function y = ffttx(x)%FFTTX  Textbook Fast Finite Fourier Transform.%    FFTTX(X) computes the same finite Fourier transform as FFT(X).%    The code uses a recursive divide and conquer algorithm for%    even order and matrix-vector multiplication for odd order.%    If length(X) is m*p where m is odd and p is a power of 2, the%    computational complexity of this approach is O(m^2)*O(p*log2(p)).x = x(:);n = length(x);omega = exp(-2*pi*i/n);if rem(n,2) == 0   % Recursive divide and conquer   k = (0:n/2-1)';   w = omega .^ k;   u = ffttx(x(1:2:n-1));   v = w.*ffttx(x(2:2:n));   y = [u+v; u-v];else   % The Fourier matrix.   j = 0:n-1;   k = j';   F = omega .^ (k*j);   y = F*x;end