 26 2? 2 29So30 31 32

a So a SO 6 44 0 46 * 2- 2 a -8 6 -6 1 -6 -4 0 -o 2 -1 4 -9 2 8 -4 1 -4 14 -4 14 -2a 6 * 4 2 a o 4 * a -6 0 -4 0 -4 2 -4 -a 0 0 -2 -4 -4 -4 -2 0 -2 0 -20 -2 a 03 8 a a 4 6 a6 4 4-2 4 * 4-2 4 0 * * *o o -2 * * 4 0 4 4 * 4 *4 a 4 4a6 2 444 & 442 4 2 40404 a 4 2 44 4S 2 0 4 0 4 -a a 20 2 0 4 * 4 -2 a . . -2 o -2 0 -a 20 2 0 2 2 06 1 a 4 a 2 a 4 22 -4 4 -2 4 -42 -4 0 -a 0 -2 -a -a -2 -2 0 -2 0 -2 0 0 0 -27 a a 4 a 4 4 a 2 4 -2 4 -4 4 -a 4 -2 0 * o -2 0 4 -2 -2 2 0 2 2 4 *6 2 a a 2 2242 040 202-20 0000 o 0-2 2 0 20 2 0 9 400 a 2 40220 4-2004-404040 -20 -200 2 40020

1* 6444442420 40 60 4-22 0 2-200004 2 402 2 a 2a 1 4 0 4 2 2 2 2 2 2 -a a -4 2 -2 4 -4 0 -2 * -a 0 -2 5 0 2 0 2 0 2 2 2 012 2 0 -2 0 -2 0 -2 0 0 -4 0 -4 o -a a -4 0 -a o -4 -2 -a -a -a . -2 2 -a 0 0 0 -213 0 0 -2 0 0 0 -4 2 0 -4 2 -2 2 -4 0 -4 -2 -a -a -a -a -a 0 -4 a 0 0 -2 2 -2 0 014 6 0 2 0 0 2 0 0 -2 -6 0 -6 -2 -6 0 -6 -4 -4 -a -6 -6 -4 -4 -6 -4 -4 -2 -4 -2 -4 -2 -4Is 4 0 2 0 0 0 0 -2 0 -6 0 -6 0 -6 0 -. -4 -6 -4 -6 -6 -6 -4 -6 -2 -6 -2 -6 -4 -4 -4 -416 2 -2 0 0 -2 -2 4 -2 -4 -8 -a -1 -4 -s -2 -1 -6 -6 -6 -6 -6 -4 -6-10 -6 -6 -6 -' -6 -6 -4 -0I? 4 2 0 2 & 2 0 0 2 0 2 -2 2 -2 2 -4 0 0 -2 -4 -a -a -a -4 0 -2 * -2 -2 . -2t6 0 1 a a a a 0 -4 4 -2 2 -2 2 -4 0 -2 0 -2 0 -4 0 -4 0 -2 0 -4 0 '- 0 -4

it 4 2 2 2 a 4 0 2 0 -2 a -2 a -a a -4 -2 -2 -2 -4 -2 -4 -2 -4 0 -a 0 -2 0 -2 0 -220 4 4 -2 4 0 2 2 -2 2 -2 2 -2 -2 0 -2 # -2 0 0 0 -2 0 0 0 0 0 0 021 2 0 0 2 # 0 0 0 0 -6 0 -4 0 -6 0 -4 -2 -4 -2 -4 -4 -4 -4 -4 -2 -4 -2 -4 -2 -4 -2 -422 4 5 2 2 * 0 0 5 -a -4 0 -4 0 -4 0 -6 -4 -2 -4 -6 -4 -4 -4 -4 -2 -4 0 -' -a -4 0 -423 4 0 2 2 2 2 0 0 0 -4 0 -4 0 -6 0 -6 -2 -4 -2 -4 -4 -4 -4 -6 0 -2 0 -4 -a -4 0 -424 4 0 2 0 0 a 0 0 -2 -6 0 -4 0 -6 0 -6 -4 -4 -2 -6 -4 -6 -4 -6 -2 -4 -a -4 -2 -4 * -425 6 4 2 4 0 4 0 4 4 0 4 -2 4 -2 4 -4 0 0 2 -2 0 0 0 -2 0 0 0 -2 0 0 0 026 9 2 6 4 2 4 2 2 2 -4 2 -4 2 -a 2 -4 0 -4 -2 -a -4 -2 -4 -4 -2 -2 -2 -4 0 -2 -2 -42? It 6 6 6 4 6 4 4 5 2 6 0 6 2 6 6 2 0 2 # 0 0 2 0 2 0 4 0 0 0 4 025 5 2 4 4 2 4 4 4 4 * 4 0 4 0 5 0 2 0 0 -2 a 0 -2 0 0 2 -2 0 6 0 029 422404 4022040404-a 0.2-a. . 22 2 20a0SO 6 0 2 2 2 2 2 0 2 -4 2 -2 2 -4 2 -6 0 -a o -a -2 0 - -a 0 0 0 -2 0 0 2 -233 42 44 a 444-24-24 56-22 62000 0*22 40 42 4222 4 60 42 0 2 0 0 2 -2 2 -4 0 -4 2 -6 -a -2 0 -4 -2 0 0 -4 0 -2 0 -2 6 -2 0 -2

FIGURE 70. Walsh Transform for Target RepresentingVertical Ulne Road.

59

A<

IALS COEFFICIENTS

1 2 3 4 5 6 7 11 0 a 0 1 12 13 14 15 16 1? 1S 19 20 21 22 23 24 2s 26 27 28 29 30 31 32

1 49 1 47 3 41 -1 43 -1 1-13 -1 -9 7 -? 5 -? -3 1 -7 t -9 -1 -9 1 7 -S 7 - 13 -S 11 -32 3 -3 1 1 -1 1 -1 -1 -13 1 -3 -1 -5 -5 -1 -3 - -1 -3 -S -3 -S 1 -5 -I -3 -1 -3 1 -13 S -1 3 3 3 1 3 5 3 -S 1 -3 3 -3 3 -3 1 -1 -1 -1 -I -I -I -1 1 -1 1 1 3 -I 3 14 3 3 a 3 -1 3 1 3 3 -3 3 -1 3 1 5 -1 1 1 1 -1 a 1 1 -1 3 1 1 5 3 3 1

1 -a -a 1 -3 a -3 a 1 -3 a -3 a 1 -3 -i -a -: -3 -3 - -1 -3 1 -3 1 -a a -a a -a7 I I a I I a - - ---3 -- 5 5 - -a -3 - -- -3 -3 -S1 -S - -3 -3 -3I 1 1 3 3 1 3 a a -3 1 -3 1 -1 I -2 -1 -1 -1 -3 -a -3 -3 -3 -1 -a -i -3 I -1 a -3

-I 3 3 - - - - -3 -I - - -3 -: -I -5 -3 I -3 -I -3

-aII3- -a - 3 - 3 -$ I -a a -a -a -a -a -3 -a I a -3 -a I I -3

10 3 3 S 3- - - I 3 1 1 1 1 :1 1 a 3 1 1 1 3 3 3 -I 3 3 3 3 -I -5 3 -$ 5 -a -a -I -a a -a -3 -3 3 -l I -a 3 -I

I I I I -a - a -a -3 a -I -a -3 -a -a a -3 1 -1 -1 1 1 -a13 3 3 1 3 - 5 -1 I I - - -3 1 5 I -a -I -I 5 -1 5 -5 1 1 5 I S I14 9 a 3 3 3 3I - -3 -3 I - - - - -3 -3 -- 3 -3 - -a a -3 a -I _ -3aS 1 5 3 3 1 3 1 1 -S 1 -5 1 -3 1 -S -1 -3 -3 -S -3 3 - - I -3 -I -5 -I -3 -1 -516 3 I I a -a I -a -a -3 -S a -- - - - - - - - -S -5 - -3 -: -3 -S -3 1 -S -S

57 7 5 5 5 5 3 3 5 - - -a I Ia -I -5 5 -5 -3 11 3 - 1 1 35a 75 1 5 7 -a I -a I a a I a - I 5 3 -1 3 -1 1 -

I : I i S 5 1 53 3 1 1 -I S -3 1 1 1 -1 -1 -1 1 -I 1 a 1 -I I I I20 55 7373111711 i-a13 531 533133313111as i 5 3 F 3 I 5 3 - 3 3 - -1 I -t -1 - -1 -1 3 3 1 - -1 -1

22 1 1 1 3 1 -3 3 - 1 I I I -3 - a I - -I - I - - a "1 3 t 1 *

23 5 - 3 3 I- -3 - a -a a - 3 -a - 2 -3 - 5 -a - 3 5 I -5 I I I -

24 5 1 a : I I -1 I I -5 I -1 - -3 1 -S -I -3 -3 -i -3S - -a -3 -3 1 -3 1 -a -a -321 5 3 3 3 " 3 3 I 3 3 1 -: ; : 3 :I -I I -I I I 3 - I 3 I26 7 a 3 3 a I I a - " - - -3 -I- -3 -3 - - - - - -I -- -3 1 "I I -327 3 3 1 3 5 3 - 3 -3 -13 -I 1 I 1 1- I I -I I : I -1 I 3 120 I I A 3 1 I 3 -I 3 -3 3 -a I -3 -1 -1 -1 -3 -1 -a -I -3 I -1 I -3 -1 -I I -129 3 I I 3 1 3 -I 1 -3 a -a 3 -3 3 -3 I -3 1 -3 -1 -3 -I -3 I -1 1 -I I I -1as S a a t a l a "$ -:3 - - -$ -a -3 -a -3 -3 - -3 -: -a -1 -s -3 -I -3 -I -3

3 1 I I 3 I 3 - - s - a I I I - -I -I -I I 3 - I 3 I

3 3 -1- a -- 3 -1--- -3 A 1 -- 3 -3 1 -3 - - 3 1 .-3 aI 51 -3

FIGURE 71. Fist Reptition of Walsh Transform for theSame Target Usd to Produce Figure 70.

60

IlLS COEFFICIENTS

1 2 3 4 5 6 7 9 10 It 12 13 14 I 1 IT 10 II 20 21 2t2a2 24 25 26 2? 20 29 30 i 2

1 49 1 59 5 45 -1 43 1 1-13 -1 -7 " - 7 - - -l -7 - -91 -I "7 -5 S13 -3 13 -32 -3 3 1 a a a 1 -1 -a a -3 1 -3 a -3 -3 -3 -a -a -3 -3 -a -3 -a -3 - 1 -5 1 -33 9 3 ? ? 5 3 s 3 3 -3 3 -a 5 -a I -a 3 I I -3 1 -1 -1 -I a a 3 1 31 3 14 5537373 5I 3717 a ?-1 33 -5-1 3335 5 355335 3 a - 1 -a 1 a 1 3 -a 3 -a 3 -1 3 -a I I a I a -1 I I I I I I I I

6 1 a 3 3 a 3 a a -3 3-3 3 -3 3 -a 1 -a -1 -a -a -a -3 -a 1 -1 -1 3 -1 1 -3

? 71 3 i 2 .3 3 3 -1 -a 5 -a 3 -a a a 1 a -1 -a - -a 3 -a 3 -a 3 1 5 -a1 3 a I -a 1 3 9 -1 3 -I 1 I a-a a a a1 -a 1 -1 a I-1 3 1 3 1

9 a -1 -a a -a a -a A a -a a -3 a -3 a3 -3 a -a -3 -a -a a -a a -a a -a a a 1 aa0 7 a 3 3 a a a 3 1 -a a -1 3 -a 3 -3 a a a -I -a a 1 -a a a a -1 a a 3 -1Is a 3 1 3 a 1 a a -3 1 -3 a -3 3 -g -a -3 -a -3 -3 -3 -3 -3 1 -a a -1 a -1 a -a12 1 a -a 1 -a a -a -a 1 -3 1 -S 1 -5 1 -3 -3 -3 -3 -s -3 -3 -3 -s -3 -3 -a -3 -1 -3 1 -313 a a a a -a a -a a a -1 3 -a a -3 -3 -a -3 -3 -3 -a -a -3 -3 a -1 -1 -3 1 -3 -a -3

14 "-1 5 a a J 3 " - - a -" -a -3 -$ -3 -3 -3 -5 -s -3 -3 -5 -1 -s -a -S -3 -s -a -s15 -a 3 3 a -a 3 a -1 -3 1 -a - 1 -S -3 -3 -3 -3 -3 -$ -5 -" -1 -S -a -3 -1 -3 -1 -3as a -a a a -a a -3 -1 -3 3 -1 -" -S -" -1 -7 -5 -S - -7 - -7 -$ -? -3 -S -3 -S -3 -s -5 -5a? 3 3 a a a a a a 3 -a 3 -a 3 -a a -3 a -3 1 -a -a a a -1 1 1 3 -a a a a -aIs 5 1 3 3 3 3 1 a 3 -a 3 -a a -a a -3 1 -1 I -1 -a -a -a -3 1 -a a -a a 1 1 -aIs a a a 1 a 3 a 1 -a S -3 a -a a -3 -3 -1 -a -I -3 -a -a -5 1 -a a -t 1 -a a -aas a 1 a 3 a u a 5 3 -1 3 -a a a 3 -a a a a -a a -a -I -a a a 1 -a a -a a -aaa 5 a 1 3 -a a a a a -3 a -3 -a -3 1 -5 -a -a -a -3 -3 -3 -a -5 -a -3 -a -3 -1 -3 a -322 I a a a a 3 a a a -3 1 -s a -a a s -a -3 -3 -5 -3 -3 -3 -$ a -3 1 -3 -a -a -a -323 7 3 3 3 3 3 3 1 a -3 1 -3 1 -3 a -3 -a -3 -1 -3 -3 -3 -3 -a -a -3 -a -3 -a -3 -a -324 7 3 3 3 a a a 1 3 -3 1 -3 a -3 1 -3 -a -a -3 -5 -3 -a - -3 -3 -3 -a 3 -a -3 -1 -525 7 5 1 1 a 3 3 1 5 a 7 1 5 3 7 -a 3 a a a a a a -a s a a a 3 11 -126 9 1 3 3 1 5 S S a A a -a -a a -3 a -a a -a -1 -a -a -3 a -a a -a a -1 3 -3

37 ? 5 7 9 S 7 S 1 a 1 al 7 5 A S 1 a a a a 5 a 5 a a 5 32s $ 3 a 3 a I a a 3 - 1 - 1 -a 1 -I I -I I -a I I I -A a a 3 1 3 3 a29 5 a a 3 a a A 3 a -a a -3 a - 3 -3 1 -a a -a a - I I I I I I a a 3 3 1

30 S a a 3 a a a a a -a a -3 1 -3 a -3 -a -3 -a -a -3 -3 -3 -3 -a -I I -I I a a -331 7 3 3I -1 -1 - I I I I -I - I I I -I1 3 1 3 1 1 1 5 1

32 1 a3 3 1 a a 3 a -3 3 -3 a -a a -3 -a -3 -a -3 -a -a -a -5 a -a a -3 -a -a a -3

FIGURE 72. Second Repettion of Walsh Transform for the

Same Taret Used to Produce Figure 70. 7

61

NOW

MAL$ COEFFICIENTS

1 2 3 4 5 6 7 1 9 1 11 12 13 14 15 16 17 I9 3 20 23 22 23 24 25 26 27 26 25930 31 32

1 SO 0 56 4 44 0 44 -2 2-12 -2 -0 6 -0 6 -l -6 0 -6 0 -1 0-10 -2 6 -6 4 -' 1O -4 10 -42 6 -2 2 2 0 0 0 0 0 -6 0 -6 0 -4 0 -4 -2 -4 -4 -4 -4 -4 -6 -4 -2 -4 -2 -6 0 -4 0 -23 10 2 6 4 6 2 4 4 4 -2 4 -a 4 -2 4 -a 0 -2 0 0 -2 0 0 -2 0 0 2 0 2 -2 a 04 6 6 46262662 60 62604220202-22 4404442

3 2 0 4 0 6 0 4 4 0 4 -2 4 -2 a -2 0 -2 0 -2 0 -2 0 -2 0 0 0 0 0 0 0 -26 14 a 6 4 6 4 6 2 4 -a 4 -2 4 -a 4 -2 0 0 0 -2 -a -2 -a -4 -2 -2 0 0 a -2 0 -a7 10 a 6 6 6 6 6 6 4 0 6 0 6 0 4 0 2 2 2 0 2 0 0 0 4 0 4 0 4 0 4-2

S4444 2 6244060406042402020424242423 4 2 0 4 0 4 0 4 4 0 6 0 4 0 4 -2 2 0 2 0 0 2 2 0 2 2 4 2 2 2 4 2

30 0 4 6 6 4 4 6 4 4 0 4 0 6 2 6 0 2 a a 2 . 2 4 0 4 4 4 2 6 4 4 232 6 2 6 4 4 4 4 2 2 0 4-2 4 0 4-2 0 0 0-2 0 0 2-2 2 0 4 0 2 2 4 012 4 2 0 4 0 4 0 2 2 -2 2 -2 2 -2 4 -2 0 0 0 -2 0 -2 0 -4 0 0 2 0 2 0 0 -213 2 2 0 4 -2 4 -2 2 2 -2 4 0 4 0 4 -2 0 0 0 -2 0 0 0 -2 2 0 2 0 0 0 2 014 1 2 4 2 2 0 2 0 2 -4 2 -4 2 -2 2 -6 -2 -2 0 -4 -2 -4 -4 -4 0 -2 0 -2 0 -2 2 -2is 6 0 4 2 2 0 2 2 0 -4 0 -4 0 -4 0 -6 -2 -2 -2 -4 -2 -4 -4 -4 0 -4 0 -4 # -2 0 -416 2 -2 0 0 -2 0 -2 -2 -4 -6 -2 -6 -2 -6 0 -6 -4-6-4 -6 -6 -6 -4 - -4 -6 -2 -6 -4 -4 -4 -417 2 2 0 2 0 2 0 2 4 -2 4 -4 4 -2 4 -4 0 0 0 -2 0 -2 2 -2 0 0 0 -2 0 0 0 0to 6 0 2 2 2 2 2 2 a -a 4 -2 4 -2 4 -2 0 0 0 -2 -2 0 0 -2 2 0 2 -2 2 0 2 019 1 -2 2 0 2 2 2 0 0 -4 2 -4 0 -4 0 -4 4 -2 0 -2 -2 -2 -2 -4 0 -2 0 -4 0 -2 0 -220 2 0 -2 2 -2 0 -2 0 0 -2 0 -2 2 -2 2 -4 0 -2 0 -2 0 -2 0 -2 0 * 2 -2 0 0 2 -223 0 -2 -2 -2 -4 -2 -4 -2 -2 -6 0 -6 -2 -6 0 -6 -4 -6 -4 -6 -4 -6 -4 -4 -2 -4 -2 -4 -2 -4 -2 -422 2 -2 -2 -2 -2 -2 -2 -4 -2 -6 -2 -6 -2 -6 -2 -6 -6 -6 -6 -6 -6 -6 -6 -6 -4 -4 0 -4 -2 -4 -2 -423 2 -4 4 0 -2 -2 -2 -2 -2 -6 0 -6 0 -6 -2 -4 -4 -6 -6 -6 -6 -6 -6 -6 -4 -6 -4 -6 -4 -6 -2 -624 2 -2 -2 0 -2 0 -2 -2-4 -6-2-6 -4 -8-2 -1-6 -6 -6 -1-6 -- 6-10-4 -6-6-6 -6 -6-4 -625 2 2 0 2 0 2 0 2 2 -2 2 -4 2 -4 2 -4 -2 -4 -2 -4 -4 -2 -2 -4 -2 -2 -2 -4 -2 -2 0 -426 4 0 4 0 # 0 0 4 0 -6 0 -4 0 -6 0 -6 -2 -4 -4 -4 -6 -6 -6 -6 -4 -4 -2 -4 -2 -6 -2 -62? 4 2 4 2 2 4 2 2 2 -2 2 -4 2 -2 2 -4 0 0 0 -2 -2 -2 * -4 0 0 0 -2 0 -2 0 -228 2 8 0 2 -2 0 -9 0 0 -4 0 -4 0 -4 2 -4 0 -2 -2 -4 -2 -4 -2 -4 0 -2 0 -4 0 -4 -2 -429 0 0 0 0 -2 0 0 0 0 -4 2 -4 0 -4 0 -4 -2 -2 -2 -4 -2 -4 -4 -4 -2 -2 -a -2 -2 -2 -2 -430 4 0 2 0 0 0 2 -2 0 -6 0 -6 0 -4 0 -6 -4 -4 -4 -4 -4 -4 -4 -6 -4 -4 0 -4 -2 -4 0 -431 4 0 2 4 2 4 2 2 2 -4 2 -2 2 -2 2 -4 0 -2 0 -2 0 -2 -2 -4 0 0 0 -2 0 -2 2 -232 4 0 0 2 -1 a -2 0 0 -4 2 -4 0 -4 0 -6 -2 -6 -2 -4 -2 -4 -11 -4 -2 -a 0 -4 -2 -2 -1 -4

FIGURE 73. Third Repetition of Walsh Transform for the

Sam Target Used to Produce Figure 70.

62

low' " " ' Wow-?+ ": ++ + " :'i.

CONCLUSIONS

I. The concept of direct transforms using discreate function technology has ahigl potential for cartographic feature extraction.

2. An electro-optical system employing a plasma discharge device as a lightsource proved to be capable for producing Walsh transforms of topographic features.

3. The system can produce two-dimensional. 512 by 512 (262,144) Walshfunctions and a same number of associated Walsh coefficients in about 14 seconds.

4. In general, the signal signatures of the Walsh spectrum are less complicatedthan the spatial signal signature.

5. The significant spectral components are distributed among a few low orderWalsh transform coefficients. Further, each transform pattern is unique in itself, and canbe distinguished easily from the rest.

6. A simple decision procedure, either in hardware or software, can be imple--mented to detect and recognize the above selected cartographic features automaticalK.

7. The plasma filter of PISA has not yet reached the technical maturity to beimplemented in high reliability equipment.

8. The most attractive feature of the plasma tube is that it constitutes a largenumber of parallel-accessible electrodes in two-dimensions, thus providing the possibilityof high speed electronic scanning with discrete funtions.

63

' t

APPENDIX

.3 -02 UN 0406300&MCOEF T100003 IS ON CR00010 USING 00015 SLKS R-0000

. o1 FTN4,L0002 C...e.s*.SPROCRAM MWCOEF--REV 20/5.e....aaa...e0003 C0004 C PROGRAM TO INPUT WALSH COEFFICIENTS FROM0005 C THE PROTOTYPE IMAGE SPECTRUM ANALYZER (PISA)0006 C AND DISPLAY THEM ON THE TEKTRONIX 6010007 C0009 C0009 PROGRAM WCOEF0010 DIMENSION IDISP(1026),IVID(1026).LABEL(I0).INPUT(14)0011 DIMENSION LABL2(10),LASL3(l0)0012 DIMENSION IBUF(1026),ICOEF(1026)0013 DATA LABEL/2NUA..2HLS.2H ,2HCO,2HEF,2HFI,20CI,2HEN.2HTS-2H0014 DATA LA9L2/2HPl,2NSA.2N I,2NNP.2HUT,502N0015 DATA LABL3/2HDI, 2NSP, 2HLA, 2HY *2MOU, 2HTP, 2HUT, 3*2H0016 DATA INPUT/2HIC.2HDM.2HPC,2HTR.2MLU,2HTN.2NIT. 2HPI.2NPD. 2NDS/00 1? CI0010 C0019 ITHRS-00020 LU-20021 NCHRa?20022 MRITE(2,10)00-23 10 FORMAT(DISPLAY CHANNEL?*)0024 READ( 1,1 )ISCI0025 WRITE(2,16)

'126 16 FORMAT( ' INPUT CH4ANNEL?'027 READ( 1 15 )ISC2

0028 t5 FORMAT(K2)0029 17 MRITE(2.,20)0030 20 FORMAT('DISPLAY DIMENSION?,)0031 GO TO 2000032 C0033 C INPUT LOOPER0034 C0035 C IC--INPUT AND PROCESS COEFFICIENTS0036 C P1--PRINT RAg PISA INPUT0037 C DM--SET DISPLAY DIMENSION0038 C PC--PRINT COEFFICIENTS0035 C PD--PRINT DISPLAY SUFFER0040 C LU-- INPUT LIST LU0041 C IT-- INPUT THRESHOLD VALUE0042 C TH--TNRESHOLD DATA WITHOUT INPUT0043 C DS--DISPLAY COEFFICIENTS0044 C TR--TERMINATE PROGRAM0045 C0046 30 MRITE(2,40)0047 40 FORMAT0??")0046 READCi.5o)iN0045 50 FORMAt(a2)0050 IF ( IN.EI.INPUTUl))CALL MATOT(ISUF.LASL2,N,.N.3,LUNCNR)4051 IF (IN.EQ.INPUT(I))GO TO 100052 IF ( IN.ED.IMPUTc2))0 TO 200

0053 IF CIN.E0.INPUTU3)CALL NATOT(ICOEFLAUELNN,2,LUNCNRt)0054 IF (IN.E0IMIPUT(4))STOP0051 IF (IN.EI.INPUTcU))GO TO 4000056 IF ( IN.EI.INPUTc7)YREAD( l,e)ITNRS0057 IF CIN.E0IIPUTC6))90 TO 0

64t

= I In-- ---- vd

APPENDIX Continued

0058 IF (IN.EO.IHPUT(9))CALL NATOT(IVID,LABL3,N,N,2,LU,NCHR)0059 IF (IN.EQ.INPUT(10))CALL OSPLA(IDISP,NELS,ISCI).o60 GO TO 30

)61 C0062 C THIS SECTION PERFORMS THE FOLLOWING OPERATIONS0063 C0064 C INPUTS N X N COEFFICIENTS INTO 'IOUF" WITH *PISA*0065 C COMPUTES AOO AS TWICE THE AVG. OF ALL COEFFICIENTS0066 C SCALES COEFFICIENTS IN THE RANGE, 0-990067 C COMPUTES ACTUALL COEFFICIENTS BY SUBTRACTING 1/2 AO00068 C THRESHOLDS COEFFICIENTS AND DSIPLAY ACCORDING TO 'ITHRS'0069 C SCALES COEFFICIENTS FOR VIDEO DISPLAY0070 C0071 100 CALL PISA(IBUFHISC2)

0072 AO0O.00073 DO 140 I-2,NELS0074 140 AOO-AOO+IBUF(I)0075 IBUF.2*AOO/NELS0076 IBUF(NELS+I)=O0077 IBUF(HELS*2)s10230078 500 I-NELS+2

0079 CALL ISCAL(IBUFICOEFIO,99)0080 DO 110 I-2,HELS0081 li1 ICOEF(I).2sICOEF(I)-ICOEF0082 IVID(HELS+I)-O0083 IVID(HELS+2)-990084 00 120 I=I,NELS

0095 IF (IABS(ICOEF(I)).GE.ITHRS)GO TO 130'086 ICOEF(1).O087 IVID(I)-O

0088 GO TO 1200089 130 IVID(I)-IABS(ICOEF(I))0090 120 CONTINUE0091 I-NELS420092 CALL ISCAL(IVIDIVIOI,0,1 )0093 CALL DSGEN(IDISPIVID,O)094 GO TO 300095 C0096 C THIS SECTION INPUTS THE HEM COEFFICIENT NATRIX0097 C DIMENSION AND GENERATES THE X-Y DISPLAY COORDINATES0098 C WITH SUBROUTINE *DSGEN"0099 C0100 200 READ(t,*)N0101 MELS-N*N

0.42 IF (NELS.GT.IO24)6O TO 170103 ICBIT.IPVR2(N)0104 CALL OSGEN(IDISPIVID,-3,1CUIT,6,N,4)0101 GO TO 300106 C0107 C0106 400 READ(1I,15)LU0109 NCNRO?20110 IF (LU.EI.6)NCNR-I320111 GO TO 30112 END

v113 ENDS

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