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
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.
sRect = phased.RectangularWaveform('SampleRate',1e6,... 'PulseWidth',50e-6,'PRF',10e3);
Plot a single rectangular pulse by calling
plot directly on the rectangular waveform variable.
plot is a method of
phased.RectangularWaveform. This method produces an annotated graph of your pulse waveform.
Find the bandwidth of the rectangular pulse.
bw = bandwidth(sRect)
bw = 20000
bw, of a rectangular pulse in hertz is approximately the reciprocal of the pulse duration
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.
sRect = 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.
sRect1 = clone(sRect); sRect.PulseWidth = 10e-6;
sRect1 now specify different rectangular pulses because you changed the pulse width of
step method to return two pulses of your rectangular pulse waveforms.
y = step(sRect); y1 = step(sRect1);
Plot the real part of the waveforms.
totaldur = 2*1/sRect.PRF; totnumsamp = totaldur*sRect.SampleRate; t = unigrid(0,1/sRect.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)