Discrete Fourier series (DTFS) for periodic sequence with period N.

Problem 3: (30 points) Recall that the discrete Fourier series (DTFS) for a periodic sequence (with period N) can be expressed as N-I 2(n) = N where DTFS coefficients are N-1 a) Write a MATLAB code that automatically generates c coefficients for any arbitrary periodic sequence r(n) with period N. b) Use your code in part (a) to find the DTFS representation of the periodic sequence rn) e) Write a MATLAB code that automatically implements inverse DTFS (synthesis equation), given coefficients c and period N