gaussdesign

Gaussian FIR pulse-shaping filter design

Syntax

h = gaussdesign(bt,span,sps)

Description

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.

Examples

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);
impz(h)

Input Arguments

bt — 3-dB bandwidth-symbol time product

positive real scalar

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

span — Number of symbols

3 (default) | positive integer scalar

Number of symbols, specified as a positive integer scalar.

sps — Samples per symbol

2 (default) | positive integer scalar

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

Output Arguments

h — FIR filter coefficients

row 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

Algorithms

The impulse response of the Gaussian filter is given by

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

where

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

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.

References

[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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2013b