A The Impulse Response Hn Of Linear Time Invariant System

(a) The impulse response h[n] of a linear time-invariant system is known to be zero, except in the interval N0 ≤ n ≤ N1. The input x[n] is known to be zero, except in the interval N2 ≤ n ≤ N3. As a result, the output is constrained to be zero, except in some interval N4 ≤ n ≤ N5. Determine N4 and N5 in terms of N0, N1, N2, and N3.

(b) If x[n] is zero, except for N consecutive points, and h[n] is zero, except for M consecutive points, what is the maximum number of consecutive points for which y[n] can be nonzero?

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