Circular vs. linear convolution of 2D data

Hi, there is an example for 1D data and circular vs linear convolution here: https://de.mathworks.com/help/signal/ug/linear-and-circular-convolution.html

If I want to do this with 2D data, how do I zero-pad my data? I mean in which side of the matrix do I add zeros? Everywhere? Thank you! William

Answer 1

[Devineni Aslesha]

Hi William,

In order to zero-pad a 2D data i.e. matrix, padding should be in such a way that the row length is equal to r1+r2-1 and column length is equal to c1+c2-1 where r1 and r2 are the number of rows and c1 and c2 are the number of columns of the 1st and 2nd matrices respectively.

Use the below code for reference.

rng default; 
x = rand(2); 
y = rand(3); 
c = conv2(x,y); 
xpad = [x zeros(size(x,1),size(y,2)-1); zeros(size(y,1)-1,size(x,2)+size(y,2)-1)]; 
ypad = [y zeros(size(y,1),size(x,2)-1); zeros(size(x,1)-1,size(y,2)+size(x,2)-1)]; 
c1 = ifft2(fft2(xpad).*fft2(ypad));

[William Thielicke]

Thank you very much!