Unit - 'V Molligake digital signal proce ating he paoceat & conveatling o signal Soren © given yak to aditterga rae callec| Kipling] gal @nver(ikn, th Ke arco sign posing, Frirente CCD O sample, O94 ne bal diglel facto tape COAT) 17 Rompkel ab AGENT, conversion Iku CO arch OAT! URES molgak signal Prnesaing To cont} co 10 DAT, We COP USING epporphirg « tires OSH] sompirg rak). § ‘ BD ancaqt MT Yo en, we cP (ceepesing sorphngy wake) — Fee age keo ways £04 Sempling vale cenwecpibry nthe dgfol cornin. Tey GF + Peron sampling /decieralion, 3+ Op sampling 7 Wieopdotion. woh Ceciralfon , 1. Dedmation on Sot Fe sampling! ak ar dixgek tre cipal -xin) o faclooy My by rating) exon nb volo: Senoonttrg. Fe colpit signal yin), of the inpil ‘signal xq) Ond an ‘be on be fate sigal 5 called ta down sompe signal geprertented by yond #09). LOX xen) = 61.3.3, MOH BA,,, sn) —|mMy ayn) =x (nm) fomea . is reat Yoni = kU) = Lan) > f niftre dewte tehth pocfrmr the pro? OF coton SImphi AS calle) Cecenseinpleay 4) decimation, 7 Ve omsa dF Gory exeGrn) = 20) cytors eg) 2139) Lo): RYE q love NO) ay ylols RL =! yor,s e@de gor = kB) Few! glans BWPT iL Aes! - (3) = RG) = 4 3 4 7 Pyle a) 20 ylas a(S) =F 2» yes R(s)= V 2— nev wie) agp)” § yds 43), yore ear? Bem 4T1 a f somping yak OnveefiO» a 22 Bab whee ee) hoe +7) MT ™ Y) poidaerre of ~% Fa AQOORNE ae yma = 4/m oor Gomme. a spactaprs cheng sore SOL so | + Aspnsfogm of yp Signo), pel owl are = xo Pa) own Sample oF yw) ia oldcin by monly jy sxquente yo satan) Deo, Be 2am Bam oe = ' punt { . © alhewire- Be7° fn) aenrpind! an) fe Neo,tr 2 atm 4 ams. © they ne [gens rn) 2 fe tS Seta a dius alyiny - = yor 2 yw nee 2 yeas E Blom F” nee P ran: > on Pye Pee nie Ope — ; ‘ meee ipo yen 2 te TI ; fan pt pes 2 3 t Fs a 3 ee PT Perley de ~ wi) - ces wel b™ , nee ae <0) Ly ‘ toy } 5 aN RNT : no MAY a ' jatkn _p, Ss eny me MSs ia ee a ; mS fame aypay? 2 5 Seis GES Se levk = ) Ma mt -jamke A ee wis bE Ele me - M yo =O Korma ) ‘ a ; o (gant ie) . ™ ye) -ts M Lc3 Spectgorn of cownaarape signal: — FE Agonafoyr of yp Signal *UH = emt — Dom Forple ay Yoo, mohplia) wih tN, YP Sequmq g3cth by ween) woth peajclic hein of impllae Pm) wih oo peeyeel ty thon oprrcving M-1 sampler. grotam 2am ee ene Pini = fee age star = REAIpr) thd iz xen) n=O tm), 2aMm- ain) = ° othe of serouing M1 stnples Ww ach ve OF somplex the evipt® down somee iF *™n) va yor = te ¥ i of the lp omjone B gor by {yO} - YO ~ = ye” ‘Nlzl = = x (oan? neo ee tee ran =p => ‘Pir neo SP ; ret myer Pe 3 [Pe vei = xP) T Pm pee 1% t por pen i =n) e . vie)- & anne "i t ne cs } “ * =njen 2 2 SS RNP = neem1 ypnn = em eR EG ees Aro n--e The decele, Gogiee|, SAF spon ol of the Sql yan “79 Mo kee em “jan my) Na 2 Ee RENE oe OD ™“- 7 K wwe SE a) k=O % . Hey Vn at. ee a le ae ee ee rors) IS xe em oi) . fea : ra me io-anty Jr - Ee ne REE) | Fspm above Focsies hosan of inst siq aim i ute”) On foonjeey Thansfinm of opt Shy yte%) wohege Vik GQ Som py onifouniy Shiflec] ond sketched vesipion of x(eX9] and scaled Py 1 Foctory of Ym, shin apecbjom Of Srigral sly cele) ig linc Vmiled to Ws ni. The apetgum teeing preface with. the pajiod of van. JEAN rtAakolioging Filkeoy _ oe Apecigom bain afieey Cheon Sampling toll oveetlap the cnighsl Speckyo> % aad banded fo worn Thr oveslap | CwAes alicsing . Therefore aliasing ke’ to ™ chen Sonph ofa signal by a Facloy oP Mis obsedt theapthoe iF are) only fo oun bond limikd!) 1 + Tm, te signal 3 nat “valid fo) tren a. lowpass: filly TE qut-cff Foreuen Wr is uaecl before dovansoryahing. - she Bite js known OF Bali - ~abosing Filey. he comple poy | of ing od tem doo Splig] 15, cited, decimation. “(chs cls phen ad Pik pe 4 nT “ay a a ANS papa 7 yee | prob + ain). 7an N70 with MeQ {o theapolie a2 = aan) ew [ae in 209 ° ner > RD 2 coy é 8 ecaye 4 i RGEC 2 th) =8 Lod e e5)=10yin 8 fan) god £2) yas yao *s) guns 88) renee ° eG na PROV Tatty kt yee, wt setay= 4 yo 2) rel) eta) =4 giad= 26) eerie ga 5) 5 yee) aed yess (201° ecia}= Hy \ oO \y i nnd Lin) 5 ® cnd= Me 4 { oO alkesy J 4 : 3 ' aun) Dnt Rye t \ j way = 2 idee mye 3 T3344 2 tH 24 ims xem Xt RS IED yin =2e(Mny 5) UO), y= Rta) glare 2UN yla)= 26) gta) = eS)‘ fer opsoenpling the opscrsping spk of cixop’ | by gocton, "VE by placing (er) eawally spaced | cach pois, oF songieep, : om i Motrencticly wpsonping if “wepesenkel by . yon aoa ale Shy tau t3ab-> Jedine sign) an ke incopored cdjoes,, bekoan yor: ea neo, ° othe an) —[theye emcniay Fs 200 ent . 4 : : FleLr > = BOO KN™ eo te any 703, al seery [EES 7 YO ea) gini> 2@/a) 13x ROOKNEPe. ere a te ee, 97 Yo #LOa) # RO ot 2 yore aya) = 2R(0°5)* ° | 2 ; ya): ® (ala): 22a," ’ | | ’ | | gad 2197 (15)F0 i ic ees ger 20 8S peer e eats) ye 2S: 2ES)=O" x(eite) yess 2 ER) eelays + | af yt . gt = R0ats ES) =0 ad } yer RUB/A1 REN, “a | | ae Sie Taree SI ct yurn F opszenpling He specjom F opseping ig yee)> = = yin ° == wnja FP” He ei genstoqrn of colpot eal are Sf eme ooo poe nap = ees? oe aE : wee yer ac [yonexce’) : gol : Ne! | f ca) | Fre x horsfogm of ov POF ral’ toy tAch waging Mey Focquency pelo of opsonplry signal) yin) wilh” (1) arteliblonal feacages of Pe° Sajum , Facton, TUT wnlaing Herne (1) agee TcqoR Sampler. belurcen cele rol miEsied Ty wage. pass ‘file ash a cul sof jor 18 non” COP inpol coe «he fo Me addin of G9) sucessive Spectra of Rin), Sing, Ue A) ow saeqoontep OF dl dan be ured to opmove mages aw spec ee aig’) -Milreagin Ailleey,, +0 =a apr cten £ oe O ‘ Ae Li Stuge Re compels press of E rey oncl filleoiing i ' called OF Inleepolation. Wy) ir rm yen) ro Inlesppololion jot ROWE faa sot Crneee® acl Skelch (0) i en) ii. 30810 intenpolaled of 220m) such thot & (")>) tin tep inteepototecl of x(n) 48 R(M]a) ive Lircoally amegpolatec| xin) mM)Cs Ren) ‘ieee yind? 8D) ti peor? yiod ewe P sn yore)! ae ee ee \ glad @6)=0 | Yo 8B), eerie 82 Ai 9p inkeypstoted oF Rn). such that MAR dsloinec} by acting yegor bekotn the two Ramper. (inchdo §s wun f yor) 2 (M8) un) Bind po ae "= yore eo) *! i. qe aQa)s0 y@)= ROyerd yd 200) =0 gee 27S edd= U5/01°0 ylods eed: > ETS yoni={-110, -2, 015/00" fi. Sep iniegipulakd of zeny xh het e(nja] & oblawm by ineg a aon by inseoing & @nslat equal 40 PrRVOGF sompk helwen quo some. Pr akp Sool SS vols SK peuiowr valy avebe.) yond (J 5 5iv" Lineca ly. inka of in) i chiain by f sce ing ct wwii equal ? acer of adjrcnt samples bekwen ken Aampley, neo > Yok RO) A") gorse (lal = oreyp = ABS 1S yas 20) ork gweld? BI, Zeb: gene meta ; rode Wiad = Spe 3. yorstsoe a co ae tafe oe ae ir +H tke spedojom & a Signal am + gyenetgicl “‘Biargety po oth cngliode oF 38 ond Bexjengy toorclajien aire ne os) aiaich — Spectajom oF 1. 3a. inkeypalated yor (2) i |g. Dedmaked signal din (an) 3. the Sipal gin) = xn) OF even'n', and 0 64 gin= e(an) 8 (7/3) 2(an) i, Us ge oli to -097 8 O15 PUs. ylet? = x0?)ee a pecirmation — din)= en) wy, 1 jw-ank) ye = x eset ) M veo \ a uu -annk) Zt Ex me ko jos }(w-30 ot avy eel (2 ) hove abt Lele? nee] exe a i bs xe) ate") Sieh Fen jet cr) @ oy x(o2) af 01 x ei! se WN —— ont ont AIL) O26 ix bed of doe = =9:n§ 4024 = OD ie ons ton’ 01395 wei | ons one ‘ \ ie) ony orStinging opie re) by ‘a gato! acs} Cositee, the sampling te: conversion Y @ foxchny * an\ Fe sampling ace a (x 2M ie ree 2 7 ; : | Ss a ke \ [ rotineedl . om kon a a =x (nh), eer) is) > pebet « “ F mt ™ } voM ote ™ ; Fe TL ye , ifs tee een “3 | se wonng ack ie Fs tke SomPe 20K convegision by faactoy IM Gon be tag atiy fast pearing mete \y a GL! andl Then packing decimation by ack M... eS 7F] ee) Saas) vr = wy) AL, lew ang rh pea \ dow | 8 = | ee, ve tm wee) tlle 1 mp ie om pe ba iad pedi ¥-lnyp af ye OE oe yo ( Fler [¥ : ery Pali wenin(¥ 3) fe ob-choveg, He] Hyis) — ord ont. imogg ile, Holt Gere opel ot the Home samling sale, Hn an te se pliad by Tile 19 oh 4aarskey fonction Weel, The fe har a cul offFaery F wee Minimoe Eye) ren N(eM) = a = yo) 3 jww-ary ak ath) Ag my Ne 0] oRe) jo: a (el re ne jtw-ak) -ank) o Ww ) ence M4 : eotecank) «Sw cat) Coherons eS") | MH downrcrmples ong Fados FL OPP (Re cance facto oot ontin ody H&S inteaychongable wth ro change in pst ancl f ON, trond M csp Co-pumes. , Lames, ‘ey! 5 Ue ert gest he ah | moro > > yior=ator gene yer) io gat) @(%2) <0 so yore ©) oe i gorev* gereyGal =o gary ere 8 "ylol = Kaos} ! yla)> 22(8/2)°0 ya = eee) 6 yi) 2 (/a)20 yay { 4 qe)= 8) 8 yet) = 8) 0Se ano = fil eahit) : 0) gel? xian = (ash 2 neo? yr = aera qure ee) =F yor'= gla) t nso ylo)= yrto)=Q ) net a y= pea 2 Ys YOU 8 gint =Laroisy payphone ecomposifon fare! » , te poyphore stooge ey FIR Feo cep develpec! efficient implernerfation of sanpling pte Srvc POF consicle the “Hor ke fondin of Fin Hes), y(a)=0 ¥ : mck Comping in Fie filley* Bothy d N-t Wes Shee nso af a : BS a : a © ines shot HUA) to) a hove HE AWE? ALTE ral i digas ¥ eRe thls] Z S+ hong hres tet us cplixe fre agaten eto exe ection ko. N-3 1 ) tea wae Heys! hie) + nares Kahler ey et (notaher hy h13) a anne : “ys Sf 2 egvha vn) a ynunk +h 26 ott?) = ho) hte) % ret ahtayy"& ey (aa)= ha thee? ahr Ww a) +a! a te) = role y act e8)SR ts A meneame As crf Le B= EG@)7 FT ‘guste? eal) x fetiy on a Fro ran setae) = TERIA | Gib , day xz) } f 2 fl + \ MoE Og rd 1 Ea a be) ele te grea enn eqeaton io” bien be woke’ on “A tri ve Oy, ee on Sea) en Be) Hy) Fol? *) F ex x) Tak Fgh) ar yPeri a ae BAR acmsing eek gatdin feb mM wt HT i the Tener Rnckion of “ cinti-ctiaring FIR Sil. : gi the tmp f decimarby- hh oacksy “eros erepatotn in ‘ rin “Ska ceconposion Gn be Qpplied fo FIR Ay do Ceom pore % Sub-Alka> “i (alee x aa setaaeal ve : — [roa t pg ain Le ae : ; ro = b. teen - aes wey i Dy es “ pighone shodtoge F rep ‘ Tek Woe be the “erste, adion of crt irhaging Fe filley at the colpot of niente. fonts bathe the emyplatons, in Fe files, pr cheompesilion can be eee AR = “© deonpore ido et = sub lof” 2 inergin |) ag oer,‘——— R 2 Moltalage design of sorpling nate conves|SO wy Rompling gak convaysion, when somping Ak Grerin actos, PL cy | OR voy lange then the motistage sorolg rerk, Conveeision twill be cempotionally efficient aeration. Decimation by a Facts Mm, whee M may be Richey inD a pajocloct of pot Inkyeops - Me OM; , y Fie) yo al te ( sop: up ive Ps clogs om aye PAT mars Mh Bg Foofaatog sb aan ole odes I a “patel of eee ear we flay io [tu | \Tr fas} tea at \ soy soy 5 Sy Fe ae bs Fhe Sky Ny aga twF wtar4 MOTE) wm | —, | geaaibion | Peso yes) | | } | | DNA bi 6 ra ap: aipie ta possbard ‘geda: s S- apRe chyphoond, ip: pordond ody Fisorgrs e- Biyo Lord ed pf FAI ovecyl\ Atle, cregquicyerent & a 1. bo cet sompiig Seeing © pete Fel ined decirection te ' 3+ phe B-h s-8 7 Nir ~aolog | 54) -8 PON N= 101% (35%) “15 pad 644| ‘ mika) co-stars chcimale 69) ocoing spovtiction. scumping ole fhe inpol Seam = aH, "M100 1 Powbincl = O-toWn ‘pqession banch= FO - 50H, passhord wippke gp= 0-0 sicyonel sige Bye 6-088. Me ASX = mM © Qyon sampling ‘Bequenyy BH. MENS i ™ = 100 | posslond = ote = 4p HOHE | steptord sipple | SS= 0-009 een or jason bord + pe FAS 2, o£ F< 50: y 4s= SONF, 5 | fo | “atk “ i i 84 . a ae = BuO We ' pao 2 8 BUH Mm 8 BUD = aOne a : i «fl Fie Faop 41% 3 BHO - so4fs 10900 sao 2° 10500 BOWE IOW Terorynin henelAsets patel yotst< Aq past bond! « Ag - Sb af: *& Fou = 3Q0- 40 “Fo = B1000 = CAT O03T yu-SOh i gd Ny? 66-51 2] oF *Slogpa = on 49- Gop + f+ eo 1632 1.Imsrent oy astage dectmaby, tory sspecifiertion « Scenphng ack oof yp spore: ane, MIO, passhonct © > Ty, Tetamed, so ty TORS Ap: Oo! > Ss- 0 002 Sp= oo SS= 0-008 passion} = o _ 92 a0» Fie ot mj Fe fo. 2 sunt om an - fH . SW. aont. Fo ima a ‘ : Slag ! = | Fr- fetop 2 F< & ae Fi Bop s fo a & fot 2h a = sho — 30 £4 10500 Apo & ee Teanarion bard « SSO) spe fey 50 2 F< HO~1009 = 0082+ wre 10 logio (sp3-8 : 6 AF mot 30 2 fe tno 2 f< 480 -honssion bone) Ape 2f5 5D « £410 AG: ‘BP 1 = 40-30 “uo OF, Ny = login ( oie Om") Hb x 0-104 = grays 224 -10| 1p (0 x 0-008) - 13 146 %0-082) * ya3s, -Btroph ae cA hue Stop cectimation 69 Glow specif ation ping we af “he pat stpal = 00K, se passhond =O te FO HY, “TDiarBition band = to to DHE, pashon) sie o. skpbond aide = 0-002, i f Meso, $3 = 0-01, Sp20.000 , 0 afehh ; fe MOF, spetef; $S= SOU, Me aSxa= mm, hos $450 os stag Be Rey ten b= Foy, $9009 = scout Mr m as” Nye fie SL. SOO = ele leah fe Te ete ge Gel) FR ~ feop 2 F* fi Re « = Flop f. % so @ 600-50 < fz HH =y 5504 fs 3500 y w fe SH | WO. oom 4 19000 nie “elofjo (853) “Bla bge (o-01 x0-009) m6 af <= 144-6. 0-634 degar ica fo eps fa f goo - 50 2 P2 ass F4 300 fy = 250290 , 200 + OGRE / 600 600 4-80ee Finite worl length effect Fass dee +b. quantization « tnpob quantyalion cepsjor + pgocluct quantization copjor’ 5. ae co-eticient! quantization esjgo (Mn) olor ane 4 peerdl- off Noire. co Mficienk ) fimit cycle oncitlation. EH z ® He) = Mav" lees e Repoigrentation FE Norober we on sepayeret © numb, oN 40 ony desinge acunacy fy a fae aeien NE a oii whee 's0dix. Taper of wipiabeioh Oe fred point \sepicnertation ancl Sign mogritede for. 3+ once Complement fog’ (15) 3.0% complement Bam b. Hoaleg point steprerertation i c Block sleting pois orpoyerenttion \. Fixed point sepererentation - geal M1001 + lod ' rmbt). pont fapchond! pat. 7 a Sgn meagniticl ar ‘ Vy regatve reomtey, othnal 07 por, rembeo, n 1° 1 = O01 -O1 OH), PAR * 6000! «OF Neg = neo!a 8 a eo iy AWR the) posillve pombco| Fig aqpor ented ag Q sgn magnitoce nolalion. Bob othe ragalive rombtsy %% loin, by completing ll the. bils .of postive comb. res), “FO: N00) & COB 9 < (00011), ® comp yebee. @-ab), iF we do we git tay fom vale. binag benof bi Heeger - 3 2 ep fm ee QSH)ig = (o- 1000) g om eos We alias Cost)g, ph endo}, a Bp: valie in 3% Omp qin ead a: loating post appsjererlotion ee i Our: Aim then, positive: .nombee &:, orepeeraect oa (= aoe), whaye MM Mbukea: Modis | YaeMe!) C= exponent Cary be, Wve ]-ve) a ee Qa > a easy Halnssnoo~ trios = Peay ’ “(P0103 aol (a'6i0) faioyy bos ] t préboll — olay = aoeias | : a =(%. 001) — sepaenatn in thoy. poi S. negative Ffoating ; oe This Gepenenkd Af erate the Imanlis3ct as a fixed pid. The syst bt of trcinlfosa aqpremt he sign of the seating poisk) “miinben 10+ 1 jfooting poinl Ropsesentaton ~ te Gubinlion of fre! pont ond lealng pont p wl & sigrlt 3 dwide| inko bocke caret Speyationg within the bhsk crey fivelporit coir od only oF oye fhe] loch ft Shred . per OD peeforn addition (OS) igt (O14) 4 Ez. We 3 plod! uk 0-100 0 -00l COtoNg —posiive. CorS)o% C0698), 0100 0-10! go", = regatve. call 0” Sgn tall - — the vee flow ecousy bor Comat be aepaeaaited in the sbit wry OAD —~ OF \0 Yodo YR A OP.