Consider the cascade connection of two LTI systems in Figure P2.30: (a) Det...

Consider the cascade connection of two LTI systems in Figure P2.30:

(a) Determine and sketch w[n] if x[n] = (−1)ⁿu[n]. Also, determine the overall output y[n].

(b) Determine and sketch the overall impulse response of the cascade system; i.e., plot the output y[n] = h[n] when x[n] = δ[n].

(c) Now consider the input x[n] = 2δ[n] + 4δ[n − 4] − 2δ[n − 12]. Sketch w[n].

(d) For the input of part (c), write an expression for the output y[n] in terms of the overall impulse response h[n] as defined in part (b). Make a carefully labeled sketch of your answer.