Convolution in Matlab

Question

I got the following matrix:

9 18 27 36 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

and core:

-0.5+0.8662i 1 -0.5-0.8662i

I am trying to convolution using a valid mode:

ans = conv2(matrix,kernel,'valid');

Return Matlab:

0.0000+15.5916i 0.0000+15.5916i 0.0000+15.5916i

My question is how can I achieve the same results as matlab. I try to do in matlab in the first paragraph, but the results are different.

 a = matrix(1,1) * kernel(1); a = a + matrix(1,2) * kernel(2); a = a + matrix(1,3) * kernel(3); 

Result: 0-15.5916i

For some reason, the imaginary sign is positive with convolution. Why?

Answer 1

I believe that convolution is usually done by “flipping” the kernel (from left to right, up and down), and then shifting it along the matrix to perform the sum of multiplications.

In other words, what the matrix actually calculates:

 a = matrix(1,1) * kernel(3); a = a + matrix(1,2) * kernel(2); a = a + matrix(1,3) * kernel(1); 

Answer 2

In the process of convolution, the core is upside down. So you have to flip it too on the check; i.e. swap kernel(1) and kernel(3) as shown below:

 >> a = matrix(1,1) * kernel(3); >> a = a + matrix(1,2) * kernel(2); >> a = a + matrix(1,3) * kernel(1) a = 27.0000 +15.5916i 

This corresponds to the result of the convolution:

 >> A = conv2(matrix,kernel,'valid'); >> A(1,1) ans = 27.0000 +15.5916i