dsp intro slides

8/6/2019 DSP Intro Slides

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1-1LECTURE 1Copyright 1998, Texas Instruments Incorporated All Rights Reserved

What Is DSP?

a bit loudAnalog Computer

Digital Computer

ADC

DSP

DAC OUTPUT

1010 1001


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A Typical DSP System

DSP Chip

Memory

Converters (Optional) Analog to Digital

Digital to Analog

Communication Ports Serial Parallel

DSP

MEMORY

ADC

PORTS

DAC


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Multiply and Add

Most Common Operation in DSP

A = B*C + D

Multiply, Add, and Accumulate

E = F*G + A

..

.

MAC Instruction

1+2 = 3

+

0001

0010

0011

Add Multiply5*3 = 15

Typically 70 Clock Cycles WithOrdinary Processors

MAC Operation

0101

xxxx

8421

0011001100110011

xxxx

00000011

00000011

=5 3

Shifted and

addedmultiple times

Typically 1 Clock Cycle WithDigital Signal Processors


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Drop in Multiplication Times

0

100

200

300400

500

600

1971 1976 1998

YEARS

TIME (ns)

5 ns


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Digital Computers

STOREDPROGRAM

ANDDATA

ARITHMETICLOGIC

UNIT

INPUT/

OUTPUT

von Neuman Machine

Harvard Architecture

STOREDPROGRAM

ARITHMETICLOGIC

UNIT

INPUT/

OUTPUTSTORED

DATA

A

DD

D

AA

A = ADDRESS

D = DATA


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An ExampleTMS320C31 Architecture

P = PROGRAM D = DATA

D31-D0

A23-A0

DMA SERIALPORT 0

TIMER 1

TIMER 0

RAM 01K x 32

CACHE64 x 32

RAM 11K x 32

7 SEPARATE BUSES ( P / D )

MULTIPLIER ADDER

MULTIPLEXER

PERIPHE

RAL

BUS

(P\D)

FLOATING POINT ARITHMETICLOGIC UNIT


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DSP Development

DSP

ASSEMBLER

HIGH-LEVEL LANGUAGE

EMULATOR

ADD A, B

Tools of the Trade

TEST

S/W DESIGN

OK?

Y

N

PRODUCT

CODE

11100010010100001001


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Why Digital Processing?

Advantages to Digital Processing

Programmability

Stability

Repeatability

Special Applications

ADC DACPROCESS


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One Hardware = Many Tasks

Upgradability and Flexibility Develop New Code Upgrade Analog Solder New Component

Programmability

LOW-PASS FILTER

MUSIC SYNTHESIZER

MOTOR CONTROL

SOFTWARE 1

SOFTWARE 2

SOFTWARE N

SAMEHARDWARE.

...


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Analog Variability

Analog Circuits are affected byTemperature

Aging

Tolerance of ComponentsTwo Analog Systems using the same design andcomponents may differ in performance

1k + 10 years = 1.1k


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Digital Repeatability

Perfect Reproducibility Nearly identical performance from unit to unit

Performance not affected by tolerance

No drift in performance due to temperature or aging

Guaranteed accuracy

A CD player always plays the same musicquality


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Performance

Some special functions are best implemented digitally

f

f1 f2

phase

frequency

gain

frequency

Lossless Compression

Linear Phase Filters Adaptive Filters


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Practical DSP Systems

Hi-Fi Equipment

Toys

VideophonesModems

Phone Systems

3D Graphics

Image Processing

And More ...


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Analog Advantages

Low cost and simplicity in some applications Attenuators/amplifiers

Simple filters

Wide bandwidth (GHz) Low signal levels

Infinite effective sampling rate Infinite resolution in frequency

No aliasing/reconstruction issues

Infinite resolution in amplitude No quantitation noise


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Digital Signal Processing (DSP)

Advantages Repeatability

Low sensitivity to component tolerances

Low sensitivity to temperature changes

Low sensitivity to aging effects

Nearly identical performance from unit to unit

Matched circuits cost less

High noise immunity

In many applications DSP offers higher

performance and lower cost CD players versus phonographic turntable


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Analogs Place in DSP

Most transducers are analog by nature Microphones, speakers, etc.

Analog circuits are required to pre-process low

level signals before ADC Analog filters may be required to limit the

bandwidth of signals Anti-alias (before ADC) and reconstruction filters (after

DAC) Analog circuits may be required to drive output

transducers A power amplifier is required to enable a DAC to drive

a speaker


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Number Systems Represent numbers digitally

Decimal 3 in binary

Any number can be represented as a series of 1s and 0s

Decimal 26 in binary

Decimal 128 64 32 16 8 4 2 1

2DigitNumber 27 26 25 24 23 22 21 20

DigitNumber 7 6 5 4 3 2 1 0

Decimal 0 0 016+ 8+ 02= 0 26

2DigitNumber 27 26 25 24 23 22 21 20

DigitNumber 7 6 5 4 3 2 1 0

Binary 0 0 0 1 1 0 1 000011010

Decimal 0 0 0 0 0 0 2+ 1= 3

2Digit Number

27

26

25

24

23

22

21

20

Digit Number 7 6 5 4 3 2 1 0

Binary 0 0 0 0 0 0 1 1 0000 0011


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Binary and Hex

Decimal 0,1,2,.,9

Binary 0,1Hex 0,1,2,..,A,B,C,D,E,F

16 Decimal 0x10 Hex20 Decimal 0x14 Hex

4 bits of binary system is represented by a single hex digit

Decimal 26 in binary and hex

Decimal 8+ 4+ 2+ 1=15

2DigitNumber 23 22 21 20

Binary 1 1 1 1 1111

Hex F F

Decimal 0 0 016+ 8+ 02= 0 26

2DigitNumber 27 26 25 24 23 22 21 20

Digit Number 7 6 5 4 3 2 1 0

Binary 0 0 0 1 1 0 1 000011010

Hex 1 A 1A


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Signed Integers

Signed magnitude integers

Signed

BinaryDecimalHex

Sign Number

2 00000002 0 0000000000000000000000000000010

3 00000003 0 0000000000000000000000000000011

-2 80000002 1 0000000000000000000000000000010

-3 80000003 1 0000000000000000000000000000011


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Twos Complement Notation

2Digitnumber -27 26 25 24 23 22 21 20

Decimal -128 64 32 16 8 4 2 1

Binarytwoscomplement 3 0 0 0 0 0 0 1 1

Decimal

calculation0 0 0 0 0 0 +2 +1= 3

Binary

twoscomplement-2 1 1 1 1 1 1 1 0

Decimal

calculation-128 +64 +32 +16 +8 +4 +2 +0= -2


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Twos Complement

Conversion to twos complement notation

Twos complement addition

BinaryAction Decimal

Sign Number

Signedinteger -2 1 0000000 000000000000000000000010

Stripsignbit 0 0000000 000000000000000000000010

Invert 1 1111111 111111111111111111111101

Addone 1 1

Twoscomplement 1 1111111 111111111111111111111110

Hex F F F F F F F E

TwosComplementBinaryDecimal HexSign Number

-2 FFFFFFFE 1 1111111 111111111111111111111110

3 00000003 0 0000000 000000000000000000000011

-2+3=1 00000001 0 0000000 000000000000000000000001


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Fixed-Point NotationConventions

Number range is between 1 and -1 Decimal point is always in a fixed location (e.g., 0.74, 0.34, etc.) Multiplying a fraction by a fraction always results in a fraction and will

not produce an overflow (e.g., 0.99 x 0.9999 = less than 1) Successive additions may cause overflow

Why?

Signal processing is multiplication-intensive Fixed-point notation prevents overflow (useful with a small dynamic

range) Fixed-point notation is less expensive

How is fixed-point notation realized in a DSP? Most fixed-point DSPs are 16 bits

The range of numbers that can be represented is 32767 to -32768 The most common fixed-point format is Q15

Q15 Notation

Bit15 Bits14to0

sign twoscomplementnumber


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Q15 Format

Dynamic range in Q15

Number representations in Q15

Rules for operationsAvoid operations with numbers larger than 1

2.0 x (0.5 x 0.45) = (0.2 x 0.5 x 0.45) x 10 = (0.5 x 0.45) + (0.5 x 0.45)

Scale numbers before the operation

0.5 in Q15 = 0.5 x 32767 =16384

Number Biggest Smallest

Fractional number 0.999 -1.000

ScaledintegerforQ15 32767 -32768

Decimal Q15=Decimalx215 Q15Integer

0.5 0.5x32767 16384

0.05 0.05x32767 1638

0.0012 0.0012x32767 39


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Q15 Operations

Addition

Multiplication

2 x 0.5 x 0.45 =

Decimal Q15 Scaleback

Q15/ 32767

0.5+0.05=0.55 16384+1638=18022

0.55

0.50.05=0.45 163841638=

Decimal Q15 BacktoQ15

Product/ 32767

Scaleback

Q15/ 32767

0.5x0.45=0.225 16384x14745=

241584537

7373

0.225+0.225=0.45 7373+7373=

14746

0.45


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TMS Floating-Point Format

Conversion equationsBinary Decimal Equation

s = 0 X = 01.f x 2e

X = 01.f x 2e 1

s = 1 X = 10.f x 2e

X = ( -2 + 0.f ) x 2e 2

Special cases = 0 X = 0 e = -128

e = exponent is a signed twos compliment 8-bit field and determinesthe location of the binary Q point

s = sign of mantissa (s = 0 positive, s =1 negative)

f = fractional part of the mantissa; an implied 1.0 is added to this fractionbut is not allocated in the bit field since this value is always present

TMS single-precision floating-point format31 ... 24 23 22 .............. 0

e s f

8 bits 1 bit 23 bits

Bit No

Exponent (e)

Hextwos comp. 00 01 7F FF 80

Decimal 1 127 -1 -1280


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Floating-Point Numbers

Calculate 1.0e0In hex 00 00 00 00In binary 0000 0000 0000 0000 0000 0000 0000 0000

s = 0 Equation 1 applies: X = 01.f x2e

01.0 x 20 = 1.0

e = 0

f = 0

Calculate 1.5e01In hex 03 70 00 00

In binary 0011 0111 0000 0000 0000 0000 0000 0000s = 0 Equation 1 applies: X = 01.f x2e

0011 e = 3s111 f = 0.5 + 0.25 + 0.125 = 0.875

X = 01.875 x 23

= 15.0 decimal

...


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More on Floating Point

Calculate -2.0e0In hex 00 80 00 00In binary 0000 0000 1000 0000 0000 0000 0000 0000

s = 1 Equation 2 applies: X = ( -2.0 + 0.f ) x 2e

( -2.0 + 0.0 ) x 20 = -2.0

e = 0

f = 0

Addition

1.5 + (-2.0) = 0.5

Multiplication1.5e00 x 1.5e01 = 2.25e01 = 22.5


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Dynamic Range

Numbers Base 2 Decimal

TwosComplement

Hex

Largest Integer 231

- 1 2 147 483 647 7F FF FF FF

Smallest Integer - 231 -2 147 483 648 80 00 00 00

Largest Q15 215

- 1 32 767 7F FF

Smallest Q15 - 215 -32 768 80 00

Largest Floating Point ( 2 - 2-23

) x 2127

3.402823 x 1038 7F 7F FF FD

Smallest Floating Point -2 x 2127

-3.402823 x 1038 83 39 44 6E

Ranges of number systems

The dynamic range of floating-point representation is very large Conclusion

Largest integer x (1.5 x 10 29 ) ~ = largest floating point

Largest Q15 x (1.03 x 10 34 ) ~ = largest floating point


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Fixed vs. Floating Point

Characteristic Floating point Fixed point

Dynamic range much larger smaller

Resolution comparable comparable

Speed comparable comparable

Ease of programming much easier more difficult

Compiler efficiency more efficient less efficient

Power consumption comparable comparable

Chip cost comparable comparable

System cost comparable comparable

Design cost less more

Time to market faster slower

Comparison

DSP devices are designed as floating point or fixed point

Fixed-point devices are usually 16-bits, e.g. TMS320C5x Floating-point devices are usually 32-bits, e.g. TMS320C3x Floating-point devices usually have a full set of fixed-point instructions Floating point devices are easier to program Fixed-point devices can emulate floating point in software

S


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TMS320 Family

16-Bit Fixed Point Devices

C1x Hard-Disk Controllers

C2x Fax Machines

C2xx Embedded Control

C5x Voice Processing

C54x Digital CellularPhones

32-Bit Floating Point Devices

C3x Videophones

C4x Parallel Processing

Other Devices

C6x Advanced VLIWProcessor

Wireless BaseStations/PooledModems

C8x Video Conferencing


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TMS320C54x Architecture

Tregister

A(40) B(40)

Multiplier (17y17)

Fractional

0

er

ystemcontrointerface

rograma ressgeneratonogc

ataa ressgeneratonogc

PC, IPTR, RC,, ,

ARAU0, ARAU1AR0-AR7

ARP, BK, DP, SP

Memoryan

externainterface

erp eranterace

Sign ctr Sign ctr

MUX

gn ctr gn ctr gn ctr

Barrel

MUX

TR

select

CAB D

BAAB

A Accumulator AB Accumulator B

ata usata us

E EBdatabusM MACunitP PBprogrambus

arre s terregster

egen

E


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ALU Functional Diagram

MUX

CB15 - CB0

DB15 - DB0

MUX

Sign ctr

40

Sign ctr

40

MUX

A B

ACCALU

Y X

SXM

40

4040

Shifter output (40)

OVM

C16

C

OVA/OVB

TC

SXM

ZA/ZB

T

A B T DC S

MACoutput

A M U B A Accumulator AB Accumulator BC CB data busD DB data busM MAC unitS Barrel shifterT T registerU ALU

Legend:


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Two C54x Memory Maps

8000h

2000h

4000h

6000h

C000h

E000h

FFFFh

0000h External

On-chip DARAM

ReservedOVLY=1

OVLY=0

0000h-007Fh

'541 Data Memory'541 Program Memory

0080h-13FFh

0000h-13FFh

In terrupt vec tors(ex ternal )

ExternalMP/ MC =1 9000h-FF7Fh

FF80h-FFFFh

MP/ MC =0 On-chip ROM9000h-FF7Fh

I n t e r ru p t v e c t o r s(internal)

FF80h-FFFFh

8000h

A000h

2000h

4000h

6000h

C000h

E000h

FFFFh

0000h

External1400h-8FFFh

0000h-005Fh

0060h-007Fh

0080h-13FFh On-chip DARAM

Scratch-pad DARAM

Memory-mapped regis ters

External1400h-DFFFh

External

Reserved

DROM=1

DROM=0

E000h-FEFFh

FF00h-FFFFh

E000h-FFFFh

On-chip ROM

A000h


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Direct Addressing Block Diagram

Data bus EB(16)

CPL

Data bus DB(16)

SP(16)

DP(9)

7 LSBs from IR (dma)

EA = SP + offset(IR)

EA = DP : offset(IR)

DAGEN

DAB(16) (read)

EAB(16) (write)or

CAB(16)

(32-bit read)

1

0

CPL

Legend: EA Effect ive address

IR Instruction register


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C54x Program Memory

PAGEN

R C

Repeat registers

B R C

RSA

REA

PC


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C54x Pipeline

Prefetch Fetch Decode Access Read Execute/write

L o a d s P B w i t h t h e

f e t c h e d i n s t r u c t i o nw o r d

L o a d s P A B w i t ht h e P C ' s c o n t e n t s

L o a d s I R w i t h t h e c o n t e n t so f P BD e c o d e s t h e I R ' s c o n t e n t s

L o a d s D B w i t h t h e d a t a 1r e a d o p e r a n dL o a d s C B w i t h t h e d a t a 2r e a d o p e r a n dL o a d s E A B w i t h t h e d a t a 3w r it e a d d r e s s , i f r e q u i r e d

L o a d s D A B w i t h t h e d a t a 1 r e a d

a d d r e s s , if r e q u i r e dL o a d s C A B w i t h t h e d a t a 2 r e a da d d r e s s , if r e q u i r e dU p d a t e s a u x i l i a r y r e g i s t e r s a n ds t a c k p o i n t e r

E x e c u t e s t h e i n s t r u c t io n

a n d l o a d s E B w i t h w r i t ed a t a

Time


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Serial Port Interface Block

Diagram

B y t e / w o r dc o u n t e r( C l o c k )

( C l e a r )( C l e a r )

( C l o c k )

D a t a B u s

L o a dc o n t r o l

l o g i c

L o a dC o n t r o l

L o g i c

D R R ( 1 6 )

R S R ( 1 6 )

B y t e / w o r dc o u n t e r

X S R ( 1 6 )

D X R ( 1 6 )

F S X

C L K XC L K R

F S R

( L o a d )

( L o a d )

16

16

16

16R I N T o n

R S R - D R Rt r a n s f e r

X I N T o nD X R - X S Rt r a n s f e r

DXDR


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C54x External Bus Interface

EB WriteCB/DB Reads

PB Fetch

FetchReadReadWriteD(15 - 0)

A(22 - 0)

CLKOUT

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