A sequence x[n] is the output of an LTI system whose input is s[n]. The system is
Chapter 10, Problem 10.46(choose chapter or problem)
A sequence x[n] is the output of an LTI system whose input is s[n]. The system is described by the difference equation x[n] = s[n] - e8 a s[n - 8], where 0 < a < 1. (a) Find the system function X(z) H1 (z) = S(z), and plot its poles and zeros in the z-plane. Indicate the region of convergence. (b) We wish to recover s[n] from x[n] with an LTI system. Find the system function H ( ) = Y(z) 2 z X(z) such that y[n] = s[n]. Find all possible regions of convergence for H2(z), and for each, tell whether or not the system is causal or stable. (c) Find all possible choices for the unit impulse response h2 [n] such that y[n] = h2[n] * x[n] = s[n].
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