gaussdesign

Gaussian FIR pulse-shaping filter design

Syntax

``h = gaussdesign(bt,span,sps)``

Description

example

````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

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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

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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.

Number of symbols, specified as a positive integer scalar.

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

Output Arguments

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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

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

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: $span×sps+1.$

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.

Version History

Introduced in R2013b