Gaussian window

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

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

where
–(*L* – 1)/2 ≤ *n* ≤ (*L* – 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* = (*L* – 1)/(2*α*).

[1] Hansen, Eric W. *Fourier
Transforms: Principles and Applications*. New York: John Wiley & Sons,
2014.

[2] Oppenheim, Alan V., Ronald W.
Schafer, and John R. Buck. *Discrete-Time Signal Processing*. Upper
Saddle River, NJ: Prentice Hall, 1999.