DSP Complete Manual

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Digital Signal Processing Lab Manual -- 06ECL57 V semester

DEPARTMENT OF TELECOMMUNICATION ENGINEERING

DR.AMBEDKAR INSTITUTE OF TECHNOLOGY

BANGALORE – 560056

DIGITAL SIGNAL PROCESSINGLAB MANUAL

06ECL57

V Semester

Lab In charge:

PRAVEEN K B

Lecturer !EP" #$ "CE

NAME OF THE STUDENT :

USN NUMBER :

BATCH :

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Table of Cotets

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SL.No.

List of Experiments : PaeNo.

Staff sinat!re

Part A"C#$%e&'($

Verification of Sampling t%eorem.09

&#mpulse response of a gi'en s(stem

12

)Linear con'olution of t*o gi'en se+uences.

14

,Circular con'olution of t*o gi'en se+uences

17

5 "utocorrelation of a gi'en se+uence an 'erification of its properties. 19

6Cross correlation of gi'en se+uences an 'erification of its properties.

21

7Sol'ing a gi'en ifference e+uation.

24

Computation of / point D of a gi'en se+uence an to plot magnituean p%ase spectrum.

27

1Linear con'olution of t*o se+uences using D an #D.

32

$0Circular con'olution of t*o gi'en se+uences using D an #D

32

$$Design an implementation of #2 filter to meet gi'en specifications

35

$&Design an implementation of ##2 filter to meet gi'en specifications.

39

Part B"C#$%e&)(

CCS #ntrouction43

1Linear con'olution of t*o gi'en se+uences.

44

2Circular con'olution of t*o gi'en se+uences.

45

3Computation of /- Point D of a gi'en se+uence

46

4#mpulse response of first orer an secon orer s(stem

47

52eali3ation of an #2 filter 4an( t(pe to meet gi'en specifications .%e input

can be a signal from function generator speec% signal.

49

6 /oise " noise abo'e )893 an t%en remo'e: #nterference suppression

using ,00 93 tone.

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Intr%&uct'%n t% (A"LAB

The name MATLAB stands for MATrix LABoratory. MATLAB is a high-performance language for technical computing. It integrates computation,

visualization, and programming environment. It has powerful built-in routines

that enale a very wide variety of computations. It also has easy to use

graphics commands that ma!e the visuali"ation of results immediately

availale. Matla is especially designed for matrix computations# solving

systems of linear e$uations, computing eigenvalues and eigenvectors,

factoring matrices, and so forth. In addition, it has a variety of graphicalcapailities, and can e extended through programs written in its own

programming language. Many such programs come with the system% a

numer of these extend Matla&s capailities to nonlinear prolems, such as

the solution of initial value prolems for ordinary di'erential e$uations.

Typical uses:

(. Math and computation

). Algorithm development

*. +ata ac$uisition

. Modeling, simulation, and prototyping

. +ata analysis, exploration and visuali"ation

. /cienti0c and engineering graphics

1. Application development

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MATLAB Softwae !ow "ia#a$

%ow to Po#a$&

S': Clic( t)e Ico* o* t)e Des(top

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S.: Ceate New /0$1 2le fo witi*# a Matla3 co"e

S4: E*te t)e co"e i* e"ito a*" sa5e it wit) appopiate *a$e0

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Part "

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EXPERIMENT No ! "er#f#$at#o of Sa%&l#' t(eore%.

!im5 )o verify Sampling theorem for a signal of given frequency.

)heory5

• Sampling is a process of con'erting a continuous time signal 4analog signal ;4t into aiscrete time signal ;


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Sampling at t%e /(+uist rate results in samples sin4In *%ic% are ienticall( 3ero! i.e.! *e are

sampling at t%e 3ero crossing points an %ence t%e signal component is completel( misse. %is

can be a'oie b( aing a small p%ase s%ift to t%e sinusoi. %e abo'e problem is not seen in

cosine *a'eforms 4e;cept cos410n. " simple reme( is to sample t%e analog signal at a rate

%ig%er t%an t%e /(+uist rate. %e ig$.& s%o*s t%e result ue to a cosine signal

4;$cos4&GpiGfGn$:

ig.$.& Plots of a sample cosine *a'e of &0093

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EXPERIMENT NO )* I%&ulse res&ose of a '#+e syste%

!im5 )o fin" the impulse response h0n of the given L)I system whose response y0n

to an input :0n is given.

)heory5

ig.&.$ " L# s(stem

• " iscrete time L# s(stem 4also calle igital filters as s%o*n in ig.&.$ is represente b(

o " linear constant coefficient ifference e+uation! for e;ample!

=:&


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!)L!9 rograms5

( input4%e output se+uence (4n of t%e s(stem:

;input4t%e input se+uence of t%e s(stem:

%econ'4(!;:

isp4t%e impulse response of t%e s(stem is:

isp4%:

Fgrap%ical ispla( part

/lengt%4%:

n0$/-$:

stem4n!%:

;label4ime ine; n:

(label4"mplitue:

title4impulse response of a s(stem

FVerification

('con'4;!%:isp4t%e 'erifie output se+uence is:

isp4('

ig. &.$ #mpulse 2esponse 4Program $

,esult5%e output se+uence (4n of t%e s(stem


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stem4;&:

;label4time ine; n:

(label4amplitue :

title4plot of ;&:

,esult

Enter first se+uence


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Level 2 rogram 0)wo si"e" sequencesFmain part of computation

;$


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EXPERIMENT NO /* C#r$ular $o+olut#o of t-o '#+e seue$es.

!im5 )o otain circular convolution of two finite "uration sequences.

)heory5

• "s seen in t%e last e;periment! t%e output (


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!lgorithm5$. #nput t%e t*o se+uences as ; an %.

&. Circularl( con'ol'e bot% to get output (.

). Plot t%e se+uences.

!)L!9 rogram5

FCircular Con'olution Program

;


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EXPERIMENT NO 0* Auto$orrelat#o of a '#+e seue$e a1 +er#f#$at#o of #ts

&ro&ert#es.

!im5 )o otain autocorrelation of the given sequence an" verify its properties.

)heory5• Correlation is mat%ematical tec%ni+ue *%ic% inicates *%et%er & signals are relate an in a

precise +uantitati'e *a( %o* muc% t%e( are relate. " measure of similarit( bet*een a pair of

energ( signals ;


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!)L!9 rograms

FEnerg( signals

Fsimple se+uence

;&


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EXPERIMENT NO 2*Cross $orrelat#o of a '#+e seue$e a1 +er#f#$at#o of

#ts &ro&ert#es.

!im5 )o otain cross correlation of the given sequence an" verify its properties.

)heory5 • Cross Correlation %as been introuce in t%e last e;periment. Comparing t%e e+uations for

t%e linear con'olution an cross correlation *e fin t%at

=


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4 C%m+utat'%n %$ Cr%ssc%rre-at'%n Seuence us'ng /c%rr $unct'%n

; input4(pe in t%e reference se+uence :

( input4(pe in t%e secon se+uence :

F Compute t%e correlation se+uence

n$ lengt%4(-$:

n& lengt%4;-$:

r ;corr4;!(:

F


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ig.6.& Cross correlation output using ;corr

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EXPERIMENT NO 3 Sol+#' a '#+e 1#ffere$e euat#o

!im5 )o otain the impulse responsestep response of a system "escrie" y the

given "ifference equation

)heory5• " ifference e+uation *it% constant coefficients escribes a L# s(stem. or e;ample t%e

ifference e+uation *2n3 0,8*2n93 0,6*2n3 /2n3 0,7/2n13 0,5/2n93 escribes a

L# s(stem of orer ). %e coefficients 0.! 0.7! etc are all constant i.e.! t%e( are not

functions of time 4n. %e ifference e+uation (


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!)L!9 rogram5


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EXPERIMENT NO 4. Co%&utat#o of N &o#t DFT of a '#+e seue$e a1 to

&lot %a'#tu1e a1 &(ase s&e$tru%.

!im5 )o compute '() of the given sequence.

)heory5• Discrete ourier ransform 4D is use for performing fre+uenc( anal(sis of iscrete

time signals. D gi'es a iscrete fre+uenc( omain representation *%ereas t%e ot%er

transforms are continuous in fre+uenc( omain.

• %e / point D of iscrete time signal ;


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;label4 8:

(label4l;8l:

title4Magnitue spectrum:

F p%ase spectrum

figure4&:

stem4n!angle4;8:

;label4 8:(label4angle4;8:

title4p%ase spectrum:

figure4):

n$0$lengt%4;-$:

stem4n$!;:

;label4 n:

(label4;


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ig..)

ig..,

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ig..5

ig .6

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EXPERIMENT NO !!. Des#' a1 #%&le%etat#o of FIR f#lter to %eet '#+e

s&e$#f#$at#os

!im5 )o "esign an" implement a (I, filter for given specifications.

'>SI;&I&; !& (I, (IL)>, 0using win"ow metho"5

etho" I5 Bi'en t%e orer /! cutoff fre+uenc( fc! sampling fre+uenc( fs an t%e *ino*.• Step $ Compute t%e igital cut-off fre+uenc( c 4in t%e range -I H c H I! *it% I

corresponing to fs& for fc an fs in 93. or e;ample let fc,0093! fs00093

c &GIG fc fs &G I G ,00000 0.$G I raians

or M"L"@ t%e /ormali3e cut-off fre+uenc( is in t%e range 0 an $! *%ere $

correspons to fs& 4i.e.!fma;. 9ence to use t%e M"L"@ commans

*c fc 4fs& ,004000& 0.$

/ote if t%e cut off fre+uenc( is in raians t%en t%e normali3e fre+uenc( is compute as

*c c I

• Step & Compute t%e #mpulse 2esponse %4n of t%e re+uire #2 filter using t%e gi'en

ino* t(pe an t%e response t(pe 4lo*pass! banpass! etc. or e;ample gi'en a

rectangular *ino*! orer /&0! an a %ig% pass response! t%e coefficients 4i.e.! %>&)!)I?& ?( )7> (I, (IL)>,$. ?nce t%e coefficients of t%e #2 filter %


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&. Con'ol'e input se+uence ;&)!)I?& #2$ unction

@ #2$4/!n esigns an /t% orer lo*pass #2 igital filter an returns t%e filter

coefficients in lengt% /O$ 'ector @. %e cut-off fre+uenc( n must be bet*een 0 H n H $.0!*it% $.0 corresponing to %alf t%e sample rate. %e filter @ is real an %as linear p%ase! i.e.! e'en

s(mmetric coefficients obe(ing @48 @4/O&-8! 8 $!&!...!/O$.

#f n is a t*o-element 'ector! n


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;&sin4&GpiGnGf&fs:

;)sin4&GpiGnGf)fs:

;


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Enter passban ege fre+uenc( in 93$00

Enter stopban ege fre+uenc( in 93&00

Enter sampling fre+uenc( in 93$000

/ ))

Plots are as in ig.$0.$ an $0.&

/otice t%e ma;imum stopban attenuation of 5) @ from plot $0.&

ig.$0.$ ig.$0.&

ig.$0.)4using filter comman ig.$0.,4using con' comman

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ig.$0.5 re+s f$$50:f&)00:f)$70:fs$000:

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EXPERIMENT NO !). Des#' a1 #%&le%etat#o of IIR f#lter to %eet '#+e

s&e$#f#$at#os

!im5 )o "esign an" implement an II, filter for given specifications.

etho" I5

Bi'en t%e orer /! cutoff fre+uenc( fc! sampling fre+uenc( fs an t%e ##2 filter t(pe 4butter*ort%!c%eb($! c%eb(&.

• Step $ Compute t%e igital cut-off fre+uenc( c 4in t%e range -I H c H I! *it% I

corresponing to fs& for fc an fs in 93. or e;ample let fc,0093! fs00093

c &GIG fc fs &G I G ,00000 0.$G I raians

or M"L"@ t%e /ormali3e cut-off fre+uenc( is in t%e range 0 an $! *%ere $ correspons

to fs& 4i.e.!fma;. 9ence to use t%e M"L"@ commans

*c fc 4fs& ,004000& 0.$

/ote if t%e cut off fre+uenc( is in raians t%en t%e normali3e fre+uenc( is compute as *c

c I

• Step & Compute t%e #mpulse 2esponse


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Part @

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EXPERIMENT NO !

A#%* )o perform linear convolution for the given sequences

%e linear con'olution sum is ∑∑ +∞

−∞=

+∞

−∞=

−=−=∗=k k

k hk n xk nhk xnhn xn y =


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EXPERIMENT NO )

A#%* To &erfor% $#r$ular $o+olut#o of t-o '#+e seue$es

%e circular con'olution sum is ( ) [ ]∑+∞

−∞=

−==k

N k n xk hnh N n xn y =


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EXPERIMENT NO* ,* Co%&utat#o of N8 Po#t DFT of a '#+e seue$e

A#%* To $o%&ute t(e N 9:/;4;!2< &o#t DFT of t(e '#+e seue$e

T(eory*

%e / point D of iscrete time signal ;


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EXPERIMENT /

A#%* To f#1 t(e I%&ulse res&ose of t(e '#+e f#rst or1er ; se$o1 or1er

syste%

T(eory*" linear constant coefficient ifference e+uation representing a secon orer s(stem isgi'en b( =:&


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Result 9o st1 out<0.067500 0.&$&05) 0.&&0$& 0.&),0, 0.$5$167 0.07677$ 0.0&50$7 -0.00)016

-0.0$)66 -0.0$,57$ -0.0$01)$ -0.006,71 -0.00&1) -0.0006)& 0.000,7$ 0.00000

0.0007&0 0.000,1& 0.000&66 0.000$00

%e plot obtaine using grap% is s%o*n in ig. 7.$

MATLAB +er#f#$at#o*


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EXPERIMENT NO 0

A#%* Real#=at#o of a FIR f#lter 9 ay ty&e < to %eet '#+e s&e$#f#$at#os. T(e

#&ut $a be a s#'al fro% fu$t#o 'eerator ; s&ee$( s#'al .

Prereu's'te: #nput is gi'en from t%e signal generator of amplitue $ ' p-p an fre+uenc( U &0

93.

!SK >'t: Plug in t%e signal generator op to line in an line out of MS to C2? @efore compiling!

Cop( %eaer files `s867$).% an `s867$)aic&).% from

C_CCStuio').$_c6000_s867$)_inclue an paste it in t%e current proAect foler

C Pro'ra%

înclue #2cfg.%

înclue s867$).%

înclue s867$)aic&).%

float filterCoeff


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DS67$)init4:

%Coec DS67$)"#C&)openCoec40! config: G Start t%e coec G

DS67$)"#C&)setre+4%Coec! $:

*%ile4$ W G 2ea a sample to t%e left c%annel G

*%ile 4dDS67$)"#C&)rea4%Coec! linput:

G 2ea a sample to t%e rig%t c%annel G

*%ile 4dDS67$)"#C&)rea4%Coec! rinput:

-%ut+ut


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EXPERIMENT NO 2

No#se re%o+al &ro'ra%s*

9#< A11 o#se abo+e ,>?= a1 t(e re%o+e 9us#' a1a&t#+e f#lters<

9##< Iterfere$e su&&ress#o us#' /66 ?= toe

T(eory*

#n t%e pre'ious e;periments in'ol'ing ##2 #2 filters! t%e filter coefficients *ere

etermine before t%e start of t%e e;periment an t%e( remaine constant. %ereas "apti'e filters

are filters *%ose transfer function coefficients or taps c%ange o'er time in response to an e;ternal

error signal. (pical applications of t%ese filters are E+uali3ation! Linear Preiction! /oise

Cancellation! ime-Dela( Estimation! /on-stationar( C%annel Estimation! etc. Different t(pes of

aapti'e filter algorit%ms are t%e alman aapti'e filter algorit%m! LMS aapti'e filter algorit%m

an 2LS aapti'e filter algorit%m.

ig.6.$ "apti'e Structure for noise cancellation ig.6.& "apti'e ilter 4#n program t%e

coefficients 4*eig%ts a replace b(

*


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C Pro'ra%

înclue /Ccfg.%

înclue s867$).%

înclue s867$)aic&).%

êfine beta $E-$) rate of con'ergenceêfine / )0 aapti'e #2 filter lengt%-'ar( t%is parameter obser'e

float ela(


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*%ile 4dDS67$)"#C&)*rite4%Coec! routput:

G Sen op to t%e rig%t c%annelG

DS67$)"#C&)closeCoec4%Coec: G Close t%e coec G

signe int aapti'efilter4int linput!int rinput #S2

W

s%ort i!output:

float (n0! E0! plusn0!esire!noise:

esire linput:

noise rinput:

plusn 4s%ort4esire O noise: esireOnoise

ela(


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Sam+-e V'a V%ce uest'%n:

$. %at is M"L"@

&. %at are t%e applications of M"L"@

). State sampling t%eorem.

,. %at is meant b( /(+uist rate an /(+uist criteria

5. %at o (ou mean "liasing %at is t%e conition to a'oi aliasing for sampling

6. E;plain scaling an superposition properties of a s(stem.

7. %at is meant b( linearit( of a s(stem an %o* it is relate to scaling an superposition

. E;plain t%e statement- t 00.0000050.05

1. %at is impulse function

$0. %at is meant b( impulse response$$. %at is energ( signal 9o* to calculate energ( of a signal

$&. %at is po*er signal 9o* to calculate po*er of a signal

$). Differentiate bet*een e'en an o signals.

$,. E;plain time in'ariance propert( of a s(stem *it% an e;ample.

$5. %at is memor( less s(stem

$6. %en a s(stem is sai to %a'e memor(

$7. %at is meant b( causalit(

$. E;plain linear con'olution an circular con'olution.

$1. %at is t%e lengt% of linear an circular con'olutions if t%e t*o se+uences are %a'ing t%e

lengt% n$ an n&

&0. %at are ourier series an ourier transform

&$. %at are t%e a'antages an special applications of ourier transform! ourier series! >

transform an Laplace transform

&&. 9o* to perform linear con'olution using circular con'olution

&). %at is meant b( correlation

&,. %at is auto-correlation

&5. %at is cross-correlation

&6. %at are t%e a'antages of using autocorrelation an cross correlation properties in signal

processing fiels

&7. Differentiate bet*een ##2 filters an #2 filters.

&. %at is t%e proceure to esign a igital @utter*ort% filter

&1. %at is t%e ifference bet*een @utter*ort%! C%eb(s%e' # an C%eb(s%e' ## filters

)0. %at are ifference e+uations an ifferential e+uations

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)$. %at is filter

)&. %at is *ino* met%o 9o* (ou *ill esign an #2 filter using *ino* met%o.

)). %at are lo*-pass an ban-pass filter an *%at is t%e ifference bet*een t%ese t*o

),. E;plain t%e comman Q /ceil46.6Gpitb

)5. %at is CCS E;plain in etail to e;ecute a program using CCS.

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$). Design an implement a igital ##2 lo* pass @utter*ort% filter using bilinear transformation

met%o.

$,. Design an implement a igital ##2 lo* pass C%eb(s%e' filter using bilinear transformation

met%o.

$5. Design an implement a igital #2 lo* pass filter using 9amming ino*.

PAR" B:

0$. Compute an 'erif( using C program t%e linear con'olution of t%e t*o gi'en se+uences.

0&. Compute an 'erif( using C program t%e circular con'olution of t%e t*o gi'en se+uences.

0). Compute a 'erif( using C program t%e D of a gi'en se+uence.

0,. Compute an 'erif( using C program to fin t%e impulse response of t%e gi'en first secon

orer s(stem.

05. Compute an 'erif( using C program to 2eali3ation of an #2 filter 4an( t(pe to meet gi'en

specifications .%e input can be a signal from function generator speec% signal.

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DSP Complete Manual