MATLAB: How to perform 2-D DFT via 1-D DFT

please show me how to do it

Take the 1-D DFT of one image, first row-wise 1-D DFT and followed by column-wise 1-D DFT to create the resulting F1(u,v) .

Best Answer

It actually doesn't matter, but you can do this

 X = randn(8,8);
 Y = fft2(X);
 % ok let's first take the DFT along the rows
 rowdft = fft(X,[],2);
 % now take it along the columns
 coldft = fft(rowdft,[],1);
 max(max(abs(coldft-Y)))

See the maximum difference in absolute value is only on the order of 10^(-15)

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MATLAB: DFT

Hi Lisa, you had a couple problems with your code:

N= 4; 
x=1:4;
for k=0:3
    for n = 0:3;
y(n+1) = x(n+1).*exp(-(1j*2*pi*k*n)/N);
    end
    xdft(k+1)= sum(y);
end

compare to

fft(x)

MATLAB: Unknown line in code

This line:

F=-Fs/2:Fs/Nfft:Fs/2-Fs/Nfft;

defines the frequency vector for a two-sided fft, where 0 Hz is in the centre of the plot. Here, ‘Fs’ is the sampling frequency, undefined in the code you posted (but is probably 1/Ts).

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MATLAB: DFT

MATLAB: Unknown line in code

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