Question

FFT code issue

Asked by: montu_12

Hi guys,

I am having hard time to figure out the 8 point FFT algorithm, I am passing thie input array which is currect according to the requirement but my FFT algorithm is not working and not giving me right values

Please check my code and see - what am i doing wrong....

Please Help
Its urgent

x = 0:1:40;
t = 0:1:40;
 
phas1 = 0;
phas2 = (2*pi)*(1/8);
phas3 = (2*pi)*(2/8);
phas4 = (2*pi)*(3/8);    
phas5 = phas4;
 
i(1) = 0;
 
for i= 2:9
    x(i) = x(i - 1) + phas1;
end
 
for i = 10:17 
    x(i) = x(i - 1) + phas2;
end
 
for i = 18:25 
    x(i) = x(i - 1) + phas3;
end
 
for i = 26:33 
    x(i) = x(i - 1) + phas4;
end
 
for i = 34:41 
    x(i) = x(i - 1) + phas5;
end
 
 
for i = 1:41 
    x(i) = cos(x(i));
end
 
 
stem(t, x);
 
s = ones(1,8);
fft(s)
 
% Bit Reversal 
% To do Bit Reversal we need to Flip the array values     
 
temp = x(1);
x(1) = x(8);
x(8) = temp;
 
temp = x(2);
x(2) = x(7);
x(7) = temp;
 
temp = x(3);
x(3) = x(6);
x(6) = temp;
 
temp = x(4);
x(4) = x(5);
x(5) = temp;
 
% Bit Reversal End
 
%%%%%%%% STAGE 1 %%%%%%%%%
 
x(1) = x(1) - x(2);
x(5) = x(2) + x(1);
 
x(3) = x(3) - x(4);
x(7) = x(4) + x(3);
 
x(2) = x(5) - x(6);
x(6) = x(6) + x(5);
 
x(4) = x(7) - x(8);
x(8) = x(8) + x(7);
 
 
%%%%%%%% STAGE 2 %%%%%%%%%
w = -0.707;
 
 
x(1) = x(1) - x(3);
x(5) = x(2) - x(4);
 
x(3) = x(3) + x(1);
x(7) = (x(4)* w) + x(2);
 
x(2) = x(5) - x(7);
x(6) = x(6) - x(8);
 
x(4) = x(7) + x(5);
x(8) = (x(8) * w) + x(6);
 
%%%%%%%% Stage 3 %%%%%%%%
 
x(1) = x(1) - x(5);
x(5) = x(2) - x(6);
 
x(3) = x(3) - x(7);
x(7) = x(4) - x(8);
 
x(2) = x(5) + x(1);
x(6) = (x(6)*w)  + x(2);
 
x(4) = (x(7) * w* w) + x(3);
x(8) = (x(8)* w *w *w) + x(4);
 
 
 
x(1)
x(2)
x(3)
x(4)
x(5)
x(6)
x(7)
x(8)

                                  
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Asked On
2009-05-09 at 17:57:00ID24395379
Topic

MatLab Programming Language

Participating Experts
2
Points
500
Comments
4

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Answers

 

by: yuk99Posted on 2009-05-10 at 16:33:10ID: 24350494

Can you attach any doc describing the algorithm you are implementing? Then I can check it. Also if possible please tell what result do you expect.

Your code is very unvectorized, not Matlab style. For example, to show 1st 8 values of x just use x(1:8).
To flip values you can say x(1:8)=x(8:1);

I would also recommend to add zones: Signal Processing and Math & Science. If you cannot do it yourself ask EE for help.

 

by: KendorPosted on 2010-06-02 at 14:20:55ID: 32903283

ok i looked at your code and i guess you are on the right track. I scanned you the image out of the book when I had to learn all that stuf fin detail and I believe this to be very helful for your task.  Try to follow what you see.

bt as yuk99 mentioned you can do the flip by:
x(1:8) = x(8:-1:1);

I added the checking code - so that you can compare your result with what you want to get out of your dft

% just doing the check:
what_we_want =1/length(x)*fftshift(fft(x)); % use fftshift to have zero frequency in the center
freqscale=-length(x)/2+1/2:length(x)/2-1/2; % we want zero freq to be uin the center 
figure, stem(freqscale,what_we_want); title('it should look like this'); axis tight;

                                              
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by: KendorPosted on 2010-06-02 at 14:30:55ID: 32903347

and if you really can not do it... check the following code which i think is pretty awesome :)

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

                                              
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