Find using Matlab the $1616$ square discrete Fourier transform $($DFT$)$ matrix for $16-$point input signal vectors. Display the real and imaginary parts of DFT matrix separately. An input signal is defined as

$x(n)=cos({}_{1}n)+cos({}_{2}n)$

where ${}_1=2*\frac{3}{16}$ and ${}_2=2*\frac{5}{16}.$ Find the DFT of $x(n)$ using your DFT matrix by writing a matrix$-$vector product. Plot it$.$ Then find the FFT of $x(n)$ and plot it$.$ Use magntiude plots only.