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I am doing a project where I have to use the fourier domain for convolution. I have been reading Digital Image processing by Rafael Gonzalez but I unsure about one thing, and I could not find anything in the book or online to answer my questions

The book states, in order to preserve a filter's odd symmetry you would place the filter in the center of a padded array before doing the fourier transform. If for example a filter is of size 4x4, which has a center defined at (1,1) which does not exhibit any symmetry (or can't in this manner), and I have an image of size 31x31, so the Padded Array size would be 34x34 for the image and filter. Do I still need to place the filter in the center of the padded array before doing the fourier transform to get the same results as convolving in the spatial domain?

In addition to, do I need to place the image in the center of the padded array, or is the padding there just to get rid of any wrap around error?

Thanks

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  • $\begingroup$ The padding is to get rid of circular convolution effects (probably what you are calling "wrap around error"). If you don't center the image and the filter, then the resulting image may end up shifted or offset $\endgroup$ – hotpaw2 Jul 18 '15 at 5:13
  • $\begingroup$ I tried centering the image and filter but the results are not the same as when I convolve spatially $\endgroup$ – DSP_Student Jul 18 '15 at 22:16

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