Consider the periodic discrete-time exponential time signal x[n] = eim(27TIN)n. Show

Chapter 1, Problem 1.35

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Consider the periodic discrete-time exponential time signal x[n] = eim(27TIN)n. Show that the fundamental period of this signal is No = Nlgcd(m, N), where gcd(m, N) is the greatest common divisor of m and N-that is, the largest integer that divides both m and Nan integral number of times. For example, gcd(2, 3) = 1, gcd(2, 4) = 2, gcd(8, 12) = 4. Note that No = N if m and N have no factors in common.

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