dsp mitra chap1

8/10/2019 DSP Mitra Chap1

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Copyright 2002 S. K. Mitra1

Signals and Signal ProcessingSignals and Signal Processing

Signals play an important role in our dailylife

A signal is a function of independent

variables such astime,distance,position,

temperature,andpressure

Some examples of typical signals are shownnext


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Examples of Typical SignalsExamples of Typical Signals Speech and music signals- Represent air

pressureas a function of timeat a point in

space

Waveform of the speech signal I like

digital signal processing is shown below

0 1 2 3-1

-0.5

0

0.5

1

Time, sec.

Amplitude


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Examples of Typical SignalsExamples of Typical Signals

Electrocardiography (ECG) Signal-Represents the electrical activity of the

heart

A typical ECG signal is shown below


4/125Copyright 2002 S. K. Mitra4

Examples of Typical SignalsExamples of Typical Signals The ECG trace is a periodic waveform

One period of the waveform shown belowrepresents one cycle of the blood transfer

process from the heart to the arteries

P

R

Q

S

T

Millivolts

Seconds



Examples of Typical SignalsExamples of Typical Signals Electroencephalogram (EEG) Signals-

Represent the electrical activity caused bythe random firings of billions of neurons in

the brain




Seismic Signals- Caused by the movementof rocks resulting from an earthquake, a

volcanic eruption, or an underground

explosion

The ground movement generates 3types of

elastic waves that propagate through thebody of the earth in all directions from the

source of movement




Typical seismograph record


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Examples of Typical SignalsExamples of Typical Signals Black-and-white picture- Represents lightintensityas a function of two spatial

coordinates

I(x,y)


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Video signals - Consists of a sequence of

images, called frames, and is a function of 3variables:2spatial coordinatesand time

1Frame 3Frame 5Frame

Video

videotheonClick


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Signals and Signal ProcessingSignals and Signal Processing

Most signals we encounter are generatednaturally

However, a signal can also be generated

synthetically or by a computer


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Signals and Signal ProcessingSignals and Signal Processing A signal carries information

Objective of signal processing: Extract theuseful informationcarried by the signal

Method information extraction: Depends onthe type of signal and the nature of the

information being carried by the signal

This course is concerned with the discrete-

time representation of signals and their

discrete-time processing


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Characterization andCharacterization and

Classification of SignalsClassification of Signals

Types of signal: Depends on the nature ofthe independent variables and the value of

the function defining the signal

For example, the independent variables can

be continuous or discrete

Likewise, the signal can be a continuous ordiscrete function of the independent

variables


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Moreover, the signal can be either a real-valuedfunction or a complex-valued

function

A signal generated by a single sourceis

called a scalar signal

A signal generated by multiple sourcesiscalled a vector signalor a multichannel

signal


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A one-dimensional(1-D) signalis afunction of a single independent variable

A multidimensional(M-D) signalis a

function of more than one independent

variables

The speech signalis an example of a 1-Dsignal where the independent variable is

time


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An image signal, such as aphotograph, isan example of a 2-D signalwhere the 2

independent variables are the 2spatial

variables

A color image signal is composed of three

2-Dsignals representing the threeprimarycolors:red, greenandblue(RGB)


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The 3color components of a color imageare shown below


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The full color image obtained by displayingthe previous 3color components is shown

below


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Classification of SignalsClassification of Signals Each frameof a black-and-white digital

video signalis a 2-D image signalthat is afunction of 2discrete spatial variables, with

each frameoccurring at discrete instants oftime

Hence, black-and-white digital video signal

can be considered as an example of a 3-D

signalwhere the 3independent variables are

the 2spatial variables andtime


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Classification of SignalsClassification of Signals A color video signal is a 3-channel signal

composed of three3-D signalsrepresentingthe three primary colors:red,greenandblue

(RGB) For transmission purposes, the RGB

television signalis transformed into another

type of 3-channel signalcomposed of a

luminancecomponent and 2chrominance

components


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For a 1-D signal, the independent variable isusually labeled as time

If the independent variable is continuous,

the signal is called a continuous-time signal

If the independent variable is discrete, the

signal is called a discrete-time signal


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Classification of SignalsClassification of Signals A continuous-time signalis defined at every

instant of time

A discrete-time signalis defined at discrete

instants of time, and hence, it is a sequenceof numbers

A continuous-time signal with a continuousamplitude is usually called an analog signal

A speech signal is an example of an analog

signal


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Classification of SignalsClassification of Signals A discrete-time signal with discrete-valued

amplitudes represented by a finite numberof digits is referred to as the digital signal

An example of a digital signal is thedigitized music signal stored in a CD-ROMdisk

A discrete-time signal with continuous-valued amplitudes is called a sampled-data

signal


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A digital signal is thus a quantized sampled-data signal

A continuous-time signal with discrete-

value amplitudes is usually called a

quantized boxcar signal

The figure in the next slide illustrates the 4types of signals


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signaltime-continuousA

signaldata-sampledAsignalboxcarquantizedA

tTime,

Amplitude

tTime,

Amplitude

tTime,

Amplitude

tTime,

Amplitude

signaldigitalA


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For a discrete-time 1-Dsignal, the discreteindependent variable is usually denoted by

n

For example, {v[n]}represents a discrete-

time 1-D signal

Each member, v[n], of a discrete-time signalis called a sample


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In many applications, a discrete-time signalis generated by samplinga parent

continuous-time signal at uniform intervals

of time

If the discrete instants of time at which a

discrete-time signal is defined are uniformlyspaced, the independent discrete variable n

can be normalized to assume integer values


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In the case of a continuous-time 2-Dsignal,the 2independent variables are the spatial

coordinates, usually denoted byxandy

For example, the intensityof a black-and-

white image at location (x,y) can be

expressed asu(x,y)


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On the other hand, a digitized image is a 2-Ddiscrete-time signal, and its 2independent

variables are discretized spatial variables,

often denoted by mandn

Thus, a digitized image can be represented as

v[m,n] A black-and-white video signal is a 3-D

signal and can be represented asu(x,y,t)


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A color video signalis a vector signalcomposed of 3signals representing the 3

primary colors:red,green,andblue

!!

!

"

#

$$

$

%

&

'

),,(),,(

),,(

),,(tyxbtyxg

txr

tyxu


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A signal that can be uniquely determined bya well-defined process, such as a

mathematical expression or rule, or table

look-up, is called adeterministic signal

A signal that is generated in a random

fashion and cannot be predicted ahead oftime is called arandom signal


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Typical Signal ProcessingTypical Signal Processing

ApplicationsApplications

Most signal processing operations in thecase of analog signals are carried out in the

time-domain

In the case of discrete-time signals, both

time-domainor frequency-domain

operations are usually employed


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Elementary Time-DomainElementary Time-Domain

OperationsOperations Three most basic time-domain signal

operations arescaling,delay, andaddition

Scalingis simply the multiplicationof a

signal either by a positive or negativeconstant

In the case of analog signals, the operationis usually called amplification if themagnitude of the multiplying constant,

called gain, is greater than1


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OperationsOperations

If the magnitude of the multiplying constant

is less than 1, the operation is called

attenuation

Ifx(t)is an analog signal that is scaled by a

constant (, then the scaling operation

generates a signaly(t) = (x(t) Two other elementary operations are

integrationanddifferentiation


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The integrationof an analog signalx(t)

generates a signal

The differentiationof an analog signalx(t)

generates a signal

) **' +,

t

dxty )()(

dt

tdxtw

)()( '


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OperationsOperations The delayoperation generates a signal that is

a delayed replicaof the original signal

For an analog signalx(t),

is the signal obtained by delayingx(t)by the

amount of time which is assumed to be apositivenumber

If is negative, then it is an advance

operation

)()( ottxty ,'

ot

ot


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Many applications require operations

involving two or more signals to generate a

new signal

For example,

is the signal generated by the additionof thethree analog signals, , , and

)()()()( 321 txtxtxty --'

)(3tx)(1tx )(2tx


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Theproductof 2signals, and ,

generates a signal

The elementary operations discussed so far

are also carried out on discrete-time signals

More complex operations operations areimplemented by combining two or more

elementary operations

)(1tx )(

2tx

)()()( 21 txtxty .'


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FilteringFiltering

The range of frequencies that is allowed to

passthrough the filter is called the

passband, and the range of frequencies that

isblockedby the filter is called thestopband

In most cases, the filtering operation foranalog signals is linear


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FilteringFiltering

The filtering operation of a linear analog

filter is described by the convolution

integral

wherex(t)is the input signal,y(t)is theoutputof the filter, and h(t)is the impulse

responseof the filter

) ***,' ++,

dxthty )()()(

Filt i


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FilteringFiltering

A lowpass filterpasses all low-frequency

components below a certain specified

frequency , called the cutoff frequency,and blocks all high-frequency components

above A highpass filterpasses all high-frequency

components a certain cutoff frequency

and blocks all low-frequency components

below

cf

cf

cf


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FilteringFiltering Abandpass filterpasses all frequency

components between 2cutoff frequencies,and , where , and blocks allfrequency components below the frequency

and above the frequency Abandstop filterblocks all frequency

components between 2cutoff frequencies,and , where , and passes all

frequency components below the frequency

and above the frequency

1cf 2cf 21 cc ff /

1cf 2cf 21 cc ff /

1cf 2cf

1cf 2cf


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FilteringFiltering Figures below illustrate the lowpassfiltering of an input signal composed of 3

sinusoidal components of frequencies 50Hz, 110Hz, and 210 Hz

0 20 40 60 80 100

-4

-2

0

2

4

Time, msec

Amplitude

Input signal

0 20 40 60 80 100

-1

-0.5

0

0.5

1

Time, msec

mp

u

e

Lowpass filter output


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FilteringFiltering

Figures below illustrate highpassand

bandpassfiltering of the same input signal

0 20 40 60 80 100-1

-0.5

0

0.5

1

Time, msec

mp

ue

Highpass filter output

0 20 40 60 80 100-1

-0.5

0

0.5

1

Time, msec

mp

ue

Bandpass filter output


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FilteringFiltering

There are various other types of filters

A filter blocking a single frequency

component is called a notch filter

A multiband filterhas more than one

passband and more than one stopband

A comb filterblocks frequencies that areintegral multiples of a low frequency


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FilteringFiltering

In many applications the desired signal

occupies a low-frequency band from dc tosome frequency Hz, and gets corrupted

by a high-frequency noisewith frequency

components above Hz with

In such cases, the desired signal can be

recovered from the noise-corrupted signalby passing the latter through a lowpass filter

with a cutoff frequency where

Lf

f Lff 0

cf cL fff //


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Generation of ComplexGeneration of Complex


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SignalsSignals

A signal can be real-valuedor complex-

valued

For convenience, the former is usually

called a real signalwhile the latter is calleda complex signal

A complex signalcan be generated from areal signalby employing a Hilbert

transformer



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SignalsSignals Theimpulse responseof a Hilbert

transformer is given by

Consider a real signalx(t)with a

continuous-time Fourier transform(CTFT)

X(j1)given by

tthHT 2'

1)(

)'1+

+,

1, dtetxjX tj)()(


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SignalsSignals Thus we can write

where is the portion ofX(j1)occupying thepositive frequency rangeand

is the portion ofX(j1) occupying

the negative frequency range

)()()( 1-1'1 jXjjXjX np)( 1jX

p

)( 1jn



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SignalsSignals Ifx(t)is passed through a Hilbert

transformer, its outputy(t)is given by:

The spectrum Y(j1)ofy(t)is given by the

product of the CTFTs of andx(t)

) ***,'

+

+,dxthty

HT)()()(

)(th T



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SignalsSignals The CTFT of is given by

Therefore

)( 1jHT

)(thHT

3

45

/1

01,'1

0,

0,)(

j

jjHHT

)()()( 11'1 jXjHjY HT

)()( 1-1,' jXjjXj np



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SignalsSignals As the magnitude and phase of Y(j1)are an

even and odd function, respectively, it

follows from

thaty(t)is also a real function

Consider the complex signalg(t):

g(t) =x(t) +j y(t)

)()()( 1-1,'1 jXjjXjjY np



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SignalsSignals The CTFT ofg(t)is thus given by

In other words, the complex signalg(t),

called an analytic signal, has onlypositive

frequency components

)(2)()()( 1'1-1'1 jXjYjjXjG p

6)(tx

)(tx

)(tyHilbertrTransforme

partreal

partimaginary

)()()( tyjtxtg -'


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Modulation and DemodulationModulation and Demodulation For efficient transmission of a low-

frequency signal over a channel, it is

necessary to transform the signal to a high-

frequencysignal by means of amodulationoperation

At the receiving end, the modulated high-frequency signal is demodulatedto extract

the desired low-frequency signal


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Modulation and DemodulationModulation and Demodulation There are 4major types of modulation of

analog signals:

(1) Amplitude modulation

(2) Frequency modulation

(3) Phase modulation

(4) Pulse amplitude modulation

Amplitude ModulationAmplitude Modulation


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Amplitude modulation is conceptuallysimple

Here, the amplitude of a high-frequencysinusoidal signal , called thecarrier signal, is varied by thelow-frequencysignalx(t), called the modulatingsignal

Process generates a high-frequency signal,called modulated signal,y(t)given by:

)cos( otA 1

)cos()()( ottAxty 1'


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Amplitude ModulationAmplitude Modulation Thus, amplitude modulation can be

implemented by forming theproductof the

modulating signal with the carrier signal

To demonstrate the frequency translatingproperty, let

x(t) =where

)cos( 1t1

o1 1//1


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Amplitude ModulationAmplitude Modulation Then

The CTFT of Y(j1)ofy(t)is given by

whereX(j1

)is the CTFT ofx(t)

)cos()cos()( o1 ttAty 1.1'

7 8 7 8tt AA )(cos)(cos1o21o2

1,11-1'

7 8 7 8)()()( o2o2 1-1-1,1'1 jXjXjY AA



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Spectra of the modulating signalx(t)and the

modulated signaly(t)are shown below

)( 1jY

1

o1

o1,

m1,1

o)(

o m1,1, 0

2A

)( 1j

1m1m1, 0

1

m1-1

o)(

o m1-1,



63/125



As can be seen from the figures on the

previous slide,y(t)is a bandlimited high-

frequency signal with a bandwidth of

centered at

The portion of the amplitude-modulatedsignal between and is called

the upper sideband, whereas, the portion ofthe amplitude-modulated signal between

and is called the lower sideband

m12

o1

m1-1o

m1,1o

o1

o1


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Amplitude ModulationAmplitude Modulation Because of the generation of two sidebands

and the absence of a carrier component in

the modulated signal, the process is called

double-sideband suppress carrier(DSB-SC)modulation

The demodulation ofy(t)to recoverx(t)iscarried out in two stages


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Amplitude ModulationAmplitude Modulation First,y(t)is multiplied with a sinusoidal

signal of the same frequency as the carrier:

The result indicates that r(t)is composed of

x(t)scaled by a factor 1/2and an amplitide-modulated signal with a carrier frequency

ttAxttytr o2

o cos)(cos)()( 1'1'

)2cos()()( o22 ttxtx AA 1-'

o21


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Amplitude ModulationAmplitude Modulation The spectrumR(j1)of r(t)is shown below

)( 1j

1m1m1, 0

2A

o21o21,

m1,1

o2)2(

o m1,1,

c1c1,


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Amplitude ModulationAmplitude Modulation Thusx(t)can be recovered from r(t)by

passing it through a lowpass filterwith a

cutoff frequency at satisfying the

relation The modulation and demodulation schemes

are as shown below:

c1

mcm 1,1/1/1 o2

9)(tx )(ty

tocos1

9 LowpassFilter)(ty)(tr

)(2

txA

tocos1


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Amplitude ModulationAmplitude Modulation In general, it is difficult to ensure that the

demodulating sinusoidal signal has a

frequency identical to that of the carrier

To get around the above problem, themodulation process is modified so that the

transmitted signal includes the carrier signal


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Amplitude ModulationAmplitude Modulation This is achieved by redefining the

amplitude modulation operation as follows:

where mis a number chosen to ensure that

[1 + m x(t)]is positive for all t

As the carrier is also present in themodulated signal, the process is called

double-sideband(DSB) modulation

)cos()](1[)( ottxmAty 1-'



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Figure below shows the waveforms of a

modulating sinusoidal signal of frequency

20 Hzand the amplitude-modulated carrier

with a carrier frequency 400 Hzobtained

using the DSB modulation scheme andm=0.5

0 20 40 60 80 100-1

-0.5

0

0.5

1

Time, msec

mp

u

e

Modulating signal

0 20 40 60 80 100-2

-1

0

1

2

Time, msec

Amplitude

Modulated carrier



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In the case of the conventional DSB

amplitude modulation scheme, themodulated signal has a bandwidth of ,

whereas the bandwidth of the modulating

signal is

To increase the capacity of the transmission

medium, either the upper sidebandor thelower sidebandof the modulated signal is

transmitted

m1

m12



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p tude odu at op

The corresponding procedure is calledsingle-sideband(SSB) modulation, a

possible implentation of which is shownbelow

The spectra of pertinent signals in the SSB

modulation scheme are shown in the next

slide

)(tx

)(ty

tocos1

9

9+6

tosin1

HilbertrTransforme

)(tu

)(1tw

)(2tw



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pp

)(2 1W

1o1o1, 0

2A

)(1 1jW

1o1o1, 0

2A

)( 1jY

1o1o1, 0

QuadratureQuadratureAmplitudeAmplitude


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ModulationModulation The DSB amplitude modualtionis half as

efficient as SSB amplitude modulation

The quadrature amplitude modualtion

(QAM) method uses DSBmodulation tomodulate two different signals so that they

both occupy the same bandwidth Hence, QAMtakes up as much bandwidth

as the SSBmethod



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ModulationModulation Consider two bandlimited signals and

with a bandwidth of as indicatedbelow

)(1tx

)(2tx m1)(1 1j

1m1m1, 0

)(2 1

1m1m1, 0



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ModulationModulation The two modulating signals are individually

modulated by the two carrier signals

and , respectively,

and are summed, resulting in

The two carrier signals have the samecarrier frequency but have a phase

difference of90o

)cos( otA 1 )sin( otA 1

)sin()()cos()()( o2o1 ttAxttAxty 1-1'

o1



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ModulationModulation The carrier is called the in-phase

componentand the carrier is

called the quadrature component

The spectrum Y(j1)of the composite signaly(t)is given by

)cos( otA 1)sin( otA 1

7 8 7 8}(({)( o1o12 1-1-1,1'1 jXjXjY A

7 8 7 8}(({ o2o22

1-1,1,1- jXjXj

A



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ModulationModulation y(t) is seen to occupy the same bandwidth

as the modulated signal obtained by a DSB

modulation

To recover and ,y(t)is multipliedby both the in-phase and the quadrature

components of the carrier separately,

resulting in

)(1tx )(2tx

)cos()()( o1 ttytr 1'

)sin()()( o2 ttytr 1'



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ModulationModulation Substituting the expression fory(t)in both

of the last two equations, we obtain aftersome algebra

Lowpass filtering of and by filters

with a cutoff at yields and

)2sin()()2cos()()()( o22o12121 ttxttxtxtr AAA

1-1-'

)2cos()()2sin()()()( o22o12222 ttxttxtxtr AAA 1,1-'

)(1tr )(2tr

m1 )(1tx )(2 tx



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ModulationModulation The QAM modulation and demodulation

schemes are shown below

)(12 txA

)(22 txA

-phase90o

shifter

69

9

)(1tx

)(2 tx

)(ty

)cos( otA 1

phase90o

shifter

69

9

Lowpass

filter

Lowpass

filter)(ty

)cos( ot1

6

Multiplexing andMultiplexing and


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DemultiplexingDemultiplexing For an efficient utilization of a wideband

transmission channel, many narrow-bandwidth low-frequency signals are

combined for a composite wideband signalthat is transmitted as a single signal

The process of combining the low-

frequency signals is called multiplexing



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DemultiplexingDemultiplexing Multiplexing is implemented to ensure that

a replica of each of the original narrow-bandwidth low-frequency signal can be

recovered at the receiving end The recovery process of the low-frequency

signals is called demultiplexing



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DemultiplexingDemultiplexing One method of combining different voice

signals in a telephone communicationsystem is the frequency-divisionmultiplexing(FDM) scheme

Here, each voice signal, typicallybandlimited to a low-frequency band of

width 1 , is frequency-translated into ahigher frequency band using the amplitudemodulation method

m



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DemultiplexingDemultiplexing The carrier frequency of adjacent

amplitude-modulated signals is separated by, where to ensure that there is

no overlap in the spectra of the individualmodulated signals after they are added toform the baseband composite signal

The composite signal is then modulatedonto the main carrier developing the FDMsignal and transmitted

o1 m101 2o



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DemultiplexingDemultiplexing)(1 1j

1m1m1, 0

)(2 1

1m1m1, 0

)(3 1j

1m1

111 21 31011,

)( 1jYcomp

, m1, 0

lowtheofSpectra signalsfrequency,

signalcompositemodulatedtheofSpectra



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DemultiplexingDemultiplexing At the receiving end, the composite

baseband signal is first recovered from theFDM signal by demodulation

Then each individual frequency-translatedsignal is demultiplexedby passing the

composite signal through a bank of

bandpass filters


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Ad t f DSPAd t f DSP


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Advantages of DSPAdvantages of DSP Absence of drift in the filter characteristics

Processing characteristics are fixed, e.g. by

binary coefficients stored in memories

Thus, they are independent of the externalenvironment and of parameters such as

temperature

Aging has no effect



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Advantages of DSPAdvantages of DSP Improved quality level Quality of processing limited only by economic

considerations

Arbitrarily low degradations achieved with

desired quality by increasing the number of bitsin data/coefficient representation

An increase of 1bit in the representation results

in a 6dB improvement in the SNR



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Advantages of DSPAdvantages of DSP Reproducibility

Component tolerances do not affect system

performance with correct operation

No adjustments necessary during fabrication No realignment needed over lifetime of

equipment



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Advantages of DSPAdvantages of DSP Ease of new function development

Easy to develop and implement adaptive filters,

programmable filters and complementary filters

Illustrates flexibility of digital techniques



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Advantages of DSPAdvantages of DSP Multiplexing

Same equipment can be shared between several

signals, with obvious financial advantages for

each function

Modularity

Uses standard digital circuits for

implementation



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Advantages of DSPAdvantages of DSP Total single chip implementation using

VLSI technology

No loading effect

Limitations of DSPLimitations of DSP


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Limitations of DSPLimitations of DSP Lesser Reliability

Digital systems are active devices, and thus use

more power and are less reliable

Some compensation is obtained from thefacility for automatic supervision and

monitoring of digital systems

Limitations of DSPLimitations of DSPLi i d F R f O i


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Limited Frequency Range of Operation

Frequency range technologically limited to

values corresponding to maximum computingcapacities that can be developed and exploited

Additional Complexity in the Processing ofAnalog Signals

A/D and D/A converters must be introduced

adding complexity to overall system

DSP Application ExamplesDSP Application Examples


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Cellular Phone Discrete Multitone Transmission

Digital Camera Digital Sound Synthesis

Signal Coding & Compression

Signal Enhancement

Cellular Phone Block DiagramCellular Phone Block Diagram


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DSP Core

S/W

DSP Core

S/W

ARM RISCCore

S/W

ARM RISCCore

S/W

SINGLE CHIP

DIGITALBASEBAND

ASICB

ackplane

User DisplayUser Display

KeyboardKeyboard

SIM CardSIM Card

RF

Interface

RF

InterfaceAudioInterface

AudioInterface

SpeakerSpeaker MicMic

Op AmpsOp Amps

SwitchesSwitches

RegulatorsRegulators

ReceiverReceiver

ModulatorModulator DriverDriver

RFSECTION

PowerAmp

Power

AmpSynthesizerSynthesizer

Touch ScreenTouch Screen

Cellular Phone Block DiagramCellular Phone Block Diagram

sInstrumentTexas:Courtesy

Cellular Phone Baseband

System on a Chip


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100-200 MHz DSP +

MCU

ASIC Logic

Dense Memory

Analog

System on a Chip

sInstrumentTexas:Courtesy

DiscreteDiscreteMultitoneMultitone

Transmission (DMT)Transmission (DMT)


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Transmission (DMT)Transmission (DMT)

Core technology in the implementation oftheasymmetric digital subscriber line

(ADSL) andvery-high-rate digital

subscriber line(VDSL)

Closely related to: Orthogonal frequency-

division multiplexing(OFDM)

ADSLADSL


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A local transmission system designed tosimultaneously support three services on a

single twisted-wire pair: Data transmission downstream (toward the

subscriber) at bit rates of upto9 Mb/s

Data transmission upstream (away from thesubscriber) at bit rates of upto1 Mb/s

Plain old telephone service(POTS)

ADSL


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Band-allocations for an FDM-based ADSL

system

powerTransmit

bandstream-down

rate-bitHigh

bandPOTS

bandGuard

band

upstream

rate-bitLow

Frequency

ADSLADSL


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Asymmetry in the frequency bandallocation:

to bring movies, television, video catalogs,

remote CD-ROMs, corporate LANs, and theInternet into homes and small businesses

VDSLVDSL

i l k i f i d


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Optical network emanating from twisted

pair provides data rates of 13to 26 Mb/s

downstream and 2to 3 Mb/supstream over

short distances less than about 1 km

Allows the delivery of digital TV, super-fastWeb surfing and file transfer, and virtual

offices at home

DiscreteDiscreteMultitoneMultitone

TransmissionTransmission


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TransmissionTransmission

Advantages in using DMTfor ADSLandVDSL

The ability to maximize the transmitted bit rate Adaptivity to changing line conditions

Reduced sensitivity to line conditions

OFDMOFDM


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Applications:

Wireless communications- an effectivetechnique to combat multipath fading

Digital audio broadcasting

Uses a fixed number of bits per subchannel

while DMT uses loading for bit allocation


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Digital CameraDigital CameraCMOS I i S


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CMOS Imaging Sensor

Increasingly being used in digital cameras

Single chip integration of sensor and other

image processing algorithms needed to generate

final image Can be manufactured at low cost

Less expensive cameras use single sensor with

individual pixels in the sensor covered with

either ared, agreen, or ablueoptical filter

Digital CameraDigital Camera


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Image Processing Algorithms

Bad pixel detection and masking

Color interpolation

Color balancing Contrast enhancement

False color detection and masking

Image and video compression

Digital CameraDigital Camera

Bad Pixel Detection and Masking


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g


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Digital Sound SynthesisDigital Sound Synthesis


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Wavetable Synthesis

- Recorded or synthesized musical events stored ininternal memory and played back on demand

- Playback tools consists of various techniques forsound variation during reproduction such aspitch

shifting, looping, envelopingandfiltering

- Example: Giga Sampler


S l S h i


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Spectral Synthesis

- Produces sounds from frequency domain models- Signal represented as a superposition of basis

functions with time-varying amplitudes

- Practical implementation usually consist of acombination of additive synthesis, subtractive

synthesisand granular synthesis

- Example: Kawaii K500 Demo



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Nonlinear Synthesis

- Frequency modulation method: Time-

dependent phase terms in the sinusoidal basis

functions- An inexpensive method frequently used in

synthesizers and in sound cards for PC

- Example: Variation modulation index complex

algorithm(Pulsar)


Physical Modeling


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Physical Modeling

- Models the sound production method

- Physical description of the main vibrating

structures by partial differential equations

- Most methods based on wave equationdescribing the wave propagation in solids and in

air

- Examples: (CCRMA, Stanford) Guitar with nylon strings

Marimba

Tenor saxophone

Signal Coding & CompressionSignal Coding & Compression


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Concerned with efficient digital

representationof audio or visual signalforstorageandtransmissionto provide

maximum quality to the listener orviewer

Signal Compression ExampleSignal Compression Example

Original speech0 5

1

16-bit, sampled at 44.1 kHz rate


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Data size 330,780 bytes

Compressed speech (GSM 6.10)

- Sampled at 22.050 kHz,Data size 16,896 bytes

Compressed speech (Lernout & Hauspie

CELP 4.8kbit/s)

Sampled at 8 kHz,Data size 2,302 bytes

0 1 2 3-1

-0.5

0

0.5

Time, sec.

mp

u

e



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Original music

Audio Format:PCM 16.000 kHz, 16 Bit(Data size 66206 bytes)

Compressed music

Audio Format:GSM 6.10, 22.05 kHz(Data size 9295 bytes)

Courtesy: Dr. A. Spanias



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Compressed Image

Average bit rate - 0.5 bits per pixel

Original Lena

8 bits per pixel

Signal EnhancementSignal Enhancement

Purpose:To emphasizespecific signal


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p p p g

features to provide maximum quality to the

listener or viewer

For speech signals, algorithms include

removal of background noise or interference For image or video signals, algorithms

include contrast enhancement, sharpeningand noise removal

Signal Enhancement ExampleSignal Enhancement Example

0.5

1


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Noisy speech signal

(10% impulse noise)

Noise removed speech

0 1 2 3-1

-0.5

0

0.5

1

Time, sec.

mp

u

e

0.4 0.6 0.8 1 1.2-1

-0.5

0

Time, sec.

mp

u

e



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EKG corrupted with EKG after filtering with

60 Hzinterference a notch filter

0 500 1000 1500 2000-50

0

50

100

150

time

EKG After Noise Removal

mp

tu

e

0 500 1000 1500 2000-50

0

50

100

150

time

mp

tu

e

EKG Corrupted With 60 Hz Interference



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Original image and its contrast enhanced version

Original Enhanced


Original image and its contrast enhanced version


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Copyright 2002 S. K. Mitra124Original Enhanced


Noise corrupted image and its noise-removed

version


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version

20% pixels corrupted with

additive impulse noise

Noise-removed version

dsp mitra chap1

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