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Should the discrete 2D convolution from MATLAB be multiplied with twice the nodal step size ?

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I am right now trying to verify the usage of "conv2" function in MATLAB to calculate two-dimensional convolution. My application area is not related to image processing or machine learning.
I set up a small test case where I have convolved two 2D Gaussian functions of different magnitudes. The convolution should be a Gaussian and it is what MATLAB generates.
I have discretized the nodal spacing with a value of "delta" in X and Y directions. Am I correct when I say that the final output of "conv2" should always be multiplied by "delta * delta" ? I am understanding this in terms of Riemann integral where the integration is calculated from first principles. Not sure if this is the correct way to think.
My test case's results are matching with the symbolic result from MATHEMATICA but, after the output of "conv2" is multiplied by "delta*delta".

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Matt J
Matt J 2024 年 5 月 10 日
Yes, that is correct.

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