Homework2_ solutions

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This document was uploaded on 03/06/2014 for the course EE 341 at NMT.

Ask a homework question - tutors are online