woheat ors a dilaptet filters and its types - Class Notes [Unit No Subject : DOP lecture No Faculty : KN -BHuxhen Planner (SP): S.No, —7—- of SP. Topic Inka duukion bs Filters loate Conducted : Page No yf “3 SCopEe vw oe@sEchve: warn eo ne This chaptes deals oteout the icy tee} "Rites: the thuolent can feasned about The Acts, of NR fi Hees bading Rutterwesl & ehelychey filters axe lyn Chuckie in bol amales amd oligite| demnin 3:0 INTRODUCTION Bosially Fils TS om electenic Aevice which veqeds the unwankd eae amd allows only aequined bears Generally | Fillers ane Coligovized inte Heo types beted on Ihe Signal ype. They ane o>. An alos Filters & (a- Digit filters sal Batcd on lhe Freq vanes sceporn, Ibe bites ase Clete fried ae (). Upp G)>- Ber (> DPE MY] od tee th Bee of© Class Notes the types of fiers which make use et feedback tonnection fo get the leticee Lite implementation ase known as ReuRsive bilers - Since lhe filters have infinule im pulge ponte , hence Ie ase Called as WR dpltes. NR filters are Aetigned bu Considering al the infinite — Somnples ety imple nee porte, The Impulse 7¢£Ponse rx obtained by taking inverse Pr of ideal fseq Pk Pare . These ax Ceveref techniques avatlobe hos the Aegsted pHey design havin g an infinilc dusalten impulic seepone The pepulas melsods fot Such phe det utes the technique of firs Actigning the olvgitel filler in amnales clomgin amd Athen trans bovminy the Analog Bid into om equivalent digntay B Hey® Class Notes tthe time demain eajnahon of WR Phe rs Ppren oy q m Gor) = - E ay lo-k) + E by ACn-k) kK=+ K=o The Cenvolubom of UR fittest Aven vt ; Yor ee oe h(n-K) c The dig trans hs bunch of IIR bi Hew kK Gren b $y #2) = & by 2 2 He I+ SF ae ex The omaleg tranches funchon ef Nir filter gimen by - % H,(s) = YG) _ Ze" RG) I+ Sass Ker amd also 0 Cs) = f ney eae © eseo | Class Notes For stability amd Gusality of Onaleg. Fills the amaleg trans her fench'on Chould codss fu te fellowing sequiremernts ©). Hals) Should be a aeahoneal tm of ‘o? ana the Cockh’s of 's Should Le real. 2)» poles Chould lie om Ihe leht balk of S-plane - 13)> He- ot Zeros £ NO- of poles. e The physic ln ealtcalte g Stable «ahh Hee Cannot brave a Lineas phere - Digital Piles Arubeg Eber oprala on Samples CD: Operates on Signal ~@)- Repretented by Une (ay. Repretersted bog lines dit perence enqnotions . di bpeential eqs: GB). Consists of adelers, 2. Conercts dy paatine Multipliers x debos ehements Like K,Lc- clhements G)- Piltee Cocghe ore GD: Approrierahion problem Aesgmed ts Sots hy vs Solved b Letrhy Hu), (Ww) LAdvantages of digilel [ers exe Thetenal cs, Accuracy , dynamic range, Stability @ bay Spore Progra mmabl » mulkplixing - PP? Droadvamtger of digsta filios ax bardurdleClass Notes =pemics : Det et ee Planner (SP): S.No. 2 of sp Ti > Butter sets Hilens oieden —_ ao ef Analog a Petaute the proach col char. of a biker Te nob iden#eel tp ideal char. The approximation are 3 types > Bubbeswecls appr. R25: 6 Cheleychev appre. @)- Elliphe fiHer approx. the main char. of Rutfesweeth He rs that the petsband Te marimealle Flat. 7 There aye mo Vasdation (ripples) tn pars land. Tn fies Char, the bey: ange re Colled PAcs BAND omd the Signal rs Suprerted te Called STOP BEND. The bey Separating pe ee recalled CUT-ofe “the magnitude ecaporse of LP Rutterswotl- fille oc apven by [Goo] = ———— Mey ee a) where D> cub-of f Frey ey N > Orde, of the plier yrClass Notes 4Go) dead UF * Lo wah a Bey ik fio = aN 2 4 2p ae a osdes Ay (he incresecs the funchion ideal char —_ elude 1 poene Ita ae 5 abe bond tattestitahions A> Step band attenuation Frey Seliekive fitters ase there which reqecls Granted bieat from the Ip, Synal ond _|fotbeo she degined feqi to obtain the eq Shape of ep Bimed the [ters ane of 4 types iD CEE , nis By BPF 4). asp Wt) peakiel hd shed Go] Wie ) 48 Pes] 8 pe | Ditesmete Spec A Lee es and otlenuabon where E> dllowable porch nd ctternoton A= Sllowable Stopba the celation beliveen EA, bp, fh, are Gren by = I= Se -Class Notes The magnitude funchon of omaleg Butlouest Lee Ts q@ven i In¢jas] = —-—— whee N=1,2,2--.. [it (hoes ]* Whese i> Gaztes: of the bltes Per ab-off Soeqrency. “The max. wesponte TS unity ab y=0 Where function rs monetorically dec veoking. . AL peddle l 2 l4Gval = ee v2) por mat li Gjo3) = [u(2| = 462) =H Hes) d =HGOHC Ie) [Wes + 2 tt 14 ean t+ 2% 14 Glen HOES) = (+ Ce I4(-2 9" =0 The Loluben of the above eqvotion rs Tree sg, Ree i When. gp = Ty Gaon, be bie. kK a —— , aClass Notes O-ldp = loa Ci+g%) wo), 0-1, lee 1 Mee. jo i {or 7 - cre erie Vite? | + He —- ' \ E=Vie e Wa] ( Lt 2 Mp Me At wan, , we get 2oleg|¥G|= bologt — tetegli+e (ay) fig relalis e(ef oie = lal oC] Olek s ia = 14 ve (2% yn me lke . (=) =| ae pms ovles (S) - —-f to =! ot ee 16" oe) ! Take logerstom on on groter. Olas te =) = — ost Whee 4= A ne ae £ fe@ Class Notes “| The Lot of Bubtesweslls pelynomrals ose. Butkrwwoslls polgromiat (s+) Saas +1 Cott) Ceest) Coq ores sti) (24847541) (sti) (8° o-cies +i) (674 eles +1) Cee rasasti) (Sect) (24 O:-SI7S +) z OHO fF uEpr- 8) Yew +o find dhe order A [hz Burteswosth bi Hee: | Maximalley Flat Filles] sa Consider mar. PB aHenuahon Ts Ap ab bey Ap omd min: c& atlenuaton 1s de oh Wey > - 2 i [4Civo} =) ———> >N I+ &( hop) Take log on bolt Gsdes 2 wn Qo og LCi] = lolegi — Io leg it CCE] abt v= vp, ao log Cig| = —lolegeit) = —*¢ a Xe = lo les Cite")Class Notes | (2)"= in; “e ioe, oles a We to -) “ [ | orr_, b ks ah Mig > We (10 ME) )2N > We = ve “obs 1 (lo —1)2N ® Design om ALPE that hesa —2d6 pale oHenuotion ab 20 7fec~e omd atleast —lode Sop band attenuohon at 207/ece- a op = ade. Yip = 20r/s => oe = lod@ 5 ve= 20% “. NZ224=4 Batlersorth polynomial re Ceno7ssH) (hans) | : conse oe (ee yon lets) = — Cstpo-nesstr) Cot f-eu7s +) Fes LeF, pub ct. oe Was) = 020921 a ier Co e-368664 459-394) (%435- T5445%9) feDS @ Cormpere (aa) ¢@ 2N S uw” (gay = He ©) > es)" -(%)" Class Notes Poololerc< 0). Given the Specifitaton Xp =1de, a, = 30d; “2p = 2007/see 1 Vig = C0O7/e2,° Find n> teeny $0! Nz a Oe ON eRe > 27S8 “es(-22) a Ney V vs 2). prove that We = Og ce (eer yan O15 . = ce Gli = =O = (+ 7 vo2n (ve lCiwsf = 1 ler er(ey we ev olde (ay bee et Hy Ve Me ot cee yen We : a 2 wy a CB) ew wi |Subject : DSP. eerie ae Faculty : +N: BHUSHAN Pianner (SP): S.No. of sp ~ifTopic = Chebyshev Fite lbate Conducted : Page No 2 13 NE Class Notes 32 CHEBYSHEY, FILTER AprRoxImaTION Chebyeley fiers ane of two type, CO. type-I —> AN pote Giles (2° Type-D > pele-2r0 fi lder Uwe} agai get Weir, w Le vo ' 1 We We PB co owsivieple 1 ' Tar \ rs { - & Mp Mp a CO Type -T © ryee-a “The magnitude ef ponce of ma Order. type-T filer Com be empretted ax i [+ ela Ge) l¥¢jagp = where Qld) = Cer Cn Cos'g) 1X} £1 > pe = Coth (N Coclstn) fala! > se Cy (a) = 2x G4 = Gy) » NT oa Co(m=1, G(ad=x a Swat \® Class Notes 4 ype “I chebyehev fitter, the function Clarte at the value 4 when N ts edd omd ik Sterte of ,When N TS even. I+g> The orcs of the Chebychev filter ts gen by ‘he poles of Chebychey fits tS giren by Soe Te + jin = Aceh + jbsing, where a= Mp [ wis eM} be rey ee] #24 (@x-D ir Wye? 2N The poles A chelychev filter leg ‘, ELLE herent IKE poles Ay Putkuoosty file lis om ciRcLE.© Class Notes - Cheloyshev Type“? Contains belle pelee oma Zeses- The magnitude “Square steporse rs pren | ° I oe e a e(e | on (4) Zeros ose loGlicl m imagineny @xTs ond @|" wr 'y Sy | = Sindy Poles one Gren lng CK, Ye) = Os Te y= 22K mae 2 ee hy a whee a alos te, p= b 8M bez A+ VIFARX Difhtence beelioeer, Bubleworth # Chelyehev yt Her ane QUTTERWORTH a) + Maximal Flat les yey CHEeBysHev Ud» Eayuiripgle tite, th pe/ce- Transhon bemd Ts DD. mete Lese B+ poles liek on Circle 3) Ellipse, @) cH Les NO: ay polee ts M ose | SuClass Notes The freq transhotmation in Ona in “CO. We to Lpp —s ca (D> Lpp to 4ter. —~ oe E S (2). Lpp to Bp —s cn oy Aa s(ay,-24') (4). Lpp te BcP 5 = S014) oH ayy STEPS to DESIGN BUTTERWORTH FILTER (9: From We Specifications, Find the oveles of the filter. : N omuck be soud-cfy neck tates @)- Find the potes of che filles MO). Find the trance Fin for normalized Cut-off freavency 1.) vie = Irad/ec.. Wo. Bind the Unnormalized Cub-off Frey. We = a = pub ae hee UP: svers To DeEIgn Chemysiev Filter ay. find tka order ay the filter, fron the Given Cpeei ficahons |}@- Round - of f te Ine nent integer value.ae: Class Notes al )- Brnd the minor amd mager ante ay he ell; er 1 = Vee y b= Vip [ere Ss} : Le ~_ ; we Caves, = A+ TAs] | (4)- Colentati the poles Ay Cheleytlev filter | Sy = Aleed, + | b Gin @ ess. Bind the denominator pelyromial. 6). ‘The numesetor of dhe tranche 4n Con bee Aeteemined 08 cy) Neo pub c=0. then Nv = Value di) N= Even, pubt=o then Valve _ iv p Vite mrolole ne : cD: Detign a Chelythey filter wort, max. PB @ | tation of asda at Rov/tce ond atenuation ef zoda at S07([Sec - Seal ep =asd& ; Wp =r07/eec aK. = 2ode 5 vg = Sor (secClass Notes - oe Mee tVe4) =2-6- a=bb , b=21-0L See A Cot H+) Ging, here g on, Ger oe! oo Brine 2 s-oRaPjle23 Palen 6, 62 D, = 2yo a) Sq =-2:3 ef lie-28 polynomial tS Cc4e.c) (S74 6654+343-2) N=3 4 pubtso a Nya KF & a265.29 2U2-> o, Trawe pes Punction, ta Cs) _ 2265-29 (o+6-c) Ces 6.684 242-2) Obtain om Omdles chebychey filter trawehes fanchon thet Satsefice ! a lydivy) £15 ofmer (2)- [WG] OL KN: Bue lectureNo oo: & ie 6 acne Planner(SP) :.No. 1. of sp Toric | Digital Hos bom cnales — bateconduced : Page No 74 OO RESISN, OF, NR DIGIT RLIEes, FRom, Anning The : WR filles Gannot be Aetiqned Clincethy in degitel demain. Cince it hae infinite dusation unit Somple e Lkep ecepente of degtel plea re we I-21 35 Impucse Invariance, meTHod In im, the eR biltes oo Aetrgned| Such that the unit tmpulx s The Seaton Lcbres, omaley reg om & cLigite psa ee ots Gren by = 2 ben +r Z, Lo& [- = "oF Class Notes . Fes Small velues of oe’, — 2 = Te a 2 [waa] For low peat bol thr beeqt are Uncar For leigh fee, bollr Ine east ore on Linen ard distortion tS irbaduced yohith T Knewn of wesping eae Ww we Ww f Yorn > t + Morgen The wesping thet Can be shipnticabad "Gr pevasping whe ancles filer eg so ‘ s , (22 _|preoasping Week hey Np = Eten ; Mea Bie STEPS TO DEEIGN IR DigiTH FILTER UtiING BLT @)+ ind prewes ping dancleg bseert le, vp ¢ 2). Pind IMr tranches funchyn Ike) fron lar to Se OO: Steak tte Laanpling wale, 7. iy | pall s-e[ Le] = sh jeat (5). Pind IKE Adi tal tranche functor, D> Reabde Ike choucer aA ie pie.PN Class Notes Unit No. > suet: DEP an ee Topic: Planner(sP) S.No. 4 of sp 7 . Prof [Date Conducted Page No ? 25- 3-% PROoG@LEMms Rees SNM |e ALT (D> Design a ligitel Butterworth biltes Saciztying the Constraint ores cf He ler , oss t l(c] con, In ewer ® 4 wrth T=Isec Wing IM & BLT ving @ur wo me? p Mer E ls scala al de n8s PRE nae Etat cee 3 Cel, A=ues fo o leg 1858 =1-833 165 (4) leg 2-414 ve {Nee Find poles ay IKE Hite 5, eS, SP oe h = (C2ornr Se where - st The notmalired brane hur bn 1 is Ws) AyeClass Notes Colealede the cub-off fren Bren by We = Pr _ = Be = 2redlee ean AN fes UPE . pub t> 8 = £ We 2 yal = ! Soe Virgen put s aes) Toi+e safe) = mann CDT 1+ 017162 - Chy2e(Z dt D Cy 2-28 YClass Notes The 4! ordes tranches fn al = to (seoss ti C4 t-su7e+n tubo Frey 1S giuen by ee) el ae Fo= = oSr alse CN ye pels = bow UE tye 52 (274 breast 2-¥es) (P42 Gort 2-4és) reply pasta fucken. + wt = 2 a ++— + : ~ 40-6 tfryy Se C+ ust jos st lus job : z aa it or 7weajl IY OTS 34 JVI Dg) = ee ee co taus-joe) CO S-C! ustjo0) : _s Fjord Ko ssyos 4 ieee ll ele Sa g— (cos jeus) = Coed frus) hey = A & Keq yo efe | .rs072/ ley = bust 19352! 1 | ysut 6-280 iene 4 [oo ge7eleogsse® 1701922274 ovsole*| 5a with TH/Sec_ Cs+1)($ +25 Class Notes a trply QT +o H€c) = MO 4D = 3 pu So ako Toya H(z) = oe 42!y> C 1-0: 2227 3% rely lim le above problen e Ws) = Ay BO cr 6 She 4= 2, Ba-2 #9 = 2 A c+ Ste 2 _ 2. Wes) = Fano - S-02) N Hae = ee, Se ag kt be’ pagan” 1-8 o-4b6sz7 (-0°S03 214 0-044 767% + design Chebyshev bfx uing BLT & II 7 os clece |<) O20 £02 ltels] <0.2 5 Ob6r EW EFSubject Faculty Topic 38 >: Whee Class Notes pee [Unit No 0m BN -BHUtHeEN \Lecture No 9 Special Tone hewmebons [Date Conducted : [Page No 7 24 SPEETRAL, TRANS PoRMmATIONS vohere = Sin [ Cu -%/>] Sin (0% 4%) /o.J] Wer Pe bey of lpr wp > PB bea Ab neo LPP Lpe—t> Her | 4 _fz | iad eres ox[ Cop tre] rs Cox [Cup e/~) we > pe be ab ter . | ads —Class Notes >. Upp to Bee aiipseeelh k-I i atk sega et Gy Ses: 5 = -7 Ba he ade at ty | K+ K+) where a= cox C 1, +0drh J ces! ( Wy, - 4/2) Ke cot {| Mae) = tn. Upp be BSE —__ a ake Sj [ pee hee shes ere He ee 5 eg 22 tH] He Hk voh ere ae cos ['C a+ Ve] cos fC wp, W/o] k= ban (n=) Lan YF 2 ae‘Se Tutorial | Subject DSP [unit No Ag Faculty =: KN BH Hen Ipate Conducted Topic BET + IR Dogtel LHe PHen 7 By (9+ An omvlog tilts has the -fellowing Lyclem funch on - Convert tw filter lh a dtgte lw Leng backward oll been For the clestvahve Hes) = 1 —_ C6t045 «n! - H(z) =Hed | c= j-2! T _ I [ee olf +49 = w= ° 0979 ee a 2. 1- 0-D15S2 4 0097922 (2). Convest the omales fie into igitel Fildes whore tyetem funchen rs Hs) = S402 . es enemas ag Using It (st02)4 9 "6 | 40s) = sta ia o+ay bY ' LgTutorial The System recpomce of Thi oligsta) $sHev rr =T Hl) = 1-e Ceebroe! 1-28 *Ceoeersty SM Ee whe aro2, be 3, talsee He) = I+ osrese! (+ -62102"4 0-6 703 272 (D 4 ligt) pHa with a 2d@ bendusidth of oa5n re to be Aesigned Fron the onales fila Whore Cyttem vesporme TS HC) = We ving @LT St We = Me = 2 tone 2 2 fan Oe = OES T > TF ce T H(z) are e-E[ie2 2] = 0:828 ae ot One TT t= [+z] ee RHY— 14 yalTutorial (4). Design a HpR for the Spec fications 4p =3dB, ad, =Isda, Yap = 100 /cee ke Vig = SD0Yf, dle éa! wo) 2 es MP, mes See ei URS leg WES ee cee The yl orden netmalized tranche, funchiony ts ! Cs C s*¢s4y) Mew OP old t | (10 fo aa (to = 2 Lits - Wes ie. _ looo £ = WRESz2 $3 (sooo) ( s%4 loves + loov~) 5) devign a Chebyshev fille with a marimuns perched atenuatin of asda pt Npz 2° "Tew amd top land ottenuchen of Bod Q ab ne = +See, M. ap =a sda: Vp = 2orlece de = toda ag = Pr Leee 2Tutorial — + Venu o> pee er b= ng{ wae] + nil we eden Rind Whe cenominaley per - Bind (hi wumraler diperding 2” Vax Nai@s) = 2268-76 oe (oreo) CoH 6s4-242-5)Question Bank ~ |] Subject : Dep [Unit No > OL 2B [bate Conducted : Faculty : Kn Byutions Topic WR Pile, Page No 73s 310 Descriptive Quertions (1+ Dehine on IIR Gita: Rated on peesjvencey seepome how as hilteot chow fred ? Rrctiete, aap iy >)- Comp ore she omales omd Abapted Sites B- Rabe te prse Ne Q). Compose dhe Butterworth and ©] cretychey approninahione @ Refer +o Pose: No. (4) - Membhen the techniques for digs tizing He tron fo funchon of om omaleg fite- @ Raber prs 0.Question bank 1 WG) peseus the Concept of Frequency. trans boom tn Omales. clemain [@- Reh ogee (6)- Destuss the Akeni Freq troveshommabo, @- Rebee see eases So cnr Con pore impolee invariant ana bilinces bran houneben mellseds @- Ree pose 0°Subject : DSP [Unit No ahs Faculty : KN BHUSHAN lbate Conducted : . |] Topic UR Drgte bites [Page No 7 ee Assignment Questions = 313 ASSIGNMENT, QuUECHONG (1). Delmine the ordes of a Butlerwort, low- pens filter Caltahying the fellowing Speipictons - 4p = OWH2 , ap =osdR f SKelshs , ag=IsdB, $= We (2). the Speeilpebon ef the dexiacel LPP rs o9elytwl sly oLweos3n lHtun| So's y osmeue™ benign. amabubgaes aaa PI Using lo} Unease trans bormebion . (3). Use Ihe Lackwosol diffrence Fer the derivative $0 Convert Ihe ameleog Lpe wil Sycten Funckan le git phe ottuming T=! See nts) = —— ee ors Bo V@ Assignment Questions (4) - 4pelg Impulse Invasdance melee fos I Cs43)C0t+¢) +(s) = ©): Convest the omalog bites with Sycteno dunctin Into a digtel pill uving- bilinear. trarsbetmab on pga sets Pie OaetyFaculty = K-N- BHutton page No Real Time Application Subject : DEP Unit No. : ih as : ILTERS S14 Rear, Time Appucarion, OF, Ue VF _| they one omaleg & Atgstel files Rered on the frre rence fre PerAsg, the fillers ose classified into 4 types They au LPF, HR, BRE amd BCE Tn the Signal procetcing, bitters ore of tuo type they axe IRE FIR file which axe available in bole amalo-g £ cheep td olomain We fille ane Aeegred by oltaining Infinite ne. of Sample of impulse ekponte. ne ites Caht be dezigned cinco, in the olesited coleman Gntee ik Cemtuing infin HO A Samples - Hence , biesk ik designed In the omales clemain then ib or fmrertisd ins “Atptd olomasr. Ro i, amales clomain, the app rimatbon ne thoel, aA WR fpltess axe Rutteewost46 Real Time Application Chdeyeley Crype £D), Elliptcop Plt tte. In the Atgtel demain, he Pople techniques ot fronshetming the aneleg clemein into equivalent digite ve ‘tm QLT , 40D) MzTre. Ty she cal bpe, Whe we bplers Oe weed in Ihe Communicah on Perpete Ne fleas One af Re curive. tyec- Sometimes it mary be nan- reCuvove Ye