Hello. In a software application I am attempting to smooth a data set by convoluting it with a discrete Gaussian kernel. Based upon information garnered online, I've been using this Mathematica command to generate the kernel:(adsbygoogle = window.adsbygoogle || []).push({});

kern = Table[Exp[-k^2/100]/Sqrt[2. Pi], {k, -range, range}];

where range is a user-specified parameter. For non-Mathematica speakers, my kernel is:

[tex]

\dfrac{e^{-k^2/100}}{\sqrt{2 \pi}}

\qquad

\forall \; k \; \in \{-\text{range}, \text{range}\}; k \in \mathbb{Z}

[/tex]

What is the correct relation of the parameter "range" in this kernel to the standard deviation of a continuous Gaussian function? I'm aware that a large range correlates to a larger standard deviation Gaussian over which the data is sampled, but I would like to know the precise relation. I can't seem to figure it out because the Gaussian and the discrete kernel seem to have slightly different forms.

Application: I have spectroscopic data, and I have been finding that certain "range" values yield the best-fit smoothing. I am curious whether this is related to the standard deviations of the continuous Gaussian functions that comprise the spectra that I am smoothing.

Thanks very much.

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# Interpretation of Gaussian Kernel

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