MATLAB: Fft witout using fft function

fft

how can we write program for fft without using fft function

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Assuming you mean DFT with uniformly sampled time and frequency and not F(ast)FT, convert the summation in the documentation into a matrix multiplication.

help dftmtx type dftmtx doc dftmtx (someone was smoking something when they wrote this)

Hope this helps.

Greg

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MATLAB: Fft

I think that is covered in just about any textbook. The DFT is computationally intensive to implement as a matrix-vector multiplication.

The NxN DFT matrix times a Nx1 signal vector involves N^2 multiplications and N additions.

By exploiting certain symmetries the fft() reduces that significantly.

If you just read the wikipedia page, you'll find references:

http://en.wikipedia.org/wiki/Fast_Fourier_transform

MATLAB: Fft

%Your data 2xN
t=1:0.001:10;
data=[t;sin(2*pi*50*t)+2*randn(size(t))];
%notice the sin+noise, noise added just for fun
Ts = data(1,2)-data(1,1);     % Sample time
Fs = 1/Ts;                    % Sampling frequency
L = numel(t);                 % Length of signal
y = data(2,:);                % data from signal 
plot(Fs*t(1:50),y(1:50))
title('Signal Corrupted with Zero-Mean Random Noise')
xlabel('time (milliseconds)')
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);
figure %create another figure for the other plot
% Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2+1))) 
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')

Reference: Fast Fourier transform

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MATLAB: Fft

MATLAB: Fft

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