Location: _____________ ____________________ _______
Time: ________________
Semester: Spring 2011
Section: BICSE-6ABC___
Department of Electrical Engineering CSE-304 Digital Signal Processing
Corse Instrctor: ________________________
LAB !A"#AL
CSE-304 DSP.
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List of Experiments Contents Lab1: Introduction to Matlab (Part I)........................................ I)............................................................ ................................ ............... ... Lab!: Introduction to Matlab (Part II)....................................... II).......................................................................... ................................... " Lab3: #a$ic Signal$ and S%$te&.................................. S%$te&...................................................... ......................................... ........................... ...... ' Lab4: E*+E,C DM/I, IE S/MPLI,2......................................................1! Lab: DISCEE +IE /,SM............................... /,SM............................................................. ..................................... ....... 1 Lab5: /S +IE /,SM........................ /,SM............................................ ....................................... ................................ ............. !! Lab": 6 7ran$8or 7ran$8or&................... &....................................... ....................................... ....................................... ...................................... ..................... ... 33 Lab: II DI2I/: DI2I/: ILE ILE DESI2,.............................. DESI2,.................................................. ........................................ ............................. .........40 40 Lab': ILE ILE DESI2, +SI,2 /,/L2 PPI,2...................................... PPI,2................................................44 ..........44 Lab10: LI,E/ P9/SE I ILE ILE DESI2, #/SED ,
I,DS........................4' I,DS........................4'
Lab11: I,EPL/I, I,EPL/I, /,D DECIM/I,...................... DECIM/I,........................................... ................................... .................... ...... Lab1!: 9E PLP9/SE PLP9/SE DECMPSII,.................................. DECMPSII,.............................................. ........................... .................. ...51 51 Lab13: PEIDIC /E /E 2E,E/ 2E,E/S.................................... S...................................................................... .................................. 5 Lab14: ,ISE ED+CI, /,D SI2,/L E,9/,CME,............................................ E,9/,CME,............................................ "3 Lab1: /D/PIE ILEI,2........ ILEI,2............................ ........................................ ........................................ ................................. ................. .... "" Lab15: DEM,S/I, DEM,S/I, E/L-IME E/L-IME SI2,/L PCESSI,2........................ PCESSI,2................................. .........3 3
CSE-304 DSP.
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List of Experiments Contents Lab1: Introduction to Matlab (Part I)........................................ I)............................................................ ................................ ............... ... Lab!: Introduction to Matlab (Part II)....................................... II).......................................................................... ................................... " Lab3: #a$ic Signal$ and S%$te&.................................. S%$te&...................................................... ......................................... ........................... ...... ' Lab4: E*+E,C DM/I, IE S/MPLI,2......................................................1! Lab: DISCEE +IE /,SM............................... /,SM............................................................. ..................................... ....... 1 Lab5: /S +IE /,SM........................ /,SM............................................ ....................................... ................................ ............. !! Lab": 6 7ran$8or 7ran$8or&................... &....................................... ....................................... ....................................... ...................................... ..................... ... 33 Lab: II DI2I/: DI2I/: ILE ILE DESI2,.............................. DESI2,.................................................. ........................................ ............................. .........40 40 Lab': ILE ILE DESI2, +SI,2 /,/L2 PPI,2...................................... PPI,2................................................44 ..........44 Lab10: LI,E/ P9/SE I ILE ILE DESI2, #/SED ,
I,DS........................4' I,DS........................4'
Lab11: I,EPL/I, I,EPL/I, /,D DECIM/I,...................... DECIM/I,........................................... ................................... .................... ...... Lab1!: 9E PLP9/SE PLP9/SE DECMPSII,.................................. DECMPSII,.............................................. ........................... .................. ...51 51 Lab13: PEIDIC /E /E 2E,E/ 2E,E/S.................................... S...................................................................... .................................. 5 Lab14: ,ISE ED+CI, /,D SI2,/L E,9/,CME,............................................ E,9/,CME,............................................ "3 Lab1: /D/PIE ILEI,2........ ILEI,2............................ ........................................ ........................................ ................................. ................. .... "" Lab15: DEM,S/I, DEM,S/I, E/L-IME E/L-IME SI2,/L PCESSI,2........................ PCESSI,2................................. .........3 3
CSE-304 DSP.
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SemesterSpring 2011 DSP/ Communication Lab
S.N O
Faculty
Subject
01 02 03
MrAamirjelani DrSaadQaisar MsShahidaJabeen
DSP DS P DS P
CSE-304 DSP.
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Course
Duration
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 1 La&1: Intro'ction to !atla& ()art I*
Name
CSE-304 DSP.
'eg. no.
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Lab1: Introdction to !atlab "Part I# cial Matlab ;2etting Started 2uide a?ailable in Digital or&at
Chapters 1,2,3 covered in this ab
CSE-304 DSP.
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$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department of Electrical Engineering
CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 2 La&2: Intro'ction to !atla& ()art II*
Name
CSE-304 DSP.
'eg. no.
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ia -ars /
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Lab$: Introdction to !atlab "Part II# cial Matlab ;2etting Started 2uide a?ailable in Digital or&at
Chapters !," covered in this ab $aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , # Lab# &asic Signals an3 System
Name
CSE-304 DSP.
'eg. no.
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Lab3: %asic Signals and S&stem #hat is $mp%lse& S 'n()
1, i* n)0 0, other+ise
S'nn0( ) 1, i* n)0 0, other+ise
+mpulse signal or lengt4 L 5 #1
) 31 nn)0- l imp ) .eros/,l imp/l) 1
Problem 1
/a $mplement a *%nction *or eneratin and plottin 'n( ) m4'n 5 n0(
*or a 6 n 6 b
7r8 it *or /i
n0) ",
m ) 09:,
a ) 1,
b ) 20
/ii
n0) 09
m ) 09;,
a ) 1",
b ) 1"
/iii
n0) 333, m ) 19",
a) 300,
b ) 3"0
CSE-304 DSP.
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/iv
n0) <,
m ) !9",
a)10
b)0
/b =enerate and implement the *%nction δ 'n( =
M −1
∑ A δ 'n − lP ( i
l = 0
/Al ) +eihts vector P) period >99, *or M) " and P ) 3 !
∑ A δ 'n − 3l ( l
l = 0
Problem 2
/a
A cosine +ave is 'n( ) A cos/?0 n @ enerate and plot
1 [n] = sin / B n C 1 <
0DnD2"
2 [n] = sin / B n C 1 <
, 1" D n D 2 "
x3 [n] = sin / 3 B n @ B C 2
,10DnD10
>press 3'n( %sin a *%nction other than trionometric *%nctions9 /b $mplement a *%nction *or 'n( ) A cos/? 0 n @ *or a n b A)2 ? ) B11 )0 a)20 b)20
CSE-304 DSP.
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$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , $
Lab$ F'!67!NC) DO-%+N +!8 OF S%-PL+N9
Name
'eg. no.
'eport -ars / 10
ia -ars /
Lab4: '(E)*E+C, D!.I+ /IE ' S.!PLI+
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Sampling
Ender certain conditions, a contin%o%stime sinal can be completel8 represented its val%es or samples at points eF%all8 spaced in time9 Consider the contin%o%s time sinal /t9 7his sinal can be represented as a discrete time sinal %sin val%es o* /t at GnG n%mber o* intervals spaced b8 a time interval H7sI9 )sin/10Bt Sampled Sinal /100 K.
Ny:uist Criterion
$* the reater the n%mber o* samples the reater the acc%rac8, then +h8 donGt +e sample at a ver8 hih rate& 7here are t+o reasons *or it9 Lirst o* all hih n%mber o* samples reF%ire a lot o* manip%lation on behal* o* the machineso*t+are that +e are %sin +hich res%lts in more time9 Secondl8 most o* the vital data that +e need can easil8 be obtained *rom lo+ samplin rates9 7here*ore +e need some criteria to de*ine the rate at +hich the sinals sho%ld be sampled9 7his criteria is called as GN8F%ist CriteriaG9 Accordin to it, the samplin *reF%enc8 m%st /at least be t+ice the sinal *reF%enc89 Consider the *ollo+in *i%res
CSE-304 DSP.
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Sampled Sinal /" K.
Sampled Sinal /10 K.
#e can see that +hen the samplin rate doesnIt satis*8 the N9C, +e donIt et correct in*ormation abo%t the sinal9 !ect o Sampling in Fre:uency Domain
$n time domain samplin can be represented b8 m%ltiplication o* the analo%e sinal +ith imp%lse train, in +hich each imp%lse is separated b8 samplin time9 Since Lo%rier trans*orm o* an imp%lse train is an imp%lse train, in *reF%enc8 domain it is eF%ivalent o* convol%tion o* the Lo%rier trans*orm o* the sinal +ith another imp%lse train, +hich res%lts in m%ltiple copies o* the spectr%m o* the oriinal sinal9 7his process is sho+n in the *i%res /samplin *reF%enc8 ) 100 radianssec-
CSE-304 DSP.
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Oriinal sinal
Sampled Sinal
$t is clear *rom the *i%re that +hen samplin *reF%enc8 is less than N8F%ist rate, the repeatin spectr%m o* the sampled sinals +ill overlap and aliasin +ill occ%rs9 7here*ore it is necessar8 to band limit the sinal be*ore convertin it to diital sinal in order to avoid aliasin9 $n order to reconstr%ct the sinal +e need to pass it thro%h a lo+ pass *ilter +ith c%to** *reF%enc8 *s29 7he res%lts are sho+n in the *ollo+in *i%re-
CSE-304 DSP.
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econstr%cted Sinal
Simulation o %nalogue Signals in -%(L%&
#e canGt have a p%re analo%e sinal in MA7A9 So +e %se a sim%lation *reF%enc8, +hich is m%ch hiher than samplin rate $n order to estimate *reF%enc8 spectr%m o* the sinal in analo%e *reF%enc8 domain, +e can maRe %se o* diital techniF%es9 7he *ollo+in *%nction ives the same *%nctionalit8*%nction *plot/a,*sim ) lenth/a N**t ) 2 ro%nd /lo 2/" a)**t/a,N**i rane ) 0- N**t 2 *reF%enc8 ) /raneN**i *sim plot/**1000, abs/a/rane @1 Lab !;ercises Problem 1
Lor all sim%lations taRe *sim ) ;0RK. i =enerate a sinal CSE-304 DSP.
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/t ) cos /2B*0t 0t7 Choose 7 so that 8o% have eactl8 1000 samples e99 7 ) 1000*sim ii plot aainst t9 iii plot its Lo%rier trans*orm %sin G*plotG
Problem 2
Convert the analo%e sinal to diital so that the samples are spaced b8 7s9 7he ratio o* *sim *s ) 1 /an inteer9 i Plot the res%ltin discrete timesinal +ith *s ) ; RK. ii 7aRe its D7L7 and plot it9
Problem #
Desin a reconstr%ction *ilter 'b, a( ) cheb82/:,T0, *+t +here *+t) 2/*s2 1*sim %se *reF. to vie+ its *reF%enc8 response9 Problem $
Convert the diital sinal to analo%e sinal %sin DA conversion9 $nsert .eros in bet+een the diital sinal to obtain an analo%e o%tp%t9 7hen appl8 cheb8shev *ilter to this o%tp%t9 Plot the res%ltin recovered sinal and its Lo%rier trans*orm9 Problem
7r8 the entire proced%re *or f s ) ; RK. and f 0) 2 RK., T RK., < RK. and 1" RK.9
CSE-304 DSP.
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$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! ,
Lab D+SC'!(! FO7'+!' ('%NSFO'-
Name
CSE-304 DSP.
'eg. no.
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(otal/1
Lab2: DISC(EE '*(IE( (.+S'(! Discrete (ime Fourier (ransorm
D7L7 o* a sinal 'n( can be de*ined asN1 /? ) U 'n( e jwn
n)0
$t ives *reF%enc8 spectr%m o* the sinal9 Since co is contin%o%s, its rane is contin%o%s9 So it is impossible to et a vector in MA7A +hich covers entire rane o* the D7L79 Discrete Forurier (ransorm
N point DL7 o* a sinal 'n( is de*ined asN1 /V ) U 'n( e j(2π/N)kn
n)0
and $DL7 can be obtained b8 the relationN1 /n ) 1
U 'n( e j(2π/N)kn
N n)0 N point DL7 means taRin N eF%idistant samples /Samplin in *reF%enc8 domain9 DL7 is a sampled version o* D7L79 No+ 8o% are dividin 2n in N samples9 #idth ) 2B N
$n order to estimate D7L7 o* the sinal, +e ma8 taRe DL7 o* the sinal, +hile taRin lare n%mber o* DL7 points9
CSE-304 DSP.
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FF(
LL7 is an e**icient alorithm o* calc%lation o* DL79 $t reF%ires m%ch less comp%tation, b%t it reF%ires the n%mber o* samples to be an inteer po+er o* 29 MA7A provides LL7 command to comp%te DL7 %sin LL7 alorithm Lab !;ercises Problem 1
i Lind ; point DL7 *or the sinal i) '10000000( ii i)'11111111( iii Shi*ted imp%lse '00010000(
xshift =
iv 3point bocar xb = '11100000(
v S8mmetric bocar xbsy= '11000001(
Problem 2
s[n] ) A cos(27πf n ! ")
A)2
,
" = π/#
i Comp%te the 21point DL7 o* s[n]$ Choose f so that 8o% have eactl8 1 c8cle Plot the manit%de and phase, ii epeat *or a sine +ave, iii Choose f s%ch that 8o% have eactl83 c8cles, /21point DL7 f 0
iv Choose
= 1;
and N)21 9 #hat is the res%lt & i* there is phase, +h8&
Problem # CSE-304 DSP.
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s'n( = % jω 0 n
ω 0
= Tλ
i
ω 0
ii
N
an3 N)1T Comp%te DL79
λ
="
N
and N)1T Comp%te DL7
Problem
epeat above problems %sin LL7 and $LL7 / Choose n%mber o* samples accordinl8
$aclt% !em&er:____________________
Semester:_____________
CSE-304 DSP.
Date': ________________
Section: ________________
Page 1'
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , > La&6: $AST $+#,IE, T,A"S$+,! Name
CSE-304 DSP.
'eg. no.
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Lab: '.S '*(IE( (.+S'(! Introduction DFT The FFT reduces considerably the computational requirements of the DFT. The DFT of a discrete-time signal x (nT ) is
where the sampling period T is implied in x (n) and N is the frame length. The constants W are referred to as twiddle constants or factors, which represent the phase, or and are a function of the length N .
DFT Equation can be written for k !, ", . . . ,N - ", as
#ince this equation is in terms of a comple$ e$ponential, for each specific k there are (N - ") comple$ additions and N comple$ multiplications. This results in a total of (N % - N ) comple$ additions and N % comple$ multiplications. &ence, the computational requirements of the DFT can be 'ery intensi'e, especially for large 'alues of N . FFT reduces computational comple$ity from N % to N logN .
The FFT algorithm taes ad'antage of the periodicity and symmetry of the twiddle constants to reduce the computational requirements of the FFT.
CSE-304 DSP.
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From the periodicity of W ,
and from the symmetry
of W ,
For e$ample, let k %, and note that W "! W %, and from W -W %.
DECIMATION-IN-FREQUENCY FFT ALGORITHM WITH RADIX-2 *et a time-domain input sequence x (n) be separated into two hal'es+
Taing the DFT of each set of the sequence gi'es us
*et n n N % in the second summation X (k ) becomes
CSE-304 DSP.
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where WkN % is taen out of the second summation because it is not a function of n. /sing
X (k ) becomes
0ecause (-")k " for e'en k and -" for odd k ,abo'e equation can be separated for e'en and odd k , or
#ubstituting k %k for e'en k , and k %k " for odd k , e'en and odd parts can be written for k !, ", . . . , ( N %) - " as
CSE-304 DSP.
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0ecause the twiddle constant W is a function of the length N , it can be represented as WN . Then W %N can be written as WN %. *et
1bo'e Equation can be written more clearly as two (N %)-point DFTs,
Figure " shows the decomposition of an N -point DFT into two (N %)-point DFTs for N 2. 1s a result of the decomposition process, the X 3s in Figure " are e'en in the upper half and odd in the lower half. The decomposition process can now be repeated such that each of the (N %)-point DFTs is further decomposed into two (N 4)-point DFTs, as shown in Figure %, again using N 2 to illustrate. The upper section of the output sequence in Figure " yields the sequence X ( !) and X (4) in Figure %, ordered as e'en. X ( %) and X () from Figure % representthe odd 'alues. #imilarly, the lower section of the output sequence in Figure " yields X (") and X (5), ordered as the e'en 'alues, and X (6) and X (7) as the odd 'alues. This scrambling is CSE-304 DSP.
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due to the decompos decompositi ition on pr proces ocess. s. The final order order of the out output put sequence sequence X (!), (!), X (4), (4), . . . in Figure Figure % is shown to be scrambled.
Figure" Decomposition of an N -point -point DFT into two (N ( N %)-point DFTs for N 2
Figure % Decomposition of a 8 9oint DFT into four 84 9oint DFTs 82. CSE-304 DSP.
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The output sequence X sequence X (k ) represents the DFT of the time sequence x sequence x (n). This is the last decomposition, since we now ha'e a set of ( N %) two-point DFTs DFTs,, the lowest decomposition for a radi$-%. For the two-point DFT DFT,, X (k ) in FFT be written as
%pi% since W " e- j %pi% -".1bo'e -".1bo'e equations equations can be represent represented ed by the flow grap graph h in Figure 6, usually referred to as a butterfly .
Figure 6 Two 9oint FFT 0utterfly
This algorithm is referred to as decimation-in-frequency (D:F) because the output sequ se quen ence ce X (k ) is dec decomp ompose osed d (de (decim cimate ated) d) into sma smalle llerr sub subseq sequenc uences, es, and this process continues through M stages or iterations, where N %M %M . The output X output X (k ) is comple com ple$ $ wit with h bot both h rea reall and ima imagin ginary ary com compon ponents ents,, and the FFT alg algori orithm thm can accommodate either comple$ or real input 'alues.
CSE-304 DSP.
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The FFT is not an appro$imation of the DFT. :t yields the same result as the DFT with wi th fe fewe werr co comp mputa utati tions ons re requi quire red. d. Thi This s re reduc ducti tion on bec becom omes es mo more re and and mo more re important with higher-order FFT.
DECIMATION-IN-TIME DECIMATION-I N-TIME FFT ALGORITHM WITH RADIX-2
;herea ;her eas s th the e D:F pr proc oces ess s dec ecom omp pos oses es an ou outp tput ut se seq que uenc nce e in into to sm smal alle lerr subseq sub sequenc uences, es, decima decimation-in tion-in-time -time (D:T) is a process that decomposes the input sequence into smaller subsequences. *et the input sequence be decomposed into an e'en sequence and an odd sequence, or
and
;e can apply DFT equation to these two sequences
/sing ;%8 ;8% abo'e equation can be e$pressed as two 8% point DFTs.
*et
CSE-304 DSP.
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<() can be written as
Equation needs to be interpreted for k = (N (N %) - ". /sing the symmetry property of the twiddle constant, W k N % -W -W k ,
e$ample, for N 2, FFT 'ia Decimation in time is gi'en by
Figure 4 shows the decomposition of an eight-point DFT into two four-point DFTs with the D:T procedure. This decomposition or decimation process is repeated so that each four-point DFT is further decomposed into two two-point DFTs, as shown in Figure 5. #ince the last decomposition is ( N %) two-point DFTs DFTs,, this is as far as this process goes.
CSE-304 DSP.
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Figure 4 Decomposition of eight-point DFT into four-point DFTs using D:T.
Figure 5 Decomposition of two four-point DFTs into four two-point DFTs using D:T.
INVERE FAT FOURIER TRANFORM The in'erse discrete Fourier transform (:DFT) con'erts a frequency-domain sequence X (k ) into an equi'alent sequence x (n) in the time domain. :t is defined as
CSE-304 DSP.
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>omparing :FFT equation with the DFT equation definition, it can be seen that the FFT algorithm (forward) described pre'iously can be used to find the in'erse FFT (:FFT) with the two following changes+ !" 1dding a scaling factor of " N 2" ?eplacing W nk by its comple$ con@ugate W
Ank
;ith the changes, the same FFT flow graphs can be used for the :FFT.
L#$ E%&rci'&'
E%&rci'& ("!) :mplement a "%2-point radi$-% FFT of a real-time input sinusoid with a frequency of 6 &B and an appro$imate amplitude of %C p-p. /se a sampling frequency of "&B. btain a plot of the output and e$plain the results. ;hat is the output frequency when the input signal frequency is &B and "!&B E$plain.
E%&rci'& ("2) :mplement a %5-point radi$ FFT on real time audio input. /se T:3s optimiBed FFT function.
CSE-304 DSP.
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$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , ?
Lab? @ ,(ransorm
Name
'eg. no.
Lab5: 6 7ransform 8eor&: CSE-304 DSP.
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'eport -ars / 10
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#e +ill start o%r investiation o* the W7rans*orm b8 looRin at the mappin *rom the splane to the .plane +hich is developed d%rin the derivation o* the W7rans*orm9 #e +ill looR at the properties o* the trans*orm itsel* in a separate eample9 7o aid in o%r st%d8 o* this mappin *rom the splane to the .plane, +e +ill consider t+o speci*ic sin%soidal sinals, /t and 2/t9 7he sinals are iven b8 1/t ) cos /2t 2/t ) cos /22t 7hese t+o sinals +ill be sampled +ith an ideal imp%lse sampler operatin +ith a samplin period 7 ) pi10 seconds9 7his corresponds to a samplin *reF%enc8 +s ) 20 rs9 Onehal* o* the samplin *reF%enc8 is obvio%sl8 #s2 ) 10 rs9 Xo% sho%ld recall that +ith ideal imp%lse samplin, the val%e o* the sampled sinal /t eactl8 eF%als the contin%o%stime sinal /t at samplin instants, t ) n7, +here n is an inteer9 #hen +e +orR +ith contin%o%stime sinals Y s8stems in the trans*orm domain, +e %se the aplace 7rans*orm9 7his trans*orm is a *%nction o* the comple variable s, +hich has a real part /sima and an imainar8 part /omea9 7he imainar8 part, omea, is the variable +hich is the *reF%enc8 o* sin%soidal sinals, s%ch as 1/t and 2/t9 7he real part, sima, is the variable associated +ith the rate o* deca8 o* eponential sinals9 #hen +e +orR +ith discretetime sinals, +e %se a di**erent trans*orm, called the W7rans*orm /a*ter o*tiWadeh9 7his trans*orm is a *%nction o* the comple variable ., +hich also has real and imainar8 parts9 Ko+ever, +ith the W7rans*orm, +e enerall8 are interested in the manit%de and phase o* ., rather than its real and imainar8 parts9 7he .plane is the comple plane associated +ith the W7rans*orm, j%st as the splane is the comple plane associated +ith the aplace 7rans*orm9 #hen the W7rans*orm is derived b8 samplin a contin%o%stime sinal, the comple variable . is de*ined in terms o* the comple variable s b8 the *ollo+in epressions9 s ) Z @ j? . ) es7 ) e/ Z @ j?7 ) eZ 7 9 e j?7 )[.[
∠
.
[ . [ ) eZ 7 ,
∠
. )?7
#ith the de*inition o* . ) ep/s7, it can be easil8 seen that the manit%de o* the comple variable . is related to the real part o* s /m%ltiplied b8 7, and the phase o* . is related to the imainar8 part o* s /m%ltiplied b8 79
CSE-304 DSP.
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#e +ill bein o%r st%d8 o* the mappin *rom s to . b8 looRin at the splane9 $n the Li%re 1, note that the *reF%encies o* the t+o sinals 1/t and 2/t are sho+n, and that hori.ontal lines correspondin to + ) @ #s2 and + ) +s2 are also sho+n9 #hen samplin a contin%o%stime sinal, that part o* the splane bet+een @+s2 and +s2 is called the primar8 strip9 Note the distances *rom +s2 %p to +1 and *rom @ +s2 %p to +29 #hen the real part o* s is neative, the manit%de o* . is less than 19 7here*ore, the le*thal* o* the splane maps into the interior o* a circle centered at the oriin +ith radi%s ) 19 #hen the real part o* s is positive, the manit%de o* . is reater than 19 7here*ore, the rihthal* o* the splane maps into the eterior o* that same circle9 #hen the real part o* s is eF%al to .ero /j+ ais, the manit%de o* . eF%als 19 7here*ore, the j+ ais maps into the bo%ndar8 o* the circle9 7his circle centered at the oriin +ith radi%s) l is called the %nit circle9 7h%s, the de*inition o* . in terms o* s ives %s a comple plane +here the %nit circle is the important thin, and iss%es s%ch as stabilit8 and *reF%enc8 response +ill be dealt +ith in terms o* the %nit circle rather than the j+ ais9 %t there is even more to this mappin *rom s to .9 eali.in that 7 ) 2pi+s, i* +e let *reF%enc8 + in the splane be eF%al to +s2, +e et a phase anle *or . o* pi radians9 $* +e let + ) @+s2, +e et a phase anle *or . o* @pi radians9 $* +e let sima ) 0, and let omea o *rom +s2 to @+s2 in the splane, +e et one complete revol%tion in the .plane *rom pi to @pi radians, +ith %nit manit%de9 7hat is, +e et the complete %nit circle9 $* sima 6 0, +e et the complete interior o* the %nit circle as omea oes *rom +s2 to @+s29 7he shame thin happens *or sima \ 1 and the eterior o* the %nit circle9 7here*ore, the primar8 strip in the splane maps into the entire .plane9 7he same complete mappin occ%rs *or an8 hori.ontal strip in the splane +hich has a Keiht o* +s rs9 7here*ore, the splane maps into the .plane an in*inite n%mber o* times9 EniF%e points in the splane +ill map into the same point in the .plane d%e to this relationship bet+een s and .9 No+ +e +ill looR at the .plane9 $n the net *i%re, the %nit circle is sho+n9 7he interior o* that circle corresponds to the le*thal* o* the splane, the eterior corresponds to the rihthal* o* the splane, and the circle itsel* corresponds to the j+ ais9 Note that the t+o distinct *reF%encies in the splane, ]v] and +2, have mapped into the same point in the .plane, namel8 their phase anles are eF%al and their manit%des are both eF%al to 19 7he mappin o* the t+o *reF%encies into the .plane is sho+n in the eF%ations9 . ) es7)\ e j?7) e j2B??s .1 ) e j092B ) 09;0:0@j09";<; .1 ) e j292B ) 09;0:0@j09";<; [ . 1[ ) [ . 2[ )1 , 6.1 ) 6.2 ) 3T^
CSE-304 DSP.
Page 33
Lrom the *i%re o* the splane /Li%re 1, 8o% co%ld see that +1 and +2 have identical positions relative to the bottom /or top or middle o* a strip in the splane +hich maps into the entire . plane9 7hat is, the *reF%enc8 +1 ) 2 rs is 12 rs above the bottom o* the primar8 strip, +hich starts at 5 +s2 ) 10 rs, and the *reF%enc8 +2 ) 22 rs is 12 rs above the bottom o* the net strip, +hich starts at @ +s2 ) @10 rs9 /An alternate vie+ is- +1 is 2 rs above 0 rs, and +2 is 2 rs above +s ) 20 rs9 Lrom the de*inition o* . in terms o* s, this means that the *reF%encies +1 and +2 map into the same point in the .plane9 $* the samplin *reF%enc8 had been a di**erent val%e, the *reF%encies +1 and +2 +o%ld have mapped into distinct points in the .plane9 7here*ore, the val%e o* the samplin period 7 /or samplin *reF%enc8 +s determines +here on the %nit circle *reF%encies *rom the j+ ais +ill end %p9 #hat is the sini*icance o* the t+o contin%o%stime *reF%encies +1 and +2 mappin into the same point in the .plane& 7he ans+er is the t+o sinals, 1/t and /t have eactl8 the same val%es at all sample times +hen the samplin period 7 pi10 seconds9 7hat is, i/t ) 2/t at ever8 discrete point in time de*ined b8 n79 7here is no +a8 to tell one sinal *rom the other based on their samples9 7here is also no +a8 to o bacR *rom the discretetime samples to the contin%o%s time sinals9 emember that the Lo%rier 7rans*orm o* a sampled sinal contains all the *reF%encies o* the contin%o%stime sinal pl%s copies o* those *reF%encies displaced b8 all inteer m%ltiples o* the samplin *reF%enc8 +s, as sho+n in the *ollo+in eF%ation9 _
_
/j?) 1U ' j/?n?s( ) 1U ' j/?n?s( 7 n)_
7 n)_
7he *irst *e+ *reF%encies +hich appear in 1/j+ /+1 ) 2 rs +hen 7 ) pi10 s are'!2 3; 22 1; 2 2 1; 22 3; !2( rs in the primar8 strip, 10 rs to @10 rs9 7heoreticall8, the sinal 1 /t co%ld be reconstr%cted *rom the sampled sinal (/t b8 %sin an ideal lo+pass *ilter9 7he oriinal *reF%encies @ 2 rs are there, and the8 are the onl8 terms +hich appear 7he *irst *e+ *reF%encies +hich appear in 2/jG+ /+2 ) 22 rs +hen 7 ) pi10 s are'T2 !2 22 1; 2 2 1; 22 !2 T2( rs Kere +e see that the oriinal *reF%encies @ 22 rs sho+ %p, b%t the8 are not in the primar8 strip9 7he onl8 *reF%encies +hich do appear in the primar8 strip are @ 2 rs, the *reF%encies o* i/t not o* 2/t9 7here*ore, i* the discretetime sinal 2/t +as passed thro%h an ideal lo+pass *ilter +ith a band+idth o* ]vs2 ) 10 rs, the sinal that +o%ld be reconstr%cted +o%ld be 1 /t instead o* 2 /t9
CSE-304 DSP.
Page 34
Points in the splane *rom o%tside the primar8 strip become indistin%ishable *rom points in the primar8 strip +hen mapped into the .plane9 7his is the reason +h8 a contin%o%stime sinal m%st be sampled at a *reF%enc8 reater than t+ice the hihest *reF%enc8 in the sinal i* it is to be recoverable *rom its samples9 7he net *i%re /Li%re 3 sho+s the t+o contin%o%stime sinals +ith their sampled val%es +ith 7 ) pi10 seconds9
Li%re 1
Li%re 2
CSE-304 DSP.
Page 3
Li%re 3
!:uialency betAeen @"transorm an3 t4e D(F(
_ /. ) U 'n( .n
and
n)_ _ /? ) U 'n( ej?n
n)_
Simpl8 replace W +ith e j+ in W`trans*orm to et the *reF%enc8 response9
CSE-304 DSP.
Page 35
P%ttin . ) ejo /i9e9 eval%atin W trans*orm alon a %nit circle +e can *ind D7L79 Lor a s8stem to be stable and ca%sal all poles sho%ld lie inside the %nit circle9 -%(L%& Comman3s 'elate3 Ait4 @ (ransorm
'K , ?( ) *reF. /, A, N 'K,7( ) imp./,A,N .plane/.,p '., P, R( ) t*2.p/,A ',A( ) .p2t*/.,P,R ',P,V() resid%e./,A
Lab !;ercises Problem 1
i K/. )
.1
3!.1 @ . 2 ii K/. ) 1 @ 09!2 .1 1 5 09; 2.1 @ 09T!. 2 a >val%ate and plot the .trans*orm on %nit circle, i9e9 *ind K/e j? 0 ? 2B9 b ocate and plot the .eros and poles c Determine d Lind
the
the
inverse
partial
.trans*orm o*
*raction epansion9
e Lind the radii o* all poles and .eros9
CSE-304 DSP.
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K/. 9i9e9 *ind imp%lse response9
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , B
LabB ++' D+9+(% F+L(!' D!S+9N
Name
'eg. no.
Lab9: II( DII.: 'ILE( DESI+ First Or3er LoAPass ++' Filter
K/. ) b/1@ .1 /1 a.1 CSE-304 DSP.
Page 3
'eport -ars / 10
ia -ars /
(otal/1
?c) /* c * s 2B =c) 10 5Ac20 ) /=c 1 =c2 tan/?c 2 a) / 1 /1@ b) /1@ Problem 1
=iven * s, * c and Ac , desin *irst order $$ *ilter, * s) 10000 /i * c) 1000, /ii * c ) 1000,
Ac )3d> Ac )09!Tdb
/Plot *reF%enc8 response o* /i and /ii in the same *i%re /iii * c )3"00, /iv * c )"00,
c3d Ac)OATd
/Plot *reF%enc8 response o* /iii and /iv in the same *i%re Lirst Order KP Lilter Problem 2
K/. ) b /1 .1 1 a.1 =c) 10 5Ac20 ) /=c 1 =c2 tan/?c 2 a) / 1 /1@ b) /1@ /i * c ) 1000, /ii * c ) 1000,
Ac )3d Ac )09!Td
/Plot *reF%enc8 response o* /i and /ii in the same *i%re /iii f % = 3"00 , CSE-304 DSP.
A c=3&' Page 3'
/iv f c = 3"00 ,
Ac = 09!T d
/Plot *reF%enc8 response o* /iii and /iv in the same *i%re Complementary Nature O LP an3 P Filter Problem #
Lor * s 10000 , * c ) 1 RK., Ac ) 3 d i9 Desin a lo+pass *ilter and plot *reF%enc8 response, ii9 Desin hihpass *ilter and plot *reF%enc8 response, iii9 Lind and plot the s%m o* *reF%enc8 responses o* P and KP *ilters9 /All plots sho%ld be in the same *i%re Notc4 ++' Filter Design Problem $
K/. ) b /1 2cos?0 .1 @ .2 1"2cos 0 E"1 <2b"1= E2
) /1=2 = tan/f?2 = ) 10A 20 b)
1 1@ Lind K/. and plot its *reF%enc8 response9 * s ) 10RK. i9 ii9
* 0 ) 19<" RK. f* )"00 K. * 0)3d * 0 )19<" RK. f* )"00 K. A )10d
iii9 * 0) 19<" RK. f* ) 100 K. A ) 3 d iv9 * 0)19<" RK. f* ) 100 K. A ) 10d Peaing / 'esonator ++' Filter Design
K/. )
/1 b /1 .2
1"2cos 0 E"1 <2b"1= E2
) /1=2 = tan/f?2 b)
1
CSE-304 DSP.
Page 40
1@ Problem
Lind K/. and plot its *reF%enc8 response9 * s ) 10RK. i9 ii9 iii9 iv9
* 0 ) 19<" RK. f* )"00 K. * 0 )19<" RK. f* )"00 K. * 0) 19<" RK. f* ) 100 K. * 0)19<" RK. f* ) 100 K.
* 0)3d * 0 )10d * 0 ) 3 d * 0 ) 10d
Complementary Nature O Peaing %n3 Notc4 Problem >
Lor * s ) 10RK. , * 0 ) 19<"RK., f* ) "00 RK., A )3d a b c
Desin a notch *ilter *or above parameters and plot the *reF%enc8 response9 Desin a resonator *ilter *or above parameters and plot the *reF%enc8 response9 Add the *reF%enc8 response o* notch and resonator and plot it9
/All three plots sho%ld be in the same *i%re
CSE-304 DSP.
Page 41
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , G
LabG F+L(!' D!S+9N 7S+N9 %N%LO9 P'O(O()P+N9
Name
'eg. no.
'eport -ars / 10
ia -ars /
Lab: 'ILE( DESI+ *SI+ .+.L P(,PI+
CSE-304 DSP.
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(otal/1
+ntro3uction
7he traditional approach to desin $$ diital *ilters involves the trans*ormation o* an analo *ilter into a diital *ilter meetin prescribed speci*ication beca%se 19 7he art o* analo *ilter desin is hihl8 advanced and since %se*%l res%lts can be achieved, it is advantaeo%s to %tili.e the desin proced%res alread8 developed *or analo *ilters 29 Man8 %se*%l analo desin methods have relativel8 simple closed*orm desin *orm%las9 7here*ore diital *ilter desin methods based on s%ch analo desin *orm%las are rather simple to implement9 39 $n man8 applications it is o* interest to %se a diital *ilter to sim%late the per*ormance o* an analo linear *ilter
-et4o3s o %nalog"3igital transormation 1. +mpulse +nariance
One method o* trans*ormin an analo *ilter desin to a diital *ilter desin corresponds to choosin the %nit sample response o* the diital *ilter as eF%all8 spaced samples o* imp%lse response o* the analo *ilter9 7hat is h/n = h / n
2. &ilinear (ransorm
7he bilinear trans*ormation is a mathematical mappin o* variables9 $n diital *ilterin, it is a standard method o* mappin the s or analo plane into the . or diital plane9 $t trans*orms analo *ilters, desined %sin classical *ilter desin techniF%es, into their discrete eF%ivalents9 7he bilinear trans*ormation maps the splane into the .plane b8 s =
21 − * −1 ( 1 + * −1
&utterAort4 Filter
CSE-304 DSP.
Page 43
%tter+orth *ilters are de*ined b8 the propert8 that the manit%de response is maimall8 *lat in the passband9 Another propert8 is that the approimation is monotonic in the passband and the stopband9 7he sF%ared manit%de o* %tter+orth *ilters is o* the *orm7he sF%ared manit%de o* %tter+orth *ilters is o* the *orm-
7he sF%ared manit%de o* %tter+orth *ilters is o* the *orm + / jΩ
2
=
1 1 + / jΩ jΩ c 2 N
C4ebys4e (ype + Filter
7he Cheb8shev t8pe $ *ilter minimi.es the absol%te di**erence bet+een the ideal and act%al *reF%enc8 response over the entire passband b8 incorporatin an eF%al ripple o* p d in the passband9 Stopband response is maimall8 *lat9 7he transition *rom passband to stopband is more rapid than *or the %tter+orth *ilter9
CSE-304 DSP.
Page 44
C4ebys4e (ype ++ Filter
7he Cheb8shev t8pe $$ *ilter minimi.es the absol%te di**erence bet+een the ideal and act%al *reF%enc8 response over the entire stopband, b8 incorporatin an eF%al ripple o* s d in the stopband9 Passband response is maimall8 *lat9 7he stopband does not approach .ero as F%icRl8 as the t8pe $ *ilter /and does not approach .ero at all *or evenval%ed n9 7he absence o* ripple in the passband, ho +e ve r, is o* ten an im po rt an t advantae9 !lliptic Filter
>lliptic *ilters are eF%iripple in both the passband and stopband9 7he8 enerall8 meet *ilter reF%irements +ith the lo+est order o* an8 s%pported *ilter t8pe9 =iven a *ilter order n, passband ripple p in decibels, and stopband ripple s in decibels, elliptic *ilters minimi.e transition +idth9 SF%ared manit%de o* elliptic *ilters can be estimated b8 the *ollo+in eF%ation + ) / jΩ
2
=
1 1 + ε 2, N 2 /Ω
+here EN/ is a Jacobian elliptic *%nction9 ω
Lab !;ercises CSE-304 DSP.
Page 4
Problem 1
Ese help command to learn the %se o* *ollo+in commands b%tter, b%ttord, cheb8l, cheblord, cheb82, cheb2ord, ellip, ellipord Problem 2
/i
=enerate 100 samples o* the *ollo+in sinal
/t ) cos / 1 1 2π × 10t − cos/ 2λ × 30t + cos/ 2λ × "0t 3 "
/* s)200 Plot the D7L7 o* above sinal /ii emove the lo+est *reF%enc8 component o* sinal %sin all above mentioned *ilters9 Ese *reF. to plot the *reF%enc8 response o* *ilters %sed9 Plot inp%t and o%tp%t sinals9 /iii epeat part /ii to remove intermediate *reF%enc8 component /iv epeat part /ii to remove the hihest *reF%enc8 component /Save the res%lt as *i *iles, as % +ill be needin these res%lts in net lab *or comparison /p%rpose Problem #
Comment on the res%lts obtained b8 %sin di**erent *ilters/phaselinearit8, transition band+idth, *ilter order reF%irement *or achievin the same per*ormance
CSE-304 DSP.
Page 45
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 10
Lab10 L+N!%' P%S! F+' F+L(!' D!S+9N &%S!D ON 8+NDO8S
Name
CSE-304 DSP.
'eg. no.
Page 4"
'eport -ars / 10
ia -ars /
(otal/1
Lab10: LI+E.( P;.SE 'I( 'ILE( DESI+ %.SED + I+DS (4eory
LreF%enc8 o* an ideal lo+pass *ilter is
− ω c ≤ ω ≤ ω c
+ α /ω
)
1, 0, other+ise
$ts imp%lse response is iven b8 ω c λ
hα /n
)
,
R)0
sin/ ω c k λ k
,
other+ise
Ca%sal L$ Lilters can be obtained b8 g 7r%ncatin the imp%lse response o* the ideal *ilter to maRe its lenth *inite9 g And shi*tin the tr%ncated response to maRe it ca%sal9 7he process introd%ces phase dela8 /linear +ith *reF%enc8 and ripples in passband and stopband9 7he reason behind this phenomenon can be eplained b8 considerin the tr%ncation operation as m%ltiplication b8 a *initelenth +indo+ seF%ence + 'n( and b8 eaminin the +indo+in process in the *reF%enc8 domain9 7h%s, the L$ *ilter obtained b8 tr%ncation can be alternativel8 epressed as h1 ' n( = h& 'n(9w'n(
Lrom the mod%lation theorem, the Lo%rier trans*orm o* the above eF%ation is iven b8 π
∫
+ t /% = 1 M 2π + & /% jϕ ψ /% w−ϕ & φ jw
−π
CSE-304 DSP.
Page 4
jw
+here Kt /e and
ψ
jw
/e are the Lo%rier trans*orms o* h 1
1
' n(
and +'n(, respectivel89 7he
jw
above eF%ation implies that K /e is obtained b8 a periodic contin%o%s convol%tion o* the &
ψ
jw
desired *reF%enc8 response K /e +ith the Lo%rier trans*orm9
jw
/e o* the +indo+9 7he
process is ill%strated in the *ollo+in *i%re +ith al Lo%rier trans*orms sho+n as real *%nctions *or convenience9
ψ
Lrom the last eF%ation, it *ollo+s that i*
jw
/e is a ver8 narro+ p%lse centered at M6n6M &
jw
/ideall8 a delta *%nction compared to variations in K /e , then jw
jw
Kt /e +ill approimate Kd /e ,ver8 closel89 7his implies that the lenth 2M @ 1 o* the +indo+ *%nction co'n( sho%ld be ver8 lare9 On the other hand, the lenth 2M @ 1 o* ht'n( , and hence that o* +'n( , sho%ld be as small as possible to maRe the comp%tational compleit8 o* the *ilterin process small9 CSE-304 DSP.
Page 4'
$n order to impart desired properties to the *ilter response, +e +ill disc%ss some commonl8 %sed tapered +indo+s o* lenth 2M @ 1, +hich are /a Kannin w' n( =
b
1 2π n 1 cos − 2 N − 1 0 ≤ n ≤ N − 1
Kammin
2π n N − 1 0 ≤ n ≤ N − 1
w'n( = 09"! − 09!T cos
c
lacRman
2π n + 090; cos !π n N − 1 N − 1 0 ≤ n ≤ N − 1
w'n( = 09!2 − 09" cos
d
Vaiser
-
w' n (
=
2 2 n N − 1 N − 1 ω − − 2 2 N − 1 - ω − 2 )
)
#here
1 x k - / x = 1 + ∑ k 2 k =1 β
2
CSE-304 DSP.
Page 0
7o %nderstand the e**ect o* the +indo+ *%nction on L$ *ilter desin, +e sho+ in the *ollo+in *i%re a t8pical relation amon the *reF%enc8 responses o* the +indo+ed lo+pass *ilter, the +indo+ *%nction, and the desired ideal lo+pass *ilter, respectivel89
'elations among t4e re:uency responses o an +3eal loApass ilterH a typical Ain3oAH an3 t4e Ain3oAe3 ilter.
Since the correspondin imp%lse responses are s8mmetric +ith respect to n ) 0, the *reF%enc8 responses are o* .erophase9 Lrom this *i%re, +e observe that *or the +indo+ed *ilter, + t /% jw +ω + + t /% jw −ω ≡ 1 + t /% jw ≡ 09" c , aro%nd the c%to** *reF%enc8 w . As a res%lt, 9 Moreover, the passband and stopband ripples are the same9 $n addition, the distance bet+een locations o* the maim%m passband deviation and minim%m stopband val%e is approimatel8 c
eF%al to the +idth
c
c
∆ M/
c
o* the main lobe o* the +indo+, +ith the center at w . 7he +idth o* the ∆w = w x − w 0 ∆ M/ transition band, de*ined b8 $ is less than 9 7here*ore, to ens%re a *ast transition *rom the passband to the stopband, the +indo+ sho%ld have a ver8 small main lobe δ
+idth9 On the other hand, to red%ce the passband and stopband ripple , the area %nder the side lobes sho%ld be ver8 small9 En*ort%natel8, these t+o reF%irements are contradictor8 $n the case o* the +indo+ *%nctions o* above eF%ations /Kann, Kammin, lacRman, the δ
val%e o* the ripple does not depend on the *ilter lenth, or the c%to** *reF%enc8 wc, and is essentiall8 constant9 $n addition, the transition band+idth is approimatel8 iven b8
∆w ≈ c M +here c is a constant *or most practical p%rposes9 7he *ollo+in table s%mmari.es the essential properties o* some o* the above +indo+ *%nctions9 CSE-304 DSP.
Page 1
78pe o* +indo+
Main obe #idth
elative Sidelobe evel
∆ M/
A sl
ect9
!λ / 2 M + 1
1393 d
209: d
09:2λ M
Kann9
;λ /2 M + 1
319" d
!39: d
3911λ M
Kamm9
;λ /2 M + 1
!29< d
"!9" d
3932λ M
lacRman
12λ /2 M + 1 ";91 d
<"93 d
"9"Tλ M
c
Min9 7ransition Stopband and+idth atten%ation
∆ω
π
/al%es sho+n in the table are *or w )09! and M)12;
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 11
Lab11 +N(!'POL%(+ON %ND D!C+-%(+ON
CSE-304 DSP.
Page !
Name
'eg. no.
'eport -ars / 10
ia -ars /
(otal/1
Lab11: I+E(PL.I+ .+D DECI!.I+ Teor%
Decimation
Decimation is the process o* red%cin the samplin rate b8 an inteer *actor, M9 $n the discrete time domain, decimation o* a sinal b8 M is per*ormed b8 discardin all b%t ever8 Mth sample o* 9 $* +e denote the decimated sinal b8 j, it *ollo+s that x & / 1 = x / M1 $n other +ords onl8 ever8 Mth sample o* the oriinal sinal is retained9 S%ppose +e have a sampled version o* an analo sinal +hich has a samplin rate +hich is too hih9 7his can arise *or a n%mber o* reasons9 Lor instance, the data ma8 have been sampled b8 a data acF%isition s8stem +hich has a *ied samplin rate9 Lor reasons o* data storae or real time band+idth reF%irements, it ma8 be necessar8 to lo+er the samplin rate o* the s8stem9 On sol%tion is to convert the sinal bacR to analo and then resample at the ne+ rate9 Another sol%tion, +hich is m%ch more practical, is to per*orm the samplin rate conversion in the discrete time domain9 CSE-304 DSP.
Page 3
7he spectr%m o* the decimated sinal consists o* a s%m o* *reF%enc8 scaled and shi*ted copies o* J/co, as sho+n in *i%re-
$t is clear *rom the *i%re that *reF%enc8 spectr%m is epanded b8 M9 Since e**ectivel8 +e are red%cin samplin rate, it is necessar8 to *ilter the sinal be*ore decimation +ith a c%to** *reF%enc8 o* <7M, beca%se the *reF%enc8 components +ith *reF%enc8 reater than <7M +ill ca%se aliasin9 So process o* decimation can be s%mmari.ed b8 the *ollo+in blocR diaram-
+nterpolation
$nterpolation is the inverse operation o* decimation9 Q8 interpolation, +e are tr8in to enerate intermediate samples o* a discrete time sinal, /R9 7his corresponds to increasin the samplin rate9 One approach to interpolation +o%ld be to reconstr%ct the analo sinal and then
convert it into diital +ith the ne+ samplin rate9 7his does not need to done, ho+ever9 $nterpolation can be per*ormed entirel8 in the discrete time domain9 %
=iven an interpolation rate +hich is an inteer M, de*ine the sinal /R b8
CSE-304 DSP.
Page 4
%
/R)
R ) 0,k1,k2,999 other+ise
7he res%ltant sinal is derived *rom /R b8 .ero*illin, +hich is also Rno+n as samplin rate epandin9
7he impact o* .ero*illin in *reF%enc8 domain is compression o* D7L7 and *ilterin is reF%ired to remove the hih *reF%enc8 components introd%ced d%e to compression o* the spectr%m, as evident *rom the *i%re iven belo+,
So the process o* interpolation can be described b8 the *ollo+in blocR diaram-
CSE-304 DSP.
Page
Non"+nteger Sampling 'ate C4anges
#e have alread8 seen ho+ to increase or decrease the samplin rate o* a discrete time sinal b8 in inteer *actor9 7here are sit%ations +here it is necessar8 to chane the samplin rate b8 a non inteer *actor9 Lor instance, compact disc /CD and diital a%dio tape /DA7 are based on di**erent samplin rates9 $* +e +ish to per*orm a CD to DA7 trans*er, the record companies +o%ld pre*er that it be done b8 CDtoanalo *ollo+ed b8 analotoDA7, res%ltin in a loss o* a%dio *idelit89 $nstead, +e +ill sho+ the samplin rate conversion can be per*ormed entirel8 in discrete time domain9 eca%se the ratio o* t+o samplin rates +ill al+a8s be rational, it is not restrictive to consider onl8 the case +here the samplin rate m%st be chaned b8 a rational n%mber9 7h%s, s%ppose +e +ish to chane the samplin rate *rom 7 to 7/M this can be accomplished in t+o steps9 Lirst the samplin rate is converted *rom 7 to 7 b8 interpolation9 7his consists o* epandin the π
sinal b8 *ollo+ed b8 *ilterin +ith a lo+ pass *ilter +ith c%to** *reF%enc8 o* 9 Net, the sinal +ith sample rate 7 is decimated b8 M9 7his is per*ormed b8 *irst *ilterin the sinal thro%h a lo+ pass *ilter +ith c%to** *reF%enc8
π
M and then retainin
onl8 ever8 Mth sample9 7he net res%lt +ill be a sinal +hose samplin rate is 7/M9 7he proced%re is sho+n in *i%re-
Clearl8 +e can replace the t+o *ilters +ith a sinle *ilter, as sho+n in *i%re-
CSE-304 DSP.
Page 5
Lab !;ercises
Problem 12
a9 =enerate 32 samples o* *ollo+in sinals
i9 ii9
1
/t = 1
x 2 /t = sin/ 2π "0 t
s
/*
= 100
b9 Plot the sinal and their DL7s9 /%se LL7 and scale the ais *rom 0 to 2 c9
$nterpolate the sinals /N)29 epeat part b *or the interpolated sinals9 Observe and comment on the impact o* interpolation in time domain and *reF%enc8 domain
d9 Constr%ct *ilter *or the interpolated sinals9 Lilter the sinals and observe the sinals in both time and *reF%enc8 domains
*iltered
e9 Comment on e**ect o* *ilterin on the interpolated sinals9 Problem 2a9 =enerate 32 samples o* *ollo+in sinals i9 l /t )sF%are +ave o* *reF%enc8 2" K.9 /*s ) 100 /do not %se antialiasin *ilter b9 Plot the sinal and their DL7s9 /%se LL7 and scale the ais *rom 0 to 2 c9 Decimate the sinals /N29 epeat part b *or the decimated sinals9 Observe and comment on the impact o* decimation in time domain and *reF%enc8 domain d9 $ndicate the sinal *or +hich it is necessar8 to *ilter the sinal be*ore decimation e9 Desin *ilter +hich sho%ld be %sed be*ore decimation in this case9 *9 epeat part c a*ter *ilterin the oriinal sinals9 CSE-304 DSP.
Page "
9 Comment on res%lts obtained in part c and part *9 Problem 3Chane the samplin rates o* sinals iven in Problem 2 to <" K.9
CSE-304 DSP.
Page
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!"#0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 12
Lab12 (! POL)P%S! D!CO-POS+(+ON
Name
CSE-304 DSP.
'eg. no.
Page '
'eport -ars / 10
ia -ars /
(otal/1
Lab1$: ;E PL,P;.SE DEC!PSII+ 7he Mcomponent pol8phase decomposition provides a convenient representation o* /. +hich +ill be ver8 %se*%l +hen disc%ssin decimation, interpolation, and chanin the samplin rate b8 noninteer ratio9 S%ppose is a sinal +ith Wtrans*orm
2 / * =
∞
∑ x/k *
− k
k = −∞
O%r end oal is to *ind a convenient epression *or the Wtrans*orm o* GG +hen the samplin rate is either increased or decreased b8 a *actor o* M9 As a *irst step, +e can breaR the sinal into a disjoint collection o* elements +hose indices are separated b8 M9 7o this end, re+rite /. as /. )
+ x/0 + x/ M * − M + x/2 M * −2M +
* − / + x/1 + x/ M + 1 * − 1
M
+ x/2 M + 1 * −2 M +
* −2 / + x/ 2 + x/ M + 2 * − M + x/2 M + 2 * −2 M
+
− / M −1
*
−2 M
/ + x/ M − 1 + x/2 M − 1 *
+ x/3 M − 1 * −3M +
#e net proceed b8 *actorin .G *rom the ith ro+ o* the above set o* eF%ations, +hich ives /. )
+ x/0 + x/ M * − M + x/2 M * −2M +
* − / + x/1 + x/ M + 1 * − 1
M
+ x/2 M + 1 * −2 M +
* −2 / + x/ 2 + x/ M + 2 * − M + x/2 M + 2 * −2 M
+
CSE-304 DSP.
Page 50
* −
/ M −1
/ + x/ M − 1 + x/2 M − 1 * −
2 M
+ x/3 M − 1 * −3 M +
→ /1
7he ith ro+ o* this epression can be +ritten as .i
∞
∑ x/kM + i/ *
M
−k
k = −∞
7he s%mmation in the above eF%ation is simpl8 the Wtrans*orm o* the elements o* GG +hich are separated b8 M9 $* +e de*ine the pol8phase component Pi/.b8 Pi/. )
∞
∑ x/kM + i/ *
M
−k
k = −∞
and s%bstit%te into the last eF%ation, +e have .i
) .iPiWM
∞
∑ x/kM + i/ *
M
− k
k = −∞
Linall8, *rom eF%ation /1, +e have /.) P0/.M @ .1P1/.M @ .2P2/.M @ 9 @ ./M1PM1/.M #hich ives the Mcomponent pol8phase decomposition /. )
∞
∑W
1
Pi /W M
k = −∞
$mplementation o* the eF%ation can be described b8 the *ollo+in *i%re-
CSE-304 DSP.
Page 51
Polyp4ase Structures or Decimation
Consider the L$ decimation s8stem sho+n in *ollo+in *i%re9
7his s8stem consists o* an L$ o* lenth N *ollo+ed b8 a decimator o* rate M9 the s8stem onl8 needs to comp%te the o%tp%t samples 8/RM9 eca%se the L$ precedes the decimator, ho+ever, +e reF%ire that N m%ltiplications be per*ormed d%rin the clocR c8cle +hen 8/RM is bein comp%ted in order to maintain realtime data *lo+9 D%rin the other clocR c8cles, the s8stem is idle9 7his is clearl8 a +aste o* comp%tational reso%rces9 7his problem can be recti*ied in and eleant and simple manner %sin the pol8phase decomposition9 et K/. be a rational trans*er *%nction9 Consider the t+o s8stems in the *ollo+in *i%re9
7he *irst o* these s8stems consists o* s decimator o* rate M *ollo+ed b8 K/.9 7he second s8stem consists o* K/.M *ollo+ed b8 a decimator o* rate M9 #e can prove that these s8stems are eF%ivalent9 Clearl8, the *irst s8stem in the above *i%re is more e**icient than the second9 7he trans*er *%nction K/.M, altho%h o* hiher deree than K/., +ill have the s% n4b%5 of non*%5o co%ffici%nts as K/.9 7h%s, K/.M reF%ires the same n%mber o* m%ltiplications per c8cle as K/.9 Notice, ho+ever, that the data rate is m%ch hiher *or the con*i%ration in +hich *ilterin is per*ormed be*ore decimation9 $* the *ilter is 05%c%&%& b8 the decimator, the data arrives at the *ilter at a data rate +hich is M times slo+er9 7o see ho+ this res%lt can be %sed to derive an e**icient str%ct%re *or decimation, ass%me +e +ish to *ilter b8 K/. and then decimate b8 M9 Kence, K/. has a pol8phase decomposition iven b8 CSE-304 DSP.
Page 5!
+ / * =
M −1
∑ * + / * −1
M
i
i =0
7h%s, one possible str%ct%re *or the decimation*ilterin s8stem is iven in the *ollo+in *i%re9
An eF%ivalent str%ct%re can be b%ilt %sin the identit8 +e j%st mentioned- *ilterin b8 KJ/WM then decimatin b8 M is eF%ivalent to decimatin b8 M then *ilterin b8 K i/.9 7here*ore, +e can replace the pol8phase *ilters Ki /WM +ith the *ilters Ki /W and decimate a*ter the *ilters, as sho+n in *i%re sho+n belo+-
#hen K/. is L$ o* lenth N, the pol8phase components +ill each have at most NM non.ero m%ltiplications so that the ne+ architect%re +ill reF%ire total o* /NMM ) N m%ltiplications per o%tp%t sample9 Ko+ever, the inp%t to the *ilters arrives at 1M the clocR speed9 7h%s, the comp%tational compleit8 has been red%ced b8 a *actor o* M9 Polyp4ase Structures or +nterpolation
CSE-304 DSP.
Page 53
J%st as +ith decimation, the pol8phase representation ma8 be %sed to red%ce the comp%tational compleit8 o* interpolation9 $t is simple to sho+ that the s8stems in the *ollo+in *i%re have the same inp%t o%tp%t behavior9
/Li9 eF%ivalent s8stems *or interpolation Accordin to the eF%ation e/e j )/e jM , i* the inp%t to the samplerate epander o* the *irst θ
θ
s8stem is /R, the o%tp%t o* the epander has Wtrans*orm /.M9 7h%s, the o%tp%t o* the *irst s8stem has the Wtrans*orm K/.M/.M9 >aminin the second s8stem, the o%tp%t o* the *ilter is K/./., and aain accordin to the above eF%ation, the o%tp%t o* the epander is iven b8 K/.M/.M9 7here*ore, the t+o s8stems are eF%ivalent9 Consider the problem o* implementin interpolation in practice9 O%r theoretical model +as to *irst epand the sinal b8 M b8 .ero*illin and then lo+pass *ilterin at the increased samplin rate 7M9 $* the lo+pass *ilter is an L$ o* lenth N, each o%tp%t sample o* the *ilter reF%ires N m%ltiplications per 7M %nits o* time9 Lor even modest interpolation rates and L$ lenths, this ma8 not be possible %sin a**ordable /or even eistin hard+are9 Lort%natel8, the pol8phase representation can be %sed to lessen the comp%tational compleit8 o* the interpolator9 CSE-304 DSP.
Page 54
7his time, the transposed pol8phasedecomposition can be %sed to reali.e an e**icient str%ct%re *or interpolation9 7he *ollo+in *i%re sho+s the samplin rate epander prior to the transposed pol8phase net+orR-
7his model reF%ires N m%ltiplications per 7M seconds9 $nstead, the samplin rate epander can be moved to the riht o* the pol8phase9 7his is sho+n in the *ollo+in *i%re-
$n this net+orR, each pol8phase *ilter reF%ires NM m%ltiplications per 7 seconds, *or a total o* N m%ltiplications per 7 seconds9 7his represents a red%ction in compleit8 b8 a *actor o* M9 Lab !;ercise 'epeat t4e problems o preious lab using polyp4ase ilters.
CSE-304 DSP.
Page 5
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!" #0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 1#
Lab1# P!'+OD+C 8%! 9!N!'%(O'S
Name
CSE-304 DSP.
'eg. no.
Page 55
'eport -ars / 10
ia -ars /
(otal/1
Lab13: PE(IDIC ./E E+E(.(S
+ntro3uction
$t is o*ten desired to enerate vario%s t8pes o* +ave*orms, s%ch as periodic sF%are +aves, sa+tooth sinals, sin%soids, and so on9 A *ilterin approach to eneratin s%ch +ave*orms is to desin a *ilter K/. +hose imp%lse response h/n is the +ave*orm one +ishes to enerate9 7hen, sendin an imp%lse as inp%t +ill enerate the desired +ave*orm at the o%tp%t9 Sinusoi3al ICosinusoi3al 9enerators
7he above *ilterin approach can be %sed to enerate a /ca%sal sin%soidal sinal o* *reF%enc8 *o and sampled at a rate * s9 Denotin the diital *reF%enc8 b8 ω 0
= 2π f 0
f s
#e have the . trans*orm pair h/n ) nsin/ ω 0 n4 /n
+ / * =
6 sin ω 0 * −1 1 − 2 6 cos ω o * −1 + 6 2 * −1
And, h(n) = 6ncos( ω 0 n4 /n
⇒
+ / * =
1 − 6 cos ω 0 * −1 1 − 2 6 cos ω o * −1 + 6 2 * − 2
Dual (one -ulti Fre:uency n 9enerator
CSE-304 DSP.
Page 5"
A common application o* sin%soidal enerators is the alldiital to%chtone phone, Rno+n as D%al7one M%lti*reF%enc8 /D7ML transmitterreceiver9 >ach Re8pressed on the Re8 pad enerates the s%m o* t+o a%dible sin%soidal tones, that is9 the sinal
8/n ) cos /
n @cos/ ω /
n ω +
+here the t+o *reF%encies %niF%el8 de*ine the Re8 that +as pressed9 Lollo+in *i%re sho+s the pairs o* *reF%encies associated +ith each Re89
120:
133T
E<<
1T33
7he partic%lar val%es o* the ; Re8pad *reF%encies have been chosen care*%ll8 so that the8 do not inter*ere +ith speech9 At the receivin end, the d%altone sinal 8/n m%st be processed to determine +hich pair o* *reF%encies is present9 7his can be accomplished either b8 *ilterin 8/n thro%h a banR o* band pass *ilters t%ned at the ; possible D7ML *reF%encies or b8 comp%tin the DL7 o* 8/n and determinin +hich pairs o* *reF%enc8 bins contain s%bstantial ener89 Perio3ic 9enerators
S%ppose +e have to enerate a repeatin seF%ence mb0, b1,ll, bD1, b0, b1,G, ll, bD1, b0, b1, ,ll bD1,l99a
Esin the *ilterin approach j%st described above +e can accomplish this tasR9 S%ch a *ilter m%st have the imp%lse responseh) mb0, b1,ll, bD1, b0, b1,G, ll, bD1, b0, b1, ,ll bD1,l99a 7he reF%ired imp%lse response is sho+n in the *ollo+in *i%re-
CSE-304 DSP.
Page 5
7he *ollo+in *ilter has the reF%ired imp%lse response + / * =
b0
+ b1 * −1 + b2 * −2 + 999 + b 7−1 * −1/ 7−1 − 1 − * 7
Lab !;ercises Problem 1
i Plot the imp%lse response o* a sin%soidal enerator +ith f o ) !00 and f s) ; RK.9 /lenth )!00 samples ii Cosin%soidal enerator +ith * 0 );00 and f s) ; RK. /lenth = !00 samples
Problem 2
$mplement a *%nction dtm*en +hich sho%ld enerate a D7ML *or the diits 1: /lenth)2000 samples9 *%nction'res%lt, n( ) dtm*/Re8
Problem#
=iven the dtm*, +rite a *%nction +hich sho%ld decode the dtm* to an appropriate Re89 /Kint- Ese dt*t to detect ranes ane o* *30 K. to *@30 K.9 CSE-304 DSP.
Page 5'
*%nction detect /dtm*, n
Problem$
1 + 2 * 1 −
+ / * =
+ 3 * 2 + ! * 3 1 − * ! −
−
−
Plot the imp%lse response *or this *%nction9 /12 samples /ii >val%ate the 79L o* the *ollo+in imp%lse response9
$mplement a *ilter to prod%ce the +ave*orm9 Plot the imp%lse response o* the *ollo+in 79L9 1 + 2 * 1
+ 3 * 2 + ! * 3 ! 1 − 09" * −
+ / * =
−
−
−
/iv Plot the imp%lse response o* the *ollo+in 79L9 1 + 09" * 1
+ 2 * 2 + 3 * 3 3 1 − *
−
+ / * =
CSE-304 DSP.
−
−
−
Page "0
$aclt% !em&er:____________________
Semester:_____________
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!" #0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 1$
Lab1$ NO+S! '!D7C(+ON %ND S+9N%L !N%NC-!N(
Name
CSE-304 DSP.
'eg. no.
Page "1
'eport -ars / 10
ia -ars /
(otal/1
Lab14: +ISE (ED*CI+ .+D SI+.L E+;.+C!E+ +ntro3uction
7his lab concerns +ith removin the additive noise o%t o* the sinal9 $* the noise is additive, then the noised sinal can be represented as 'n( ) s'n(@ v'n( +here s'n( is sinal and v'n( is noise9 7here are t+o possibilitiesi #hen the *reF%enc8 spectr%m o* the desired sinal and noise do not overlap9 $t is eas8 to etract the desired sinal %sin *ilterin, as sho+n in *i%res-
Sinal
noise 9spectr%m
Spectr%m o* noised sinal be*ore *ilterin
CSE-304 DSP.
Page "!
ii #hen the *reF%enc8 spectr%m o* the desired sinal and noise overlap9 $n this case +e co%ld either blocR the noise to the maim%m b%t et a distorted desired sinal or et an %ndistorted desired sinal at the epense o* added noise9 $n practice, ideal *ilters +ith s%ch sharp edes are not reali.able9 7+o parameters are in practice i
7ransient esponse
ii
Dela8
As the pole approaches 1, the transition becomes sharper b%t introd%ces a dela8 in the o%tp%t9
γ %ff =
ln 8 ln )
⇒∞ as
) ⇒1
First Or3er ++' Smoot4er
+ / * =
N66 =
)=
b 1 − )* −1
1− ) 1+ )
⇒ N66 + )N66 = 1 − )
1 − N66 1 + N66
N61 since 0661 Lor
+ / * [ w = 0 = 1 b = 1 − )
CSE-304 DSP.
Page "3
Kish Pass 7$ Smoother + / * =
*or
b 1 − )* −1
+ / * [ w=
N66 =
π
= + / −1 = 1 b = 1 − )
1− ) 1+ )
++' Smoot4er Ait4 Prescribe3 Cuto Fre:uency + / * =
b−
b/1 + * −1 1 − * −1
1− ) 2
=
and
1 − sin wc cos wc
ab >ercises
Problem 1=enerate s'n() "
/!00 samples
v'n()092randn/1,!00 Desin a lo+ pass $$ smoother9 $np%t parameters are N9 Appl8 this *ilter to 'n( to et 8'( 9 Plot 8'n( , 'n( Plot on the same *i%re i N090" ii N0901 Problem 2=enerate a hih *reF%enc8 sinal d
s'n( ) /1 " 'n( ) s'n( @ v'n( CSE-304 DSP.
Page "4
Desin a hih pass $$ smoother i N)090" ii N)0901 9 c
Problem #Ese $$ smoother +ith c%to** *reF%enc8
8/n
$aclt% !em&er:____________________
Semester:_____________
π =
;
and /n same as Problem 19 Plot
Date': ________________
Section: ________________
Department o !lectrical !ngineering CS!" #0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 1
Lab1 %D%P(+! F+L(!'+N9
Name
CSE-304 DSP.
'eg. no.
Page "
'eport -ars / 10
ia -ars /
(otal/1
CSE-304 DSP.
Page "5
Lab12: .D.PI/E 'ILE(I+ (4e 8i3roA"o L-S %3aptie %lgorit4m
$* the *ilter is h, then h/n@1 ) h/n @ 2 µ %n y n
*or the simplest case- GhG has a sinle coe**icient9
error
%lgorit4m
1 At time n, h/n is available 2 Comp%te the *ilter o%tp%t
∧
)h/n8n
x n
3 Comp%te the estimated error
∧
%n
CSE-304 DSP.
= x n − x n
Page ""
! Comp%te the +eiht h/n@1 ) h/n @ 2 µ %n y n
" =o to net time instant n \ n @ 1 #ill have to %se *orloop
Problem 18 ) 091 randn/1,200 )09;8n @ 8n /a /b /i
µ
µ
) 093 )091 $mplement the MS A=O$7KM *or a sinle coe**icient o* HhG9 *%nction 'e,h( ) MS/;,8,m%
/ii Plot the error and the vector correspondin to the val%e o* GhG at ever8 iteration9
%3aptie Linear Combiner
CSE-304 DSP.
Page "
%lgorit4m
1
∧
) h0 /n80 /n @ 99 hm/n8m/n
x n
2
∧
%n
= x n − x n
3 hm/n@1 ) hm/n @ 2
/n
µ %n y
0 ≤ 3 ≤ M
Problem 2
Xo% are iven 80'n(9982 'n( =enerate +hile =a%ssian noises y, 81 ,82 )09;80 @ 09181 09282 $mplement the *%nction *or linear combiner *%nction
[%$ h, h1, h2 ] = lc(x$ y $y y l 2 $ 4)
m% ) 091 CSE-304 DSP.
Page "'
i plot error and h , h1, h2 Code L%nction [%$ h, h1, h2 ] = lc(x$ y $y y l 2 $ 4) h0 ) .eros / 1, lenth / y !1 h1 ) .eros / 1, lenth / y1 !1 h2 ) .eros / 1, lenth / y2 !1 e ) .eros/ 1, lenth / y *or i)0-lenth /8o x ht = h:(i)yo/i @ h1(i) y1 /i @ h2(i) y2 /i
e/i ) /i 5 hat h( i @ 1 ) h /i @2
µ %/i y o /i h1( i @ 1 ) h1 /i @2
µ %/i y1 /i h2( i @ 1 ) h2 /i @2
µ %/i y 2 /i
%3aptie Fir 8iener Filter
CSE-304 DSP.
Page 0
*or this case /n m h/n @ 1 ) h/n @ 2 µ %n y ector Lorm K/n@1 K/n @ 2
X/n
µ %n
+here X/n is the vector o* the dela8 line9 $mplement this dela8 line X/n ) '8/n 8/n1 8/n2 8/n3 99( h%n ) rand/12"T 8)randn/1,1000,3 )*ilter /h%n,1,8 then implement the *%nction *%nction 'e,h( ) adaptive*ir/8,,m% h).eros/1,2"T e).eros/1,lenth/8 hat).eros/1,lenth/8 8dela8).eros/1,2"T *or i)1-lenth/8 8dela8)'8/i8 5 dela8/1-lenth/8dela8( hat/i)h8dela8 e/i )/i 5hat/i h)h@2
µ S %/i S y − &%l)y
end CSE-304 DSP.
Page 1
Problem 1
$mplement the MS adaptive alorithm on L$ *ilter o* lenth 2"T9 h;4n = 5n&(1$2<) y = 5n&n(l$1$3)
Plot the error sinal *or
µ
) 091
$aclt% !em&er:____________________
Semester:_____________
CSE-304 DSP.
Date': ________________
Section: ________________
Page !
Department o !lectrical !ngineering CS!" #0$ Digital Signal Processing L%&O'%(O') !*!'C+S! , 1>
Lab1> D!-ONS('%(+ON OF '!%L"(+-! S+9N%L P'OC!SS+N9
Name
'eg. no.
'eport -ars / 10
ia -ars /
Lab1: DE!+S(.I+ ' (E.L-I!E SI+.L P(CESSI+ +ntro3uction
CSE-304 DSP.
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So *ar +e have desined and sim%lated di**erent diital *ilters and some applications o* diital sinal processin9 Diital sinal processin does not end here rather the practical +orR beins *rom here9 7hese *ilters are implemented in DSP boards and comp%ters /i* application has nominal comp%tational b%rden %sin prorammin lan%aes liRe assembl8 and C@@9 7he p%rpose o* this lab is to et the st%dents acF%ainted +ith real time sinal processin b8 demonstratin implementation o* di**erent *ilters, b8 %sin c%stomdeveloped data acF%isition s8stem and comp%ter so*t+are9 7he objectives o* this lab are to demonstrate g occ%rrence o* aliasin d%e to ins%**icient samplin rate g e**ect o* placement o* poles and .eros g implementation o* notch *ilter, resonator, *irst order *ilters, second order *ilters g implementation o* $$ *ilters based on classical analo%e *ilters •
implementation o* linear phase L$ *ilters based on +indo+
•
e**ect o* phase non linearit8 and phase linearit8 on distortion o*the *iltered sinal
•
application o* smoothers *or noise red%ction
%cnoAle3gement CSE-304 DSP.
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'eerences
1. Digital Signal Processing CSE-304 DSP.
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