Digital Signal Processing Lab Manual

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

Gifitdl Zifkdl ]rojbssikf BBL-:32

 Kd`b

@uad``dg Dli Nadk

Sbfistrdtiok Ku`cbr 

=4-4:3463-==6

Jldss

CJB-8D

Ikstrujtor kd`b

@d’d` Woocd Nadk

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

Ldc # =3

Cdsij Opbrdtioks ok Gisjrbtb-Wi`b Zbqubkjbs Zbqubkjbs Ocebjtivb5

Cy tab bkg oh tais ldc stugbkts will cb dclb to pbrhor` sifkdl saihtikf dkg holgikf opbrdtioks ik @DWLDC @DW LDC,, ik dggiti dggitiok ok st stugbk ugbkts ts will will cb dclb dclb to pbrhor pbrhor` ` dri drita` ta`bti btijj opbrdti opbrdtioks oks li linb nb dggikf dggikf,, suctrdjtikf or `ultiplyikf sifkdls oh gihhbrbkt lbkftas. ]rb-Ldc5 Aow to `dnb d hukjtiok ik @DWLDC

D hukjtiok ik @DWLDC is linb d hukjtiok ik J/J++. Okjb d hukjtiok is `dgb it jdk cb jdllbg ik dky otabr hukjtiok/sjript eust linb J/J++. Kotb tadt sjript is eust d jogb cut hukjtiok is `orb linb d sbpdrdtb ocebjt or bktity. Eust linb J/J++ tabrb is d syktdx hor `dnikf d hukjtiok ds fivbk  cblow. i.

i ii

Hukjtiok () jo jo`` ``dkg dkg is us usbg bg to gb gbhi hikb kb d hu hukj kjti tiok ok ds  hukjtiok ^output4 output3 output:P 0  hukj_kd`b(ikput4, ikput3, ikput:) .  Cogy oh tab hukjtiok5 Vritb jogb to output:P  pbrhor` d jbrtdik d tdsn bkg D hukjtiok hukjtiok `dy `dy cb writt writtbk bk ik d sbpdrdtb sbpdrdtb @-hilb @-hilb.. Dlso, Dlso, it is dlso dlso possiclb possiclb to writb writb `orb `orb tabk tabk okb hukjtioks ik d sikflb @-hilb. Bdja Bdja hukjtiok hukjtiok `ust `ust advb d gistikj gistikjtt kd`b dkg tab hilb hilb `us `ustt dlso cb sdvbg sdvbg wita wita tab sd`b kd`b. Ih dk @-hilb advikf tab hukjtiok wita d kd`b “dvbrdfb‐ is sdvbg cy tab kd`b oh  “dvf‐, tabk tais hukjtiok will kot worn propbrly wabk jdllbg ik dkotabr hilb.

Jdllikf d hukjtiok ik @DWLDC?

4. Ik orgbr to to jdll d hukjtiok hukjtiok ik ik dkotabr hilb hilb tab girbjto girbjtory ry oh cota hilbs hilbs `ust `ust cb sd`b. sd`b. 3. Cbho Cbhorb rb jdllik jdllikf f tab tab hukj hukjti tiok ok,, ikpu ikputs ts kbbg to cb gb gbhi hikb kbg g ik tab sj sjri ript pt hi hilb lb or jo jo`` ``dk dkg g wikgow. :. Zuppos Zupposbb wb advb d hukjti hukjtiok ok cy tab kd`b oh “dvbrdf “dvbrdfb‐ b‐ tadt tdnbs tdnbs tab dvbrdf dvbrdfbb oh tarbb ku`cbrs k4, k3 dkg k: dkg rbturks dvbrdfb dvf , tabk hollowikf jogb `dy cb usbg to ik jo``dkg wikgow or sjript to jdll tais hukjtiok

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

or si`ply, ^dvfP 0 dvbrdfb (4=,-2, 3=)> % hukjtiok jdllbg girbjtly 7. Ih tab tab ikputs ikputs drb drb kot gbhikb gbhikbg g tab hukjti hukjtiok ok jdll jdll will will progujb progujb dk brror `bssdfb. `bssdfb. Hukjtioks jdkkot cb ruk usikf tab pldy tab pldy cuttok  cuttok ik `-hilb uklinb sjripts. Zo`b rblbvdkt @DWLDC jo``dkgs to fbkbrdtb gihhbrbkt typb oh sifkdls (Zbb ablp oh hollowikf) Blb`bktdry @dtrijbs dkg @dtrix @dkipuldtiok I Okbs ]i Sdkg Sdkg` zbros Blb`bktdry hukjtioks Jos Bxp I`df rbdl  

Fbkbrdtikf Fbkbrd tikf d sifkdl sifk dl ik @DWLDC

D sifkdl x^kP ik @DWLDC is gbhikbg usikf two drrdys or  sbqubkjbs, okb drrdy rbprbsbktikf tab `dfkitugbs “x‐ dkg tab otabr drrdy gbhikikf tab ti`b ikgbxbs i.b. tab sifkdl fivbk ik tab hifurb (ok rifat sigb) will cb gbhikbg ds ;; k 0 =57> ;; x 0 ^8, 44, 47, 2, =P It is oh i` i`po port rtdkj dkjbb to `bkt `bktio iok k tadt tadt dk dky y op opbr brdt dtio iok k  pbrhor`bg ok tais sifkdl i.b. saihtikf, holgikf btj. will cb  pbrhor`bg ok cota tab `dfkitugbs “x‐ dkg ti`b ikgbx “k‐. Zo`b otabr typb oh sifkdls Sbdl-vdlubg bxpokbktidl Zbqubkjb

Wab opbrdtor “.[‐ is rbquirbg to i`plb`bkt d rbdl bxpokbktidl sbqubkjb. k

Hor bxd`plb, to fbkbrdtb  x ( k )0( =.9 ) , = ≧k≧4=, wb will kbbg tab hollowikf sjript5 ;; k 0 ^=54=P> ;; x 0 (=.9).[k> Jrbdtb d hukjtiok (@-hilb) to fbkbrdtb dk bxpokbktidl bxp okbktidl sbqubkjb. Rsb tab prbvious bx bxd`plbs d`plbs ds your fuigb.

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

Jogb5

Output5

Jo`plbx-vdlubg bxpokbktidl Zbqubkjb D cuilt-ik @dtldc hukjtiok “bxp‐ is usbg to fbkbrdtb bxpokbktidl sbqubkjbs. Hor bxd`plb, to fbkbrdtb  x ( k )0bxp ^( 3 + e : ) k P , = ≧k ≧ 4=, wb will kbbg tab hollowikf sjript5 ;; k 0 ^=54=P> ;; x 0 bxp((3+:e)*k)>

 Kotb tadt you kbbg gihhbrbkt plot jo``dkgs hor plottikf rbdl dkg i`dfikdry jo`pokbkts. Zikusoigdl sbqubkjb D cuilt-ik @dtldc hukjtiok “jos‐ (or sik) is usbg to fbkbrdtb sikusoigdl sbqubkjbs. Wo fbkbrdtb  x ( k )0:jos ( =.4 ύk + ύ / : )+ 3sik ( =.2 ύk) , = ≧k≧4= , wb will kbbg tab hollowikf sjript5 ;; k 0 ^=54=P> ;; x 0 :*jos(=.4*pi*k+pi/:) + 3*sik(=.2*pi*k)> Sdkgo` Zbqubkjbs

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

D rdkgo` or stojadstij sbqubkjb drb jadrdjtbrizbg cy pdrd`btbrs oh tab dssojidtbg procdcility gbksit gbks ity y hukjti hukjtioks oks or tabir tabir stdtis stdtisti tijdl jdl `o`bkt `o`bkts. s. Ik @DWLDC @DWLDC,, 3 typbs typbs oh (psbugo (psbugo)) rdkgo` rdkgo` sbqubkjbs drb dvdldclb5 “rdkg(4,K)‐ fbkbrdtbs d lbkfta K rdkgo` sbqubkjb waos blb`bkts drb ukihor`ly gistricutbg cbtwbbk = dkg 4. “rdkgk( “rd kgk(4,K 4,K)) fbkbrdt fbkbrdtbs bs d lbkfta lbkfta K fdussid fdussidk k rdkgo` rdkgo` sbqubkj sbqubkjbb wita wita `bdk `bdk = dkg 





vdridkjb 4. Ot Otab abrr rd rdkg kgo` o` sb sbqub qubkj kjbs bs jd jdk k cb fb fbkbr kbrdt dtbg bg us usik ikf f tr trdks dksho hor` r`dt dtio iok k oh ta tabb dc dcov ovbb hukjtioks.

]briogij sbqubkjb

D sbqubkjb is pbriogij ih x(k) 0 x(k +K). Wo fbkbrdtb ] pbriogs oh x(k) hro` okb pbriog, wb jdk jopy x(k) ] ti`bs5 ;; xtilgb 0 ^x,x,x,x...,xP> Dk blbfdkt dpprodja is to usb @DWLDC’s ikgbxikf jdpdcilitibs5 Fbkbrdtb d `dtrix joktdikikf ] rows oh x(k) vdlubs. Jokjdtbkdtb ] rows ikto d lokf row vbjtor usikf tab jokstrujt (5). Advb to usb `dtrix trdkspositiok opbrdtor (‑) to provigb tab sd`b bhhbjt ok rows5 ;; xtilgb 0 x' * okbs(4,])> %] jolu`ks oh x> x is d row vbjtor ;; xtilgb 0 xtilgb(5)> %lokf jolu`k vbjtor ;; xtilgb 0 xtilgb'> %lokf row vbjtor

Jrbdtb dky sifkdl x dkg tabk jrbdtb its pbriogij sbqubkjb usikf tab jogb provigbg dcovb. Jogb5 hukjtiok hukjtiok ^xP  ^xP 0 bxp(k) x 0 :*jos(=.4*pi*k+pi/:) + 3*sik(=.2*pi*k)> bkg  k 0 ^=54=P>

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

^xP0 bxp(k)> sucplot(344)> stb`(k,x)> xtilgb 0 x' * okbs(4,2)> xtilgb 0 xtilgb(5)> xtilgb 0 xtilgb'> hifurb,stb`(xtilgb)>

Output5

Ik-Ldc I`portdkt Zifkdl Opbrdtioks ik @DWLDC5 4. Zi Zifk fkdl dl Zj Zjdl dlik ikf f

Ik tais Opbrdtiok bdja sd`plb is `ultiplibg cy d sjdldr. Rsb tab jo``dkg “*‐ hor sjdlikf. 3. Zi Zifk fkdl dl Zai Zaiht htik ikf f

Gurikf d saiht opbrdtiok d sifkdl jadkfbs its positiok ik ti`b wabrb bdja sd`plb oh x(k) is saihtbg  cy dk d`oukt n to octdik d saihtbg sbqubkjb y^kP.  y ( k )0 x ( k∓ n )

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

Ik @DWLDC, tais opbrdtiok is kot so si`plb, cota “x‐ dkg “k‐ kbbg to cb projbssbg sbpdrdtbly ik orgbr to fbt tab saihtbg sifkdl x^k-nP. ]brhor` hollowikf stbps to ik @dtldc to pbrhor` tab sifkdl saiht. i ii

Jabj Jabjn n wabt wabtab abrr n is is pos posit itiv ivbb or kb kbfd fdti tivb vb?? Ih n iiss positivb positivb it it `bdks saiht is towdrgs towdrgs rifat rifat i.b. i.b. x^k-nP x^k-nP tabk tabk go hollowik hollowikf f

d. sigb Ds sifkdl sifk is sd`plbs saihti saihtikf kf i.b. towdrgs towdr rifa t ti`bdtdxbs dxb “k‐ it saoulg saou lg cbkow bxtbkgbg bxtbbkg kgbgdttowdrgs towdr rifat cy dl “n‐ ih gs k isrifat bkgikf k3stabk saoulg k3 + gs n. rifat  c. Zikjb tab sifkdl ads kow `ovbg towdrgs rifat `bdkikf ikitidl “n‐ sd`plbs ik “x‐ drb b`pty so jokjdtbkdtb “n‐ zbrobs ik tab cbffikikf oh tab sbqubkjb x. iii Ih n is kbfdtivb kbfdtivb it `bdks saiht saiht is towdrgs towdrgs lbht lbht i.b. x^k+nP x^k+nP tabk go hollowikf hollowikf d. Ds sifkdl sifkdl is saihti saihtikf kf towdrgs towdrgs lbht ti`b ti`b dxbs “k‐ “k‐ saoulg saoulg cb bxtbkgbg bxtbkgbg towdrgs towdrgs lbht sigb cy “n‐ sd`plbs i.b. ih k is stdrtikf dt k4 tabk it saoulg kow stdrt dt k4 - n.  c. Zikjb tab sifkdl ads kow `ovbg towdrgs lbht `bdkikf ldst “n‐ sd`plbs ik “x‐ drb b`pty so jokjdtbkdtb “n‐ zbrobs ik tab bkg oh tab sbqubkjb x. :. Holgikf

Holgikf opbrdtiok is dlso tbr`bg ds hlippikf d sifkdl wabrb bdja sd`plb is oh x(k) is `irrorbg droukg k0= to octdik d holgbg sbqubkjb  y ( k )0 x ^∓ k P Ik @DWLDC, holgikf opbrdtiok jdk cb pbrhor`bg ik tarbb stbps i Hlip tta ab `dfkitugb sb sbqubkjb “x “x‐ ii

Hlip tab ti`b ikgbx “k‐

iii iii

Kow Kow ` `ul ulti tipl ply y ttab ab hlip hlippb pbg g ti` ti`bb vbj vbjto torr “k‐ “k‐ wi wita ta d `ik `ikus us

 Kotb tadt ik @DWLDC d cuilt-ik hukjtiok “hliplr(`) “hliplr(`) jdk cb usbg to hlip dky sbqubkjb. 7. Dgg/Zuc Dgg/Zuctrdj trdjt/@u t/@ultip ltiply ly two sifkdls sifkdls

Dggikf d sifkdl ik @DWLDC is kot ds bdsy ds ok pdpbr. Ik orgbr to dgg two sbqubkjbs x4 dkg x3 ik @DWL @DWLDC DC,, dkg cota cotgivisiok. a sb sbqu qubkj bkjbs bs `ust `ust cb oh sd sd`b `b lb lbkft kfta, a, sd sd`b `b is ta tabb jd jdsb sb ho horr su suct ctrd rdjt jtio iok, k, `ultiplijdtiok Ik sifkdl projbssikf sifkdl blb`bkts drb dggbg/suctrdjtbg or `ultiplibg jorrbspokgikf to tabir  ti`b ikgbx i.b. d sifkdl blb`bkt dt ti`b -4 will cb dggbg to tab sifkdl blb`bkt oh tab otabr sifkdl dt tab sd`b ti`b. Vb nkow tadt sifkdls jdk advb gihhbrbkt stdrtikf dkg bkgikf ti`bs, abrb wb wdkt to `ogihy ti`b ikgbxbs suja tadt cota sifkdls stdrt hro` tab lowbst ti`b ikgbx dkg bkg dt aifabst ti`b ikgbx dkg djjorgikfly jokjdtbkdtb zbros or dt tab stdrt or bkg oh tab sifkdl. Zupposb wb wdkt to dgg/`ultiply two sifkdls x4^kP spbjihibg cy x4 dkg k4 ik @DWLDC dkg x3^kP spbjihibg cy x3 dkg k3.

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

Hollowikf two stbps jdk cb hollowbg to `dnb tab lbkftas oh x4 & x3 dkg `dnikf k4 dkg k3 sd`b ds wbll. d. Jo`pdrb Jo`pdrb tab stdrtikf stdrtikf poikts poikts oh cota cota sifkdls sifkdls ti`b ikgbx ikgbx vbjtors vbjtors i.b. k4(4) k4(4) dkg k3(4) k3(4) i

Ih k4(4 k4(4)) iiss ss`d `dll llbr br tadk tadk k3 k3(4 (4)) 

Jokjdtbkdtb k3(4)-k4(4) ku`cbr oh zbros cbhorb x3



Dkg put k3(4)0k4(4)

ii Bl Blsb sb ih ih k3(4 k3(4)) is is s`dl s`dllb lbrr tadk tadk k4( k4(4) 4) 

Jokjdtbkdtb k4(4)-k3(4) ku`cbr oh zbros cbhorb x4



Dkg put k4(4)0k3(4)

 c. Jo`pdrb tab bkgikf poikts oh cota sifkdls ti`b ikgbx vbjtors i.b. k4(bkg) dkg k3(bkg). i

ii

Ih k4(b k4(bkg kg)) is is f frb rbdt dtbr br tadk tadk k3(b k3(bkg kg)) 

Jokjdtbkdtb k4(bkg)-k3(bkg) ku`cbr oh zbros dt tab bkg oh x3



Dkg put k3(bkg)0k4(bkg)

Blsb Blsb iihh k3(b k3(bkg) kg) is frbdtb frbdtbrr tadk tadk k4(bkg) k4(bkg) 

Jokjdtbkdtb k3(bkg)-k4(bkg) ku`cbr oh zbros dt tab bkg oh x4



Dkg put k4(bkg)0k3(bkg)

j. Kow `dnb `dnb d ukivbrs ukivbrsdl dl ti`b ti`b ikgbx ikgbx k0k4(4)5 k0k4(4)5 k4(bkg) k4(bkg) or k3(4)5 k3(4)5 k3(bkg) k3(bkg) g. Dgg tab `dfkit `dfkitugb ugb vbjtors vbjtors cy x0x4+x3 x0x4+x3 or `ultiply `ultiply tab` ds x4.*x3 x4.*x3 btj. Ldc Wdsns Wdsn-45 Wdnb dk bxpokbktidl sifkdl dkg pbrhor` sjdlikf opbrdtiok wita d kbfdtivb iktbfbr ds Wdsn-45 fivbk ik Ik-Ldc ik Ik-Ldc Vorn sbjtiok dkg plot tab rbsult Jogb5 k 0 ^=54=P> d0-:> x0 d*jos(4*pi*k+pi/:) x40 jos(4*pi*k+pi/:) sucplot(334)> stb`(k,x4)>

sucplot(333)>

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

stb`(k,x)> Output5

Wdsn-35 Vritb d @DWLDC hukjtiok “sifsaiht‐ hor progujikf d gbldy oh ‑n’ ik d fivbk sbqubkjb ‑x^kP’ gbhikbg cy drrdys “x‐ dkg “k‐ cy usikf tab psbugo jogb fivbk ik Ik-Ldc ik  Ik-Ldc Vorn sbjtiok. Your hukjtiok saoulg yiblg y^kP 0 x^k-nP. Hukjtiok ^y,kP0sifsaiht(x,k,n)

Jogb5

hukjtiok ^xP  ^xP 0 bxp(k,n) hukjtiok x 0^zbros(4,n),kP> bkg jlosb dll> dll> k0^4,3,:,7P> sucplot(334)> stb`(k)> n07> x0sif(k,n)> sucplot(333)> stb`(x)>

Output5

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

sbqubkj b ‑x^kP’ gbhikbg cy drrdys Wdsn-:5 Vritb d @dtldc hukjtiok “sifholg‐ hor holgikf d fivbk sbqubkjb “x‐ dkg “k‐ cy usikf tab psbugo jogb fivbk ik Ik-Ldc ik  Ik-Ldc Vorn sbjtiok. Hukjtiok ^y,kP0sifholg(x,k) Jogb5 hukjtiok hukjtiok ^xP  ^xP 0 sif(k) x 0bxp(=.32.*-k)> bkg k0-757 > x4 0bxp(=.32.*k)> sucplot(3,3,4) stb`(k,x4) ^xP0sif(k)> sucplot(3,3,3) stb`(k,x) > Output5

Wdsn-75 Vritb d @dtldc hukjtiok “sifdgg‐ hor dggikf two sbqubkjbs x4^kP dkg x3^kP cy usikf tab psbugo jogb fivbk ik Ik-Ldc ik  Ik-Ldc Vorn sbjtiok. Hukjtiok ^y,kP0sifdgg(x4,k4,x3,k3)

Jogb5

Output5

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

Wdsn-25 Rsikf tab hukjtioks gbhikbg ik tab dcovb tdsns pbrhor` tab hollowikf dkg gbtbr`ikb tab outputs

Hor  x ( k )0{4,3,44,2,1,9,6,4=,3,7,8,6,4 } d.   x 4 ( k )02 x ( k ∓2 )∓1 x ( k + 7 )  c.   x 3 ( k )01 x (∓( k ∓2 ) )+ x ( k )∖ x ( k∓3 ) Jogb5 d)

 c)

j. Output5

 

BBL-:32 GIFIWDL ZIFKDL ]SOJBZZIKF

d)

 c)

Jokjlusiok5

  Ik tais tais ldc wb pbrhor pbrhor`bg `bg sifkdl sifkdl saihtikf saihtikf dkg holgik holgikf f opbrdtiok opbrdtiokss ik @DWLDC, @DWLDC, dlso dlso wb  pbrhor`bg drita`btij opbrdtioks linb dggikf, suctrdjtikf or `ultiplyikf sifkdls oh gihhbrbkt lbkftas. Ik tab bkg oh tais ldc wb jdk `dnb d hukjtiok ik @DWLDC. I pbrhor`bg dll tab tdsn  sujjbsshully.