Consider the cascade of discrete-time systems in Figure. The time-reversal systems are defined by the equation f[n] = e[? n] and y[n] = g[? n]. Assume throughout the problem that x[n] and h₁[n] are real sequences.

(a) Express E(e^j?), F(e^j?), G(e^j?), and Y(e^j?) in terms of X(e^j?) and H₁(e^j?).

(b) The result from Part (a) should convince you that the overall system is LTI. Find the frequency response H(e^j?) of the overall system.

(c) Determine an expression for the impulse response h[n] of the overall system in terms of h₁[n].

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LTI LTI Time- reversal Time- system system reversal x\n] e[n) system S[n] g[n] system y[n) H,(e") H;(e")