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0.5 a) Hz(2) is a type-3 GLP filter and it has a zero at Z - j. Find Hz(Z) b) Convert Hz(2) to Hz(es) then calculate Hz (e)and H, (e- c) What is the relationship between the results of part (a) and part(b)? 0.6 Hap(Z) is a real all-pass filter and it has a pole at Z = + and another pole at Za bmZ- MM M Construct Hap(Z) as one block and without fractions, i.e. H(Z) - DM -1)...the taons, I.C.A z -N+N-12-(N-1)+ - ta 0.7 The system hn) is stable and it is characterized by the following difference equation y[n] - 1.3y[n - 1] +0.4y[n-2] = -2.5xin - 1] + 5x[n-2] Decompose H(Z) into a cascade of a minimum phase and an all pass filters. H(z) = 1-2 Find all possible combinations of h[n) and h[n]. In each case: find the values of h[n] and h [n] for -4 S ns4. 0.9 Find the transfer function H(s) of a Butterworth filter that satisfies the following: Passband edge frequency: 0.151 Stopband edge frequency: 0.35% Passband magnitude 20.96 Stepband magnitude 30.03

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as per HomeworkLib rule,,i need to write only one questions..please re-post the remaining questions separately..thanks..

I Answer - As we 1 a) Hz(z) is a type 3 GCP filter and it has zero at 22j then H(z) is :- - GLP filter here means generalised linear phase Filter. As we know a system has generalized linear phase if its frequency response can be written as Heiw) - Alejwe-jwc + bi where cand 6 are constant and A leiw) is a real functions. Aliw) is a real function meaning that H (@ico) = Aeim) (cos (6-0) +jsin (6-cc)) Heuw) - A leves) cos(6-cc) +0 sạn (-coc) -0. b-COC = sin(0) - nữ [6=nitwe H (Rice) - A Cedas) cos (OT) = F A cew) 1. Hesw) = I A lejow) Given that H3C2) is a type 3 GLP filter and has zero at 2=3 =) . H3C2) - A(2-3) 23

H₂(2)= A(z-i) type 3 GLP filter means system H3(z) has three pole nico at origin A-) constant j d izero - 143(2)= 3 7 - Real spole e pole-zero plot. - b) convert H₃ (2) to H3 Ce jw) H₃ (2) — H₂(eso) 2.1 D.TFT 2- transform domain to discrete-time fourier transform domain (2-domain to DTFT domain Cerco domain)) .. H3(e;W) = A(esw_l) A (pow.;) (jw)3 jaw evilla - cost tisini zotico pilla aj /izejula 45 (cima); A Celes.com> دم قدم H3 (1972). ACEST)2 - CUT/2) e jalla AC 3 T2 T/2) et 137/

Hz (Chile). A(0) 0 H(-) (--- T) (e-uri)2)3 : -A (WIl sile) J35/2 - GETH) Maliha porte)-2003.) - 2A :-e zi H (ST/2) = = 2A sin 2 = -2A Hevi/2) = 2A c) Releation between the result of part @ and part is @- H3(z)= A(Z) ® H3 (edas). A (celko-,) Ceiw)3 A(z-i Alejw_j) Acesco_JT/2) .2- 53 - : ده في زم ej3w. z=edas) z= rebo » [v=1] 1) W = 1 1 2 =) z = 0 & Tzaj [7= -> H (edit/2) = H(3) A (EJT/?_edTub) A (3-0).0 2 qj379/ 0 13 - 0

Zee-ji/ (ن) = (آنتی) (= - : (1) (دانے دانت ) A - - - (ذ-ز-) 8 ادز-م د درنی 28 .. م2 - د (نالی) A- انتی - نو )2A- ) 2 2A- ده ( - 2A sin I 2 <=) -2A |-2A) -2A from the releationship blw the result obtained in part @ and Part 0 it implies that Hz(z) is equally well as Hz (eico) رده فع) 1 = (2) 3

please give me upvote...its really neede to write more questions..thanks..