Exercise 1. Use the function fft to compute the DTFS coefficients of the periodic signal x[n] with fundamental period N-32, which is given by x[n]={0, otherwise. a. Plot the real and imaginary parts of DTFS coefficients respectively, b. The Matlab function ifft is an efficient realization of the DTFS synthesis equation. For example, x[n] can be recovered by the command >x-Niffit (a) Use ifft to synthesize x[n] from the DTFS coefficients obtained in Question 1, plot the real and imaginary part of the signal xIn]. Explain the plots. 2. Compute the DTFS XIk] and then reconstruct the signal with ift of signal: Repeat preview for the signal x[n]s cos (pi"n/30)+2*sin(pi*n/90) Find the DTFS coefficient of the following signals: One period of the signal x[n] =n 0x-Niffit (a) Use ifft to synthesize x[n] from the DTFS coefficients obtained in Question 1, plot the real and imaginary part of the signal xIn]. Explain the plots. 2. Compute the DTFS XIk] and then reconstruct the signal with ift of signal: Repeat preview for the signal x[n]s cos (pi"n/30)+2*sin(pi*n/90) Find the DTFS coefficient of the following signals: One period of the signal x[n] =n 0