ps11_solns

# ps11_solns - S Oiw‘l’ro LS Michigan State University...

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Unformatted text preview: S Oiw‘l’ro LS Michigan State University Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING Problem Set 11 Spring 2011 Issued: Friday, April 8, 2011 Due: NONE 1. Classify the following impulse responses of DT LTI systems in terms of BIBO stability, causality, and dynamic (or static). (a) Mk] = 5pc] (b) hzlk] = sin(’§'k + g) (C) hslkl = 2"u[k] . In this problem, you Will better appl’eCiate why we choose to use the unilateral z—transform (UZT) rather than the bilateral z-transfornl (BZT) in this course. The BZT is deﬁned as follows: F(z) n 2 3:: N l I Compute the BZT of f : akuUc] and f = —-a"‘u[—k —- 1] and include the region of convergence in each case. Also, what is the UZT for each of these discrete—time signals? . Using only the fact that 7"u[k] <=> z/(z — 7) and properties of the ZT, ﬁnd the ZT for the following signals: (a) kzvkulkl (b) ksulkl (C) a"(ulkl - ulk — ml) ((1) ke“2ku[k — m] L. W “103%0439‘1’0] s imam) for memo 9m 91515:“ ,m ~ a) Ee‘m‘gm =3 :MCmH: , Blibo saw/LL. F 09 4) => giﬁimjl _9 co ) Mr 131% 54m. ’> g Maw}: 212%...) 00 , mgr man 542%». "'"° PM) .0( 0 f ems“! 97510;») m W KM, 7‘6 L420 for 75<Ojo1iorwﬁ¢ MGM. 19* a Mo 916%»;ﬁW/ww «m m We fr? .mwa @110. a) “ADO: W M d‘go. b ) ‘RLCKJ : Shggz+g> mm W cﬂlnarwiw. b) £5043 : fum W W; Cglnwc. .—_—.u-—. .———.-—_ _-._.-_-———._w-_uww———.--W. ﬁrm ""“'_"“"" " _ " “- _ “' w.~._m_.—__._._—. m...“ - -.. w - K rs '23 ” 9? m m. 0. am , Hagg‘itmzzcé”: Em?" [£90 [a o [—622 <7 63" g T J ‘2 2 a r K o. "l "k W {m -auc—K-O , 43(2): gammy"... ,: a“; [darn-0‘ Kgul’a I .—’ v- ;61’ K’=*K =>¥(a)= ride/J: -30 («2" K kw [<21 00 - I 0° 15’ , gm): 42¢:an Ki” 15:0 yuan; m Jam: +\ x5? =- ,1. 1-0?- MI'; (-61“? \$9 ,aKugu-Q I -1 [2‘ <1“ [~03 Mfm, {or [321‘ ) W Trmsfotmdm‘ 1\$ m’f m-1‘o—O‘N~ 7310 06ny medm) Mﬂﬁw BETMJ'WKOC- W com/7 m (200a, mamw, 8% WA 470ko 7‘» Maw M463, MAW“ mf amoéw- @505- 3’: é‘) Kzrzuw MC Wﬂf’acw‘ 1’7 ‘K mitt: K/F‘J “M vied—g.ng 50 : kauaﬁj H ,2, (3*)“2? : 2r. (2-402 (3.402 kerM 0436—9 .83 (2"?)2r..221y(2._r3 W ...
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ps11_solns - S Oiw‘l’ro LS Michigan State University...

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