Write and test an implementation of the direct DFT matrix-vector multiplication based on Matlabs polyval function instead of explicitly building the matrix Fn as in dft_direct.m

dft_direct.m:

function x = dft_direct(x)

n = length(x);

z = exp(complex(0,-1)*2*pi*(0:n-1)/n);

F = vander(z); % the columns of the Vandermonde matrix are inverted compared to Fn

x = F*x(end:-1:1);