Question: Let x(n) be the input signal to a discrete-time filter with impulse response hi(n) and let yi(n) be the corresponding out put. (a) Compute and

Let x(n) be the input signal to a discrete-time filter with impulse response hi(n) and let yi(n) be the corresponding out put.

(a) Compute and sketch x(n) and yi(n) in the following cases. Using the same scale in all figures

x(n) 3D {1.4.2.3.5.3.3.4.5.7.6.9 hi (n) = (1. 1} h2(n) = {1.2. 1}

(b) Sketch x(n). y1(n), y2(n) on one graph and x(n), y3(n), y4 (n), y5(n) on another graph

(c) Comment on the smoothness of y2(n) and y4(n). Which factor affects the smoothness?

(d) Compare y4(n) with y5(n). What is the difference? Can you explain if?

(e) Let h6(n) = {1/2, -1/2}. Compute y6(n). Sketch x(n), y2(n), and y6(n) on the same figure and common on the results.

x(n) 3D {1.4.2.3.5.3.3.4.5.7.6.9 hi (n) = (1. 1} h2(n) = {1.2. 1} h(n) = ) ha(n) = {}.1 hs(n} = { - %3D

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