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Gaussian FIR pulse-shaping filter design

The impulse response of the Gaussian filter is given by

$$h(t)=\frac{\mathrm{exp}\left(\frac{-{t}^{2}}{2{\delta}^{2}}\right)}{\sqrt{2\pi}\cdot \delta}$$

where

$$\delta =\frac{\sqrt{\mathrm{log}2}}{2\pi BT}.$$

*BT* is the bandwidth-symbol time product specified in
`bt`

, where *B* is the 3-dB bandwidth of the
filter and *T* is the symbol time. The number of symbols between the
start and end of the impulse (`span`

) and the number of samples per
symbol (`sps`

) determine the length of the impulse response: $$span\times sps+1.$$

For more information, see FIR Gaussian Pulse-Shaping Filter Design.

[1] Krishnapura, N., S. Pavan, C.
Mathiazhagan, and B. Ramamurthi. “A baseband pulse shaping filter for Gaussian
minimum shift keying.” *Proceedings of the 1998 IEEE International
Symposium on Circuits and Systems*. Vol. 1, 1998, pp.
249–252.

[2] Rappaport, Theodore S. *Wireless Communications:
Principles and Practice.* 2nd Ed. Upper Saddle River, NJ:
Prentice Hall, 2002.