Let x[n] be an even signal, and  y[n] an odd signal.

(a) Determine whether the Fourier coefficients X_k and Y_k corresponding to x[n] and y[n] are complex, real, or imaginary.

(b) Consider x[n] = cos(2πn/N) and y[n] = sin(2πn/N) for N = 3 and N = 4, use the above results to find the Fourier series coefficients for the two signals with the different periods.

(c) Use MATLAB to find the Fourier series coefficients of the above two  signals with the different periods, and plot their real and imaginary parts. Use 10 periods to compute the Fourier series coefficients  using the fft function. Comment on the results.