Exercícios Resolvidos Oppenheim cap. 2, Exercícios de Sinais e Sistemas

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Chapter 2 Answers 2.1. (a) We know that wi[n] = 2[n] + hfnl se hlkje[n — k] (S2.1-1) k=-00 The signals x[n] and h[n) are as shown in Figure S2.1. 2 am) = | hEn] ig] -10 12h Figure S2.1 From this figure, we can easily see that the above convolution sum reduces to win) = h-Ozin+1)+Azfn — 1) 2e[n + 1) + 22[n — 1) This gives w[n] = 26fn + 1) + 46[n) + 26[n — 1) + 26[n — 2] — 26fn — 4] (b) We know that valn] = vin + 2] + hn] = ” hlkJe[n + 2 — k) =—co Comparing with eg. (S2.1-1), we see that ven] =[n+2] (c) We may rewrite eq. (S2.1-1) as o > elklhpn — k] k=-c0 3n[n) = en] + hfnl Similarly, we may write o valn) = e[n)* hn + 2]= DA elklhfn + 2 k] Comparing this with eq. (82.1), we see that ys[n] =n[n + 2] 30