# Documentation

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# gauspuls

Gaussian-modulated sinusoidal pulse

## Syntax

```yi = gauspuls(t,fc,bw) yi = gauspuls(t,fc,bw,bwr) [yi,yq] = gauspuls(...) [yi,yq,ye] = gauspuls(...) tc = gauspuls('cutoff',fc,bw,bwr,tpe) ```

## Description

`gauspuls` generates Gaussian-modulated sinusoidal pulses.

`yi = gauspuls(t,fc,bw)` returns a unity-amplitude Gaussian RF pulse at the times indicated in array `t`, with a center frequency `fc` in hertz and a fractional bandwidth `bw`, which must be greater than 0. The default value for `fc` is 1000 Hz and for `bw` is 0.5.

`yi = gauspuls(t,fc,bw,bwr)` returns a unity-amplitude Gaussian RF pulse with a fractional bandwidth of `bw` as measured at a level of `bwr` dB with respect to the normalized signal peak. The fractional bandwidth reference level `bwr` must be less than 0, because it indicates a reference level less than the peak (unity) envelope amplitude. The default value for `bwr` is -6 dB. Note that the fractional bandwidth is specified in terms of power ratios. This corresponds to the -3 dB point expressed in magnitude ratios.

`[yi,yq] = gauspuls(...)` returns both the in-phase and quadrature pulses.

`[yi,yq,ye] = gauspuls(...)` returns the RF signal envelope.

`tc = gauspuls('cutoff',fc,bw,bwr,tpe)` returns the cutoff time `tc` (greater than or equal to 0) at which the trailing pulse envelope falls below `tpe` dB with respect to the peak envelope amplitude. The trailing pulse envelope level `tpe `must be less than 0, because it indicates a reference level less than the peak (unity) envelope amplitude. The default value for `tpe `is -60 dB.

## Examples

collapse all

Plot a 50 kHz Gaussian RF pulse with 60% bandwidth, sampled at a rate of 1 MHz. Truncate the pulse where the envelope falls 40 dB below the peak.

```tc = gauspuls('cutoff',50e3,0.6,[],-40); t = -tc : 1e-6 : tc; yi = gauspuls(t,50e3,0.6); plot(t,yi)```

## Tips

Default values are substituted for empty or omitted trailing input arguments.