I have a quesiton regarding correlation (coefficient) and convolution. I know that the convolution of two Gaussian distributions is again a Gaussian distribution. So I have two estimated Gaussian PDFs (one estimated using KDE Parzen Window and one GMM). Now I though to combine both and using a predefined variance. The GMM ones uses a few hundred samples while the KDE one has only a few samples. The GMM one should be replaced by simple sampling / Dirac comb. The KDE one remains the same but with a larger variance.

Is this correct in terms of correlation (I read the following about correlation and convolution: Relation between Correlation and Convolution)? Because I tried it out in Matlab, and corr reported different resolutions if I have two Gaussians correlated and the convolution of these Gaussians correlated with a Dirac comb at the position zero.

At the end, I want to use the correlation coefficient to generate a cost function.

Thank you!



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