QUESTION

(a) Consider a system with input x[n] and output y[n] that satisfy the difference equation:

                                  Y[n] = x[n] + 0.5 x[n-2] + 0.2 x[n+1]

Find the impulse response and the step response of the above system. Sketch the sequences of the responses.

(b) Consider three LTI discrete-time systems whose impulse responses are given by h1[n], h2[n] and h3[n]. If the systems are connected as shown in the figure 1, determine the impulse response, h[n] of the system.

(c) Consider the following difference equation:

                                Y[n] -1/4y[n-1] -1/8y[n-2] = 3x[n] + 1/2x[n-1]

Represent the above system in schematic diagram.

(d) Explain the terms Sampling and Aliasing.