Circular vs. linear convolution of 2D data

Question

William Thielicke 2019-8-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/477299-circular-vs-linear-convolution-of-2d-data

评论： William Thielicke 2019-8-27

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

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Answer 1

Devineni Aslesha 2019-8-26

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https://ww2.mathworks.cn/matlabcentral/answers/477299-circular-vs-linear-convolution-of-2d-data#answer_389048

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));