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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.
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