Conv2 explanation for specific example

Hey Guys, i need some help for the conv2 implementation for given problem:

K>> conv2([1 2 3], [1 0 0], 'full')

ans =

     1     2     3     0     0

Why are the zeros on the right side? Does varies with the border depending on the kernel-center?

For this example its clear:

K>> conv2([1 2 3], [1 0 1], 'full')

ans =

     1     2     4     2     3

Thanks for your help, Leo

Answer 1

[Jan]

Because you have vectors, your example is equivalent to:

conv([1, 2, 3], [1, 0, 0])

The algorithm of CONV is described exhaustively in: doc conv

E.g. the last element of the result is "w(2*n-1) = u(n)*v(n)", which is 0 in your example. Perhaps your are searchng for the 'same' or 'valid' shapes?

[the cyclist]

I noticed with a bit of amusement that conv() calls conv2().

[Jan]

Indeed?

In Matlab 6.5 it called FILTER after reordering the inputs: CONV(A, B) equals CONV(B, A), but FILTER(B, 1, A) is faster, if length(A) < length(B).

I think I should read through all of the toolbox functions again...

Answer 2

[the cyclist]

Isn't the convolution calculation essentially doing what I have written below? Does that make it clearer where the zeros come from?

a = [1 2 3]
b = [1 0 0]

conv_a_b = b(1)*[a 0 0] + b(2)*[0 a 0] + b(3) * [0 0 a]

Answer 3

[Leo]

thank you for your really quick responses! @Jan: yeah, i read conv2, but there is no information about how MATLAB set the paddings. In my work I have to apply a shift_kernel on a matrix to center the kernel, and the shif-kernel could be a matrix too. @cyclist: not really.. should 'a' replaced by [1 2 3] -> b(1) * [1 2 3 0 0] + ... ?

best, leo

[the cyclist]

In response to what you said to Jan: There is no "padding". MATLAB is treating the trailing zeros in "b" exactly how it would treat them if they were non-zero, and giving you the result.

In response of what you said to me: Yes. What I typed is functional code, using the "a" that you defined.

Answer 4

[Leo]

Hey guys,

thanks for your answers. I had an error in reasoning. I forgot that the kernel should be mirrored.

Best!