# gmonopuls

Gaussian monopulse

## Description

example

y = gmonopuls(t,fc) returns samples of the unit-amplitude Gaussian monopulse with center frequency fc at the times indicated in array t.

example

tc = gmonopuls('cutoff',fc) returns the time duration between the maximum and minimum amplitudes of the pulse.

## Examples

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Consider a Gaussian monopulse with center frequency ${f}_{c}=2$ GHz and sampled at a rate of 100 GHz. Determine the cutoff time ${t}_{c}$ using the 'cutoff' option and compute the monopulse between $-2{t}_{c}$ and $2{t}_{c}$.

fc = 2e9;
fs = 100e9;

tc = gmonopuls('cutoff',fc);
t  = -2*tc:1/fs:2*tc;

y = gmonopuls(t,fc);

The monopulse is defined by the equation

$y\left(t\right)={e}^{1/2}\left(t/\sigma \right)\mathrm{exp}\left(-\left(t/\sigma {\right)}^{2}/2\right),$

where $\sigma ={t}_{c}/2=1/\left(2\pi {f}_{c}\right)$ and the exponential factor is such that $y\left(\sigma \right)=1$. Plot the two curves and verify that they match.

sg = 1/(2*pi*fc);

ys = exp(1/2)*t/sg.*exp(-(t/sg).^2/2);

plot(t,y,t,ys,'.')
legend('gmonopuls','Definition')

Consider a Gaussian monopulse with center frequency ${f}_{c}=2$ GHz and sampled at a rate of 100 GHz. Use the monopulse to construct a pulse train with a spacing of 7.5 ns.

Determine the width ${t}_{c}$ of each pulse using the 'cutoff' option. Set the delay times to be integer multiples of the spacing.

fc = 2e9;
fs = 100e9;

tc = gmonopuls('cutoff',fc);
D = ((0:2)*7.5+2.5)*1e-9;

Generate the pulse train such that the total duration is $150{t}_{c}$. Plot the result.

t  = 0:1/fs:150*tc;
yp = pulstran(t,D,'gmonopuls',fc);

plot(t,yp)

## Input Arguments

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Time values at which the unit-amplitude Gaussian monopulse is calculated, specified as a vector.

Center frequency, specified as a real positive scalar expressed in hertz. By default, fc = 1000 Hz.

## Output Arguments

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Monopulse of unit amplitude, returned as a vector.

Time duration between the maximum and minimum amplitudes of the pulse, returned as a scalar.

## Tips

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