function f=persistent_fft(x)% F = persistent_fft( X )%   Calculates the fft of a column vector x%   results are, theoretically, same as matlab's fft%   but you can expect discrepancies ~ 1e8 in normalized L_2 error.%%   Performs one step of the radix-2 algorithm, then calls matlab's fft%%   Vectorized, and uses persistent variables to save time%   ... but alas, still slower than matlab's fft%%   For the fft of a fixed length, this code runs several orders%   of magnitude faster on *subsequent* calls, due to the persistent%   variables (note: matlab's fft also runs faster on subsequent calls, due%   to learned "wisdom" in the FFTW algorithm)%%   Why you want to use this code over matlab's own fft()?  I do not have%   an answer to that.%%   Stephen Becker, 2/22/2008  srbecker@caltech.edupersistent weights Nn = length(x);if size(x,2) ~= 1 || n < 4 || round( n/2 ) ~= n/2    error('Input must be a column vector of even length >= 4')end% Decide whether to recalculate the weights or not:if isempty(N) || n ~= N     N = n;    w = exp(-2*pi*i / N);    helper = w .^ [1:(N/4-1)].' ;    weights = [1;helper; -i ;flipud( -real(helper)+i*imag(helper) ) ];%     weights = w .^ [0:(N/2-1)].' ;    % same thing, but slowerend% A simple radix-2 DIT:E = fft( x(1:2:N) );O = fft( x(2:2:N) );O = O .* weights;f = [ E + O ; E - O ];