Suppose a second-order causal LTI system has been designed with a real impulse response

Chapter 10, Problem 10.48

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Suppose a second-order causal LTI system has been designed with a real impulse response hi [n] and a rational system function HI (z). The pole-zero plot for HI (z) is shown in Figure P10.48(a). Now consider another causal second-order system with impulse response h2 [n] and rational system function H2 (z). The pole-zero plot for H2(z) is shown in Figure P10.48(b). Determine a sequence g[n] such that the following three conditions hold: (1) h2[n] = g[n]h 1 [n] (2) g[n] = 0 for n < 0 (3) _Lig[kJI = 3 k=O

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