The Convolution Theorem in 2D

Hello,

I have two images A and B with different size.

I want to show that:

fft2(conv2(A,B))

is equal to

fft2(A).*fft2(B)

but I get different outputs.

what is the problem?

Thanks.

[Paz INBAR]

https://en.wikipedia.org/wiki/Convolution_theorem

This is what I mean.

Answer 1

[Matt J]

The problem is that you need to zero-pad,

A=rand(10); B=rand(10);

szA=size(A);
szB=size(B);
szFull=szA+szB-1;

result1 = fftn(A,szFull).*fftn(B,szFull);

result2= fftn(conv2(A,B,'full'));

difference=norm(result1-result2,'inf')

difference = 1.0735e-12

Answer 2

[Jonas]

i suggest you have a look onto file exchange, there is an example called 2d convolution theorem

https://de.mathworks.com/matlabcentral/fileexchange/60897-2d-convolution-theorem

[Paz INBAR]

Thank you for your answer.

I ran this file but I got different images in R ( I*M ) and in R ( ifft(F X W) ) , according to names of the images in this file.

(which are the both sides of the convolution theoren).

Answer 3

[Sulaymon Eshkabilov]

Note that the sizes of A and B must match. In your inserted image array, sizes of A and B must have differed.