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Fall 2005

# Fall 2005 - ESE 337 Exam III Fall 2005 Name ID no 1(a...

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Unformatted text preview: ESE 337 Exam III Fall, 2005 Name ID no. 1. (a) Verify that an FIR ﬁlter of order N = 4 and antisymmetric coefﬁ- cients has a zero at 2 : i1. Where are its poles? (10 points) (b) Verify that an FIR ﬁlter of order N 2 3 and symmetric coefﬁcients has zeros at, z =‘1. ‘Where are its poles? (10 points) 4." HQ)..— may Jag]; + 593214 hfﬂé; + Ami—4' f 6“ {HA- 57:;me 7:) Jr] {n}: "'"JA (4‘ “n ) '3) 9‘ CO] 1' " ”L‘E‘FJ 140]: - AC3] M2] ~ ﬁx C2] M who M, 91 15% MT” [@i‘FFR 4611114, 4 9140‘, rug—3). A; Wind“ xcw 3 5;: (Ac tame 3] CH] : L‘Cbi‘k ﬂxf‘ljii-Kv [AC-132,24} £C02L31ﬁ03]: Aﬁz] JAG]: ﬁ1£23 H (2).: 9\ C0 3 +MJ2‘U M2253 4293i »3 ._ Z [A (03» £03 2 + AC1] 22+ Ania] 23] 2. Consider a desired frequency response Haw) : D(w)e‘j‘”“' with 0 09:30.8 mo): 1 1.29.42 0 2.4gwgﬁ' (a) Design a second-order type I FIR ﬁlter to match 9(a)) at w = 1.5 and 2.9. (8 points) Is it possible to match them exactly? {2 point) Is it a good ﬁlter? Given your reasons. (2 point) (b) Design a. second—order type I FIR ﬁlter to match D(w] at. w = U.5,1_.4, 1.8 and 2.9. (10 points) Is it possible to match them exactly? If not, what type of matching is that? (2 points] 2 :> OlC03+ dﬁlwoCrSJ =1 »——> W cl: ukl'ﬁ ‘ Abe); D(2.‘1)r0 :) (1931+ AQ—lcﬂéCQ'Q):O .—-—-+. SEQ-h :3 Wit»? €53me (D GMClQ mime [email protected]}+ 0-0405?ch1; I cite] _— 061210 40} o 9 z 2, | 0 Z thaw.a~a ion euiuéhmw QMJJ 4WD wkmemmgvé :LKQEMJ thLJ-s ﬂu. Mammal WWM Ci) (S LA» LC can; No) {iv} tar-ta 812ch W MOW we cLo Wei ﬂunk/mam +9143? A00) {5% we [:0 0&3 mob/xiv D. 2% out Mao‘s). “01+ éﬁlwﬁaj T C 0:321; 04190? caJa'i) ® :l'Q396. . _ _ I M _ Wﬁvtbwj kiw- meg MM chum Av. MAL,” ﬁg“ La». ’ (1,414) d9] _ ' l C I? [am t; I x — I ’) bay] 5 I do} 1 -o 252. I £®(lg) L—O O ' ~09-‘Ho | UM (3 q) @ P d D __ _ MIME/('63 tngil, 3&454 (NVH‘x P I :_ 4-0000. ”bigot ({3} 2«ooo° [ An“? ’ wow ‘Cvmoé 1‘ "9433 £f[s\.-L-.n‘_ +3. ago)”, 05' 03 Maﬁi are}: (‘- 'SO‘C+ @ 3. (a) If you are asked to design a tenth order linear—phase FIR ﬁlter to approximate the desired frequency response in Problem 2 in the least squared sense, how do you carry out the design in MATLAB‘? (8 points) (b) If you are asked to design a tenth order linear~phase FIR ﬁlter to approximate the desired frequency response in Problem 2 in the min- imax sense. Furthermore, the passband tolerance is required to be half of the stopband tolerance. How do you carry out the design in MATLAB? (8 points) ' . -» “.- _ r“. - .' 3 @- var, C.. r if? {YES rv'x. CO-qA M MU‘E/d ML“; “fa“; AB MAJ—DA J M A i L A I” f LY- Lita \ ' , a l -- "J ﬁg”? V‘s-C“. \$13le (aﬁdj ' {cm '71 M ‘ihﬁ guise } 6 '90 In“; “LAM ' id ' _.- \J I I ‘ ' II I ‘1 "In 1, -. If! .. < i. n f l I? (-53, (‘1‘, 1.} New“. it]! 1} a”; Li a: has W4 OW “i" M if”! 5 ~. i if. L.- ~J N": 19 ’ / _ u '(r ﬁj airfoil: ﬂirt-urea: LL”i£":/ FEIIZ) 2/ 2; ts: «in» " J r r- “) U lull F 0 3 :3. : r .J J i 3 37‘: L 0’ in" I "H ’ “1*“ u'J-£"'Ie\r"\.".'{ K N: j; C!) M) » [ W55 b: Maw. \ 51s 4' it. ii ‘i; A W! ﬂair SGML M 130/” LCM ft IL: {A J ; VJ: - E him I [0; ”Q; i“ 2 '3 2 [-1.2 2:] '3) Wt? E F's-u 'llul 1‘" ' w-J 4. Design a Butter-worth analog prototype ﬁlter C(s] starting from 1 M(w2) = G(s)G(_s)1s=jw = 1+w2N so that the attenuation for w 2 3 be at least. 20 dB. (20 points) No credit for using a table receive. WMW 460v W23 JAM/{30M aJlo—eurf 2031? J 2m ‘2 IO \$9310 (Ho) )‘w:3>/,2,O 2M 3 2% 2M), 4-!917 [QC/£91. 1?") ~_._._—-—'—___. : f I I 5 _ .. W : WW.MWT_W (7,5)" O—ﬁ)0+ﬂ) (/,_§)(fu+r) (HI) («3 -9“). gee-frag (3)3“! J am! (“Q A: M’Il’ﬁm. («ff Ml pie 1? ﬂue Jfﬂa-xt. HE Lane «We, Euﬂﬁmudk Z” a" QC” 3 I / ‘— _ __.. ._..p-’ _._...-~-- — We... 6+: )(ﬂ 5+!) 3734 7-35; ’3 H / ...
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Fall 2005 - ESE 337 Exam III Fall 2005 Name ID no 1(a...

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