Question: An LTI discrete-time system has an impulse response h[n] = u[n] u[n 4], and as input the signal x[n] = u[n] u[n

An LTI discrete-time system has an impulse response h[n] = u[n] − u[n − 4], and as input the signal x[n] = u[n] − u[n − (N + 1)] for a positive integer N. The output of the system y[n] is calculated using the convolution sum.

(a) If N = 4 what is the length of the output y[n]? Explain. Let N = 4, carefully sketch and label the output y[n] resulting from the convolution sum.

(b) Determine the value of N ≤ 5 for x[n] so that y[3] = 3 and y[6] = 0.

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