In matlab, `w = gausswin(M,alpha)` returns a length
window
with parameter
where
is defined, as in Harris
[101], so that the window shape is invariant with respect to
window length
:

function [w] = gausswin(M,alpha) n = -(M-1)/2 : (M-1)/2; w = exp((-1/2) * (alpha * n/((M-1)/2)) .^ 2)';

An implementation in terms of unnormalized standard deviation
(`sigma` in samples) is as follows:

function [w] = gaussianwin(M,sigma) n= -(M-1)/2 : (M-1)/2; w = exp(-n .* n / (2 * sigma * sigma))';In this case,

Note that, on a dB scale, Gaussians are *quadratic*. This
means that *parabolic interpolation* of a sampled Gaussian
transform is *exact*. This can be a useful fact to remember when
estimating sinusoidal peak frequencies in spectra. For example, one
suggested implication is that, for typical windows, quadratic
interpolation of spectral peaks may be more accurate on a
*log-magnitude scale* (*e.g.*, dB) than on a linear magnitude scale
(this has been observed empirically for a variety of cases).

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