Gaussian FIR pulse-shaping filter
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.
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');
 Rappaport T.S., Wireless Communications Principles and Practice, 2nd Edition, Prentice Hall, 2001.
 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.