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Gaussian window

`w = gausswin(N)`

w = gausswin(N,Alpha)

`w = gausswin(N)`

returns an `N`

-point
Gaussian window in a column vector, `w`

. `N`

is
a positive integer.

`w = gausswin(N,Alpha)`

returns
an `N`

-point Gaussian window with `Alpha`

proportional
to the reciprocal of the standard deviation. The width of the window
is inversely related to the value of *α*. A
larger value of *α* produces a narrower window.
The value of *α* defaults to 2.5.

If the window appears to be clipped, increase `N`

,
the number of points.

The coefficients of a Gaussian window are computed from the following equation:

$$w(n)={e}^{-\frac{1}{2}{\left(\alpha \frac{n}{(N-1)/2}\right)}^{2}}={e}^{-{n}^{2}/2{\sigma}^{2}},$$

where –(*N* – 1)/2 ≤ *n* ≤ (*N* – 1)/2 and *α* is inversely proportional
to the standard deviation, *σ*, of a Gaussian
random variable. The exact correspondence with the standard deviation
of a Gaussian probability density function is *σ* = (*N* – 1)/(2*α*).

[1] Harris, Fredric J. “On the Use
of Windows for Harmonic Analysis with the Discrete Fourier Transform.” *Proceedings
of the IEEE ^{®}*. Vol. 66, January 1978, pp. 51–83.

[2] Roberts, Richard A., and C. T. Mullis. *Digital
Signal Processing*. Reading, MA: Addison-Wesley, 1987,
pp. 135–136.