Homework2_ solutions

# P221a denote the output of s1 as wkxk 2xk 1xk 2

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Unformatted text preview: f systems S1 and S2 as shown in Fig. P2.21(a). Denote the output of S1 as: w[k]=x[k]-2x[k-1]+x[k-2] Denoting the output of S2 as y[k] (given that the input is w[k]): y[k]=w[k]+w[k-1]-2w[k-2] Substituting the first equation into the second one we’ll have: y[k]=(x[k]-2x[k-1]+x[k-2])+(x[k-1]-2x[k-2]+x[k-3])-2(x[k-2]-2x[k-3]+x[k-4]) So y[k]=x[k]-x[k-1]-3x[k-2])+5x[k-3]-2x[k-4] (iii) Calculate the input-output relationship for the parallel configuration of systems S1 and S2 as shown in Fig. P2.21(b). The outputs of systems in parallel are added: y[k]=2x[k]-x[k-1]-x[k-2] (iv) Show that the series and parallel configurations of systems D1 and S2 are LTI systems. Since both represent linear, constant coefficient differential equations then both systems are LTI systems....
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## This document was uploaded on 03/06/2014 for the course EE 341 at NMT.

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