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# gaussfir

Gaussian FIR pulse-shaping filter

## Syntax

h=gaussfir(bt)
h=gaussfir(bt,n)
h=gaussfir(bt,n,o)

## Description

 Note:   The use of gaussfir is not recommended. Use gaussdesign instead.

This filter is used primarily in Gaussian minimum shift keying (GMSK) communications applications.

h = gaussfir(bt) designs a low pass FIR Gaussian pulse-shaping filter and returns the filter coefficients in the h vector. bt is the 3-dB bandwidth-symbol time product where b is the one-sided bandwidth in hertz and t is in seconds. Smaller bt products produce larger pulse widths. The number of symbol periods (n) defaults to 3 and the oversampling factor (o) defaults to 2.

The length of the impulse response of the filter is given by 2*o*n+1. The coefficients h are normalized so that the nominal passband gain is always equal to 1.

h = gaussfir(bt,n) uses n number of symbol periods between the start of the filter impulse response and its peak.

h = gaussfir(bt,n,o) uses an oversampling factor of o, which is the number of samples per symbol.

## Examples

Design a Gaussian filter to be used in a Global System for Mobile (GSM) communications GMSK scheme.

```bt = .3;          % 3-dB bandwidth-symbol time
o = 8;            % Oversampling factor
n = 2;            % 2 symbol periods to the filters peak
h = gaussfir(bt,n,o);
hfvt = fvtool(h,'impulse');
```

## References

[1] Rappaport T.S., Wireless Communications Principles and Practice, 2nd Edition, Prentice Hall, 2001.

[2] Krishnapura N., Pavan S., Mathiazhagan C., Ramamurthi B., "A Baseband Pulse Shaping Filter for Gaussian Minimum Shift Keying," Proceedings of the 1998 IEEE® International Symposium on Circuits and Systems, 1998.

## See Also

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