Question about 2-D convolution

[kakolukia786]

Hi, I have been given two data set F = [1 0 0 1; 2 1 0 1; 1 2 1 0; 0 1 0 2] and G = [1 0; 1 2], here separated by (;) means they are different rows. I have been asked to compute the 2-D periodic convolution.
2. Homework Equations

I know how to calculate the 2-D periodic convolution for 2 equal size data set (one from the DFT convolution theorem and the other method is to inverse one of the function and slide it from the left it to the right and top to bottom over the next function and calculate the values (my teacher taught this way, it is easier).

The Attempt at a Solution

For 2 non equal data set, I know I have to pad it with zero, but I couldn't figure it out HOW ? I know how to pad for 1-D convolution, we just put zeros behind data set to make it of equal size to the other one. How do I pad in the case of 2-D, in this case G, Do I just fill in zeros like [1 0 0 0; 1 2 0 0; 0 0 0 0; 0 0 0 0] ? Any help will be appreciated. Thanks

 

[KataKoniK]

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Hi there,

Thank you for reaching out with your question. The process of padding for 2-D periodic convolution is similar to that of 1-D convolution. In this case, you would need to pad both data sets with zeros to make them equal in size. For example, in the case of G, you would pad it with zeros to make it a 4x4 matrix, similar to F.

The padding should be done in a way that maintains the periodicity of the data sets. This means that when you slide one data set over the other, the edges should match up. In your example, you could pad G with zeros in the following way:

[1 0 0 0; 1 2 0 0; 0 0 0 0; 0 0 0 0]

This would ensure that when you slide G over F, the edges will match up and the periodic convolution can be calculated accurately.

I hope this helps. If you have any further questions, please don't hesitate to ask.