Question

2. Find the region of convergence (if it exists) in the z plane, of the z transform of these signals: (a) x[n] = u[n] + [n] (b) x[n] = u[n] - u[n - 10] (c) x[n] = 4n un + 1] (Hint: Express the time-domain function as the sum of a causal function and an anticausal function, combine the z-transform results over a common denominator, and simplify.) (d) x[n] = 4n u[n - 1] (e) x[n] = 12 (0.85)" cos(2tn/10) ul-n - 1] + 3 (0.4)n+2 u[n + 2]

Answer 1

Solution a) ain) - uln)+ Ul-n) Applying ZT > x(7) + 7 7-1 z (Time reversal property] 1 Z 17171 I> 121 } 1711 11171 here Rin R2 d b) » 7 transform does not exist urn-10) using tirie Phyting property nin) *(7) Z 7-1 2012 hue 17171 7-1 - ROL = 171 > sain) Anun#1) guln+1)< AT IZI > ROC : we that know 4.2 [1] (27) **(2 962) - 43*13) -4324527 Anuin+1) old 1 47² d7 (7-1)2 (702) 147²_87 (7-1)

V [iruinto -7 d X(7) te X 2 > (4A) +13] et, + 3 87 2. ROC : / 기 d) ap) alp) = 40uto-) Z 시시 4 color) e 47 fun 3 | 0 4 ; 계기 이 ㅋ 401) 시키 '' 1<t), ㅋ 시미 uk 47 켄 </t) : 2 - ROU 리 기
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