### Matlab for the Gaussian Window

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,

`sigma`would normally be specified as a fraction of the window length (

`sigma = M/8`in the sample below). 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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Gaussian Window and Transform

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Dolph-Chebyshev Window Theory