Can't prove the convolution theorem of Fourier theorem for two dimensional matrices.
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I multiplied two 2D matrices.A, B
A=[1 2;1 1];
B=[1 2;2 1];
I convolved their respective DFTs of 512*512 samples each by using the code given in https://in.mathworks.com/matlabcentral/answers/1665734-how-to-perform-2-dimensional-circular-convolution?s_tid=srchtitle
I found the IDFT of C_fft2; and applied DFT on C
Acoording to fourier theorem
C_ifft2(1:2,1:2) should be equal to C;
C_fft2 should be equal to C_fft2_cconv2.
But neither are them are same in the results.
Could someone tell how to get it.
Issa on 27 Jul 2022
Please read about discrete convolution ....
Conv, fft and ifft
x = randi(10, 20, 1);
y = randi(20,20,1);
n = length(x)+length(y)-1;
xConvFFt = ifft(fft(x,n).*fft(y,n)) ;
xConv = conv(x,y) ;
isequal(round(conv(x,y), 4), round(xConv, 4))
Conv2, fft2 and ifft2
x = randi(10, 20, 10);
y = randi(20,20,10);
m = length(x)+length(y)-1;
n = length(x) - 1;
xConvFFt2 = ifft2(fft2(x,m, n).*fft2(y,m, n)) ;
xConv2 = conv2(x,y) ;