Need FFT Code for Matlab (not built in)

Does anyone have FFT code for Matlab? I don't want to use the built-in Matlab function.

[Walter Roberson]

You want the analytic form ?

[John]

I want the radix 2 decimation in time code in Matlab to compare.

[Walter Roberson]

radix 2 decimination is a DFT technique.

[John]

Okay I am looking for the O(n log n) algorithm for DFT then =)

[Yasin Arafat Shuva]

clear variables
close all
%%Implementing the DFT in matrix notation
xn = [0 2 4 6 8];        % sequence of x(n)
N = length(xn);        % The fundamental period of the DFT
n = 0:1:N-1;           % row vector for n
k = 0:1:N-1;           % row vecor for k
WN = exp(-1i*2*pi/N);  % Wn factor 
nk = n'*k;             % creates a N by N matrix of nk values
WNnk = WN .^ nk;       % DFT matrix
Xk = xn * WNnk;        % row vector for DFT coefficients
disp('The DFT of x(n) is Xk = ');
disp(Xk)
magXk = abs(Xk);       % The magnitude of the DFT
%%Implementing the inverse DFT (IDFT) in matrix notation
n = 0:1:N-1;           
k = 0:1:N-1;           
WN = exp(-1i*2*pi/N);  
nk = n'*k;             
WNnk = WN .^ (-nk);    % IDFS matrix
x_hat = (Xk * WNnk)/N; % row vector for IDFS values
disp('and the IDFT of x(n) is x_hat(n) = ');
disp(real(x_hat))
% The input sequence, x(n)
subplot(3,1,1); 
stem(k,xn,'linewidth',2); 
xlabel('n'); 
ylabel('x(n)')
title('plot of the sequence x(n)')
grid
% The DFT
subplot(3,1,2); 
stem(k,magXk,'linewidth',2,'color','r'); 
xlabel('k'); 
ylabel('Xk(k)')
title('DFT, Xk')
grid
% The IDFT
subplot(3,1,3); 
stem(k,real(x_hat),'linewidth',2,'color','m'); 
xlabel('n'); 
ylabel('x(n)')
title('Plot of the inverse DFT, x_{hat}(n) = x(n)')
grid

Answer 1

[Youssef Khmou]

hi John

Yes there are many versions of Discrete Fourier Transform :

 % function z=Fast_Fourier_Transform(x,nfft)
%
% N=length(x);
% z=zeros(1,nfft);
% Sum=0;
% for k=1:nfft
%     for jj=1:N
%         Sum=Sum+x(jj)*exp(-2*pi*j*(jj-1)*(k-1)/nfft);
%     end
% z(k)=Sum;
% Sum=0;% Reset
% end
% return

this is a part of the code , try my submission it contains more details :

http://www.mathworks.com/matlabcentral/fileexchange/40002-psd-power-spectral-density-and-amplitude-spectrum-with-adjusted-fft

[John]

That's the DFT, not the FFT

[Youssef Khmou]

FFT is finite Fourier transform, its fast when the length of vector on which is evaluated is ~ to 2^N where N is an integer .

what about this :

 % function z=Fast_Fourier_Transform(x)
%
% N=length(x);
% nfft=2^ceil(log2(N));
% z=zeros(1,nfft);
% Sum=0;
% for k=1:nfft
%     for jj=1:N
%         Sum=Sum+x(jj)*exp(-2*pi*j*(jj-1)*(k-1)/nfft);
%     end
% z(k)=Sum;
% Sum=0;% Reset
% end
% return

but keep in mind that its not fast at all for vectors> 1000 points, built-in fft is very fast.

[Abdullah Khan]

This is also DFT

The complexity of the code is still N x N

because

    % nfft=2^ceil(log2(N)) = nfft (on upper DTFT code )

or

     % 2^ceil(log2(N))= N

[Walter Roberson]

"FFT" stands for "Fast Fourier Transform", which is a particular algorithm to make Discrete Fourier Transform (DFT) more efficient.

Answer 2

[Tobias]

For anyone searching an educating matlab implementation, here is what I scribbled together just now:

function X = myFFT(x)

%only works if N = 2^k

N = numel(x);
xp = x(1:2:end);
xpp = x(2:2:end);
if N>=8
    Xp = myFFT(xp);
    Xpp = myFFT(xpp);
    X = zeros(N,1);
    Wn = exp(-1i*2*pi*((0:N/2-1)')/N);
    tmp = Wn .* Xpp;
    X = [(Xp + tmp);(Xp -tmp)];
else
    switch N
        case 2
            X = [1 1;1 -1]*x;
        case 4
            X = [1 0 1 0; 0 1 0 -1i; 1 0 -1 0;0 1 0 1i]*[1 0 1 0;1 0 -1 0;0 1 0 1;0 1 0 -1]*x;
        otherwise
            error('N not correct.');
    end
end

end

[Alireza Salehi]

hello, Thanks for this code could you please explain how can i use this function? and explain this more for understanding? thanx a lot

[Apostolescu Stefan]

Hello, I'm trying to understand what you have done there. Why is X equal to (Xp-tmp)? For Xp+tmp I understood, it's basically DFT, but why Xp-tmp?

[Siddhant Sharma]

can anyone explain X equal to (Xp-tmp)?

[Marco Marcon]

The total length of the final X will be N.

The first values will be given by + (remember that , and have length elements and both , are periodic of ); it can be written as for , where .

While the last values will be given by for .

Since we can get the second part of X(last values) as:

that is the reason for adding tmp in the first vector part and subtracting it in the second part.

For more details: Wikipedia: Cooley-Tukey algorithm

Answer 3

[Jan Afridi]

I think I can answer your question. Check the given link may be it will help you. And if you found any error then please inform me... check the link Matlab code for Radix 2 fft

[Jan Suchánek]

Hello i would like to ask you what had to be different if you would like to use it for harmonical function.

I tried to implement your solution but it was working only for random vectors but not for any type of harmonical.

i was using this for the harmonical function.

______________________

t2=0:1:255;

h1=sin(t2);

x=h1;

X11 = myFFT(x);

______________________

it gave me this error:

Error using *

Inner matrix dimensions must agree.

Error in myFFT (line 18)

X = [1 0 1 0; 0 1 0 -1i; 1 0 -1 0;0 1 0 1i]*[1 0 1 0;1

0 -1 0;0 1 0 1;0 1 0 -1]*x;

Error in myFFT (line 7)

Xp = myFFT(xp);

Error in myFFT (line 7)

Xp = myFFT(xp);

Error in myFFT (line 7)

Xp = myFFT(xp);

Error in myFFT (line 7)

Xp = myFFT(xp);

Error in myFFT (line 7)

Xp = myFFT(xp);

Error in myFFT (line 7)

Xp = myFFT(xp);

Error in ZBS_projekt (line 246)

X11 = myFFT(x);

Answer 4

[Ryan Black]

Function I wrote that optimizes the DFT or iDFT for BOTH prime and composite signals...

https://www.mathworks.com/matlabcentral/fileexchange/70563-rader-s-mixed-radix-fft

The forward transform is triggered by -1 and takes the time-signal as a row vector:

[Y] = fftmodule(y,-1)

The inverse transform auto-normalizes by N, is triggered by 1 and takes the frequency-signal as a row vector:

[y] = fftmodule(Y,1)

Methodology:

The algorithm decimates to N's prime factorization following the branches and nodes of a factor tree. In formal literature this may be referred to as Mixed Radix FFT, but its really just recursive decimation of additive groups and this method is easily derivable via circular convolutions :)

At the prime tree level, algorithm either performs a naive DFT or if needed performs a single Rader's Algorithm Decomposition to (M-1), zero-pads to power-of-2, then proceeds to Rader's Convolution routine (not easy to derive). Finally it upsamples through the origianlly strucutured nodes and branches incorporating twiddle factors for the solution.