Problem 3 [15 points] Given
$$x[n] = \{\dots, 12, 9, 6, 3, 6, 9, 12, 9, 6, 3, 6, 9, 12, \dots\},$$
a. [7 points] Compute its discrete-time Fourier series (DTFS) expansion. Hint: $$x[n]$$ has period
= 6, is real and is an even function.
b. [4 points] Compute its average power in the time domain.
c. [4 points] Compute its average power in the frequency domain. By Parseval's theorem,
both should match.
Note: fft in Matlab can be used to check the results, but all work needs to be shown for full credit.
