When I study some paper, I have some questions about usase of convolution theorem.
Laplacian = [0 1 0;1 -4 1;0 1 0];
F = padarray(Laplacian,[m-3+1,n-3+1]/2,'pre');
F = padarray(W,[m-3-1,n-3-1]/2,'post');
F : filter
From this, first I want use convolution theorem :
fft2(image).*fft2(F).
But, in the reference, the method is used like :
fft2(image).*fft2(fftshift(F)).
What am I doing wrong? Thanks
For the FFT, the origin is in the top-left corner, not in the middle of the image.
If you create a kernel and pad it such that the origin is in the middle of the image, then compute the FFT, you will have the FFT of a shifted kernel. Applying this will shift your result image too.
You need to use ifftshift, not fftshift, to shift the kernel’s origin to the top-left pixel. fftshift shifts the origin from the top-left back to the middle. The two functions produce the same result on an even-sized image, but not on an odd-sized one.
