Gaussian FIR pulse-shaping filter design


  • h = gaussdesign(bt,span,sps)



h = gaussdesign(bt,span,sps) designs a lowpass FIR Gaussian pulse-shaping filter and returns a vector, h, of filter coefficients. The filter is truncated to span symbols, and each symbol period contains sps samples. The order of the filter, sps*span, must be even.


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Gaussian Filter for a GSM GMSK Digital Cellular Communication System

Specify that the modulation used to transmit the bits is a Gaussian minimum-shift keying (GMSK) pulse. This pulse has a 3-dB bandwidth equal to 0.3 of the bit rate. Truncate the filter to 4 symbols and represent each symbol with 8 samples.

bt = 0.3;
span = 4;
sps = 8;
h = gaussdesign(bt,span,sps);

Input Arguments

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bt — 3-dB bandwidth-symbol time productpositive real scalar

Product of the 3-dB one-sided bandwidth, in hertz, and the symbol time, in seconds. Specify this value as a positive real scalar. Smaller values of bt produce larger pulse widths.

Data Types: double | single

span — Number of symbols3 (default) | positive integer scalar

Number of symbols, specified as a positive integer scalar.

Data Types: double | single

sps — Samples per symbol2 (default) | positive integer scalar

Number of samples per symbol period (oversampling factor), specified as a positive integer scalar.

Data Types: double | single

Output Arguments

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h — FIR filter coefficientsrow vector

FIR coefficients of the Gaussian pulse-shaping filter, returned as a row vector. The coefficients are normalized so that the nominal passband gain is always 1.

Data Types: double | single


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

[2] 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.

See Also

Introduced in R2013b

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