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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.
51
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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%
^inclue #2cfg.%
^inclue s867$).%
^inclue s867$)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%
^inclue /Ccfg.%
^inclue s867$).%
^inclue s867$)aic&).%
^efine beta $E-$) rate of con'ergence^efine / )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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8/15/2019 DSP Complete Manual
59/59
Digital Signal Processing Lab Manual -- 06ECL57 V semester
$). 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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