Matlab question:

(Include code/plots if possible)

Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) The DFT of a sequence x(n) with length N is defined: X[k] = sigma_n = 0^N - 1 x[x] W^kn for each k = 0, 1, ..., N - 1. Where W = e^-j(2 pi/N) The inverse DFT is given by: X[n] = 1/N sigma_n = 0^N - 1 x[k] W^-kn for each n = 0, 1, ..., N - 1. The Fast Fourier transform (FFT) is an efficient algorithm to compute the DFT Use 'fft' function to calculate the Fourier Transform of a sequence, x = [1, 2, 3, 4, 5, 6, 7, 8] Use 'ifft' function to calculate the inverse Fourier Transform of the result you get in (a). Re-do (a) and (b) using your own DFT and inverse DFT functions