Define the following function of time:

$$a(t)=\{\begin{array}{ll}1\hfill & 0\le t\le \tau \hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$$

Assume that a radar transmits a signal of the form:

$$x(t)=a(t)\mathrm{sin}({\omega}_{c}t)$$

where ω_{c} denotes the
carrier frequency. Note that *a(t)* represents an
on-off rectangular amplitude modulation of the carrier frequency.
After demodulation, the complex envelope of *x(t)* is
the real-valued rectangular pulse *a(t)* of duration
τ seconds.

To create a rectangular pulse waveform, use `phased.RectangularWaveform`

.
You can customize certain characteristics of the waveform, including:

Sampling rate

Pulse duration

Pulse repetition frequency

Number of samples or pulses in each vector that represents the waveform

This example shows how to create a rectangular
pulse waveform variable using `phased.RectangularWaveform`

.
The example also plots the pulse and finds the bandwidth of the pulse.

Construct a rectangular pulse waveform with a duration of 50 μs, a sample rate of 1 MHz, and a pulse repetition frequency (PRF) of 10 kHz.

hrect = phased.RectangularWaveform('SampleRate',1e6,... 'PulseWidth',5e-5,'PRF',1e4);

Plot a single rectangular pulse by calling `plot`

directly
on the rectangular waveform variable.

figure; plot(hrect)

`plot`

is a method of `phased.RectangularWaveform`

.
This `plot`

method produces an annotated graph of
your pulse waveform.

Find the bandwidth of the rectangular pulse.

bw = bandwidth(hrect);

The bandwidth of a rectangular pulse in hertz is approximately
the reciprocal of that pulse's duration. That is, `bw`

is
approximately `1/hrect.PulseWidth`

.

This example shows how to create rectangular pulse waveform signals having different durations. The example plots two pulses of each waveform.

Create a rectangular pulse with a duration of 100 μs and a PRF of 1 kHz. Set the number of pulses in the output equal to two.

hrect = phased.RectangularWaveform('PulseWidth',100e-6,... 'PRF',1e3,'OutputFormat','Pulses','NumPulses',2);

Make a copy of your rectangular pulse and change the pulse width in your original waveform to 10 μs.

hrect1 = clone(hrect); hrect.PulseWidth = 10e-6;

`hrect1`

and `hrect`

now specify
different rectangular pulses because you changed the pulse width of `hrect`

.

Use the `step`

method to return two pulses
of your rectangular pulse waveforms.

y = step(hrect); y1 = step(hrect1);

Plot the real part of the waveforms.

totaldur = 2*1/hrect.PRF; totnumsamp = totaldur*hrect.SampleRate; t = unigrid(0,1/hrect.SampleRate,totaldur,'[)'); subplot(2,1,1) plot(t.*1000,real(y)); axis([0 totaldur*1e3 0 1.5]); title('Two 10-\musec duration pulses (PRF = 1 kHz)'); set(gca,'XTick',0:0.2:totaldur*1e3) subplot(2,1,2); plot(t.*1000,real(y1)); axis([0 totaldur*1e3 0 1.5]); xlabel('Milliseconds'); title('Two 100-\musec duration pulses (PRF = 1 kHz)'); set(gca,'XTick',0:0.2:totaldur*1e3)

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