Homework2_ solutions

One period is given by 1 1 0 2 1 1 0 2 iii xkuk the

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Unformatted text preview: be a periodic signal with period K=4. One period is given by; 1 = −1 =0 [ ] = −2 1 =1 0 =2 (iii) x[k]=u[k] The response will be a causal signal (due to a unit step): y[k]=h[k]+h[k-1]+h[k-2]+…. 2.21 The series and parallel configurations of systems S1 and S2 are shown in Fig. P2.21. The two systems are specified by the following input-output relationships: S1: y[k]=x[k]-2x[k-1]+x[k-2] S2: y[k]=x[k]+x[k-1]-2x[k-2] (i) Show that S1 and S2 are LTI systems EE 341 Fall 2012 (ii) Calculate the input-output relationship for the series configuration of systems S1 and S2 as shown in Fig. P2.21(a). (iii) Calculate the input-output relationship for the parallel configuration of systems S1 and S2 as shown in Fig. P2.21(b). (iv) Show that the series and parallel configurations of systems D1 and S2 are LTI systems. (i) Show that S1 and S2 are LTI systems Use the property of linear, constant coefficient finite difference equation which represents a LTI system (ii) Calculate the input-output relationship for the series configuration o...
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