Convolution Sum-Signals and Systems-Solutions, Exercises of Signals and Systems Theory

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Chapter 2 Answers 2.1. (a) We know that yiln] = 2[n] * Afr] = > h{k]z[n — k] ($2.1-1) k=-00 The signals 2[n] and h[n] are as shown in Figure 82.1. LR 2 4h) { hii) n “oo © 2n Figure S2.1 From this figure, we can easily see that the above convolution sum reduces to i Al-Ya[n + 1] + Aftje[n - 1 Qx[n + 1] + 22[n— yin} Wl This gives alr] = 25[n + 1] + 44{n] + 25[n — 1] + 24[n — 2] — 26[n — 4] (b) We know that yoln] = a[n + 2] + h[n] = > blk]z[n + 2 — kl] k=—00 Comparing with eq. (S2.1-1), we see that galr] = vile + 2] (c) We may rewrite eq. (S2.1-1) as gil] = zl] Ale] = D7 afblafn — 4] k=-00 Similarly, we may write ysln] = 2[n] * Aln + 2] = a[k)h[n + 2 - k] k=~00 Comparing this with eq. (S2.1), we see that & ys[r] = yin + 2] 30 docsity.com