Consider the cascade of discrete-time systems in Figure P2.73. The time-reversal systems...

Consider the cascade of discrete-time systems in Figure P2.73. The time-reversal systems are defined by the equations 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^jω), F(e^jω),G(e^jω), and Y (e^jω) in terms of X (e^jω) and H₁(e^jω).

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

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