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# gauspuls() - Signal Processing

```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.```

### 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)`

### Example

```Generate a Gaussian RF PulseOpen This Example
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)```