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Define the following function of time:
Assume that a radar transmits a signal of the form:
where ωc 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:
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.
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)