Consider a system defined by (a) Suppose that the input x[n] is nonzero only for 0 ≤ n ≤ N...

Consider a system defined by

(a) Suppose that the input x[n] is nonzero only for 0 ≤ n ≤ N − 1. Show that y[n] is nonzero at most over a finite interval of the form 0 ≤ n ≤ P − 1, which is the support of y[n]. Determine P in terms of the filter order M and the input signal length N.

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(b) Suppose that the input x[n] is nonzero only for N1 ≤ n ≤ N2. What is the length of x[n]? Show that y[n] is nonzero at most over a finite interval of the form N3 ≤ n ≤ N4, which is the support of y[n]. Determine N3 and N4 and also the length of y[n] in terms of N1, N2, and M. Hint: Draw a sketch similar to Fig. 5-4 on p. 153.