How to efficiently update a discrete time FFT?

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James
James 2012-12-12
I have an application that needs to be optimized for speed. It's a realtime app that is required to perform a number of FFTs at relatively fast discrete time interval. The transform inputs are discretely sampled time histories of real time physical processes. Therefore the time history for a given interval is the same as the previous accept it is shifted one position and one end point is lost and one is point is added. I know there must be a straight forward way to implement a faster FFT. Can somebody point me in the right direction?

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Matt J
Matt J 2012-12-12
编辑：Matt J 2012-12-12
If you are doing fft(x), I assume that x(1)=x_old gets deleted and x(N) gets replaced by x_new
%pre-computations, do these only once
c=exp(pi*2i*(0:N-1)/N);
X=fft(x0); %inital FFT
%end of pre-computations
X = (X +(x_new - x_old)).*c; %update the FFT

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