If g [n] = 15 cos (?2?n/12) and h [n] = 15 cos (2?Kn) what are the two smallest positive values of K for which g [n] = h [n] for all n?

What will be an ideal response?


Answers: 11/12 and 1/12
Solution:
g[n] = 15cos(2?n/12) because it is an even function. Therefore K = 1/12 works. Since this is a discrete-time function adding 1 to or subtracting 1 from the fundamental discrete-time frequency does not change the function values. The fundamental frequency is 1/12. Therefore changing the frequency to 13/12 would yield the same function values. But changing it to -11/12 would also yield the same values and, because the function is even, 11/12 also works.

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