Convolution (Matrix Multiplication)

How I want to mutliply one matrix in such way that, For eg,

Given a 5x5 Matrix,

And another 3x3 Matrix,

Mutiply this 3x3 Matrix with 5x5 Matrix such that our resultant matrix look as

Resultant Matrix :

Such That Value of a1 = 31(-1) + 41(-1) + 61(-1) + 71(0) + 41(0) + 71(0) + 71(1) + 61(1) + 41(1) = 40

Value of a2 = 41(-1) + 61(-1) + 71(-1) + 41(0) + 71(0) + 81(0) + 61(1) + 41(1) + 91(1) = 20

Value of a3 = 61(-1) + 71(-1) + 41(-1) + 71(0) + 81(0) + 41(0) + 41(1) + 91(1) + 31(1) = -10

Value of b1 = 71(-1) + 41(-1) + 71(-1) + 71(0) + 61(0) + 41(0) + 31(1) + 31(1) + 51(1) = -70

Similarily we can find all elements of Resultant Matrix

So, Our Resultant Matrix is:

Please help with MATLAB Code of a general case that is valid for all dimensions of both the Matrix.

For e.g., If our given matrix is of 5x5, and our multiplying matrix is of 4x4, then our resultant would become 2x2

Another example, If our given matrix is 6x6, and our multiplying matrix is of 3x3, then our resultant would become 4x4.

Answer 1

[David Hill]

newMatrix=-conv2(a,b,'valid');

Answer 2

[Image Analyst]

Try conv2()

output = conv2(m1, m2, 'valid');

Your demo is either showing correlation (not convolution) or else it's showing you happens after the kernel is already flipped. If you're not getting what you want then try imfilter()

output = imfilter(m1, m2, 'valid');

or try to flip the kernel

output  conv2(m1, flipud(fliplr(m2)), 'valid');