Matérn kernel and squared-exponential one: intuition as a filter with repeated real poles

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 14:35

Summary:

This video presents the relationship of the ‘Matérn’ type kernel with the result of filtering a continuous-time white noise with a filter (spectral factor) of type $F(s)=\frac{A}{{(\tau \cdot s+1)}^m}$. It is verified that the power spectral density and autocovariance (Fourier inverse of the power density) coincide with the Wikipedia formulas based on the Gamma and Bessel functions for said Matérn kernel.

The limiting case (quadratic exponential kernel, Gaussian filter) is also discussed.

The study is done without demonstrations, based only on Matlab plots in time and frequency.

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