The most important matrix in signal processing is the matrix of the discrete Fourier 3. transform. The code dftmtx(n) gives you the DFT matrix of size n in MATLAB.

a) Write a code in MATLAB to find the eigen values and eigenvectors of the DFT of size 8? clearly mention the eigenvalues and the corresponding eigenvectors (written)

b) To compute DFT of a vector x, the command fft(x) gives the same result as dftmtx (multiple by transpose of x) in MATLAB, however it works faster. As you noticed since DFT is a complex matrix, the multiplication of DFT by a vector gives a complex vector. Consider the 8-point signal x=[1, -1, 2, 4, 5, 6, 0, 2].Write a MATLAB code to convert output of fft(x) to a magnitude and phase form. Then plot magnitude and phase in two separate plots.