This example generates a pulse train using the default rectangular pulse of unit width. The repetition frequency is 0.5 Hz, the signal length is 60 s, and the sample rate is 1 kHz. The gain factor is a sinusoid of frequency 0.05 Hz.

t = 0:1/1e3:60;
d = [0:2:60;sin(2*pi*0.05*(0:2:60))]';
x = @rectpuls;
y = pulstran(t,d,x);

plot(t,y)
hold off
xlabel('Time (s)')
ylabel('Waveform')

This example generates an asymmetric sawtooth waveform with a repetition frequency of 3 Hz. The sawtooth has width 0.2 s and skew factor –1. The signal length is 1 s, and the sample rate is 1 kHz. Plot the pulse train.

fs = 1e3;
t = 0:1/1e3:1;
d = 0:1/3:1;   
x = tripuls(t,0.2,-1);
y = pulstran(t,d,x,fs);

plot(t,y)
hold off
xlabel('Time (s)')
ylabel('Waveform')

Plot a 10 kHz Gaussian RF pulse with 50% bandwidth, sampled at a rate of 10 MHz. Truncate the pulse where the envelope falls 40 dB below the peak.

fs = 1e7;
tc = gauspuls('cutoff',10e3,0.5,[],-40); 
t = -tc:1/fs:tc; 
x = gauspuls(t,10e3,0.5); 

plot(t,x)
xlabel('Time (s)')
ylabel('Waveform')

The pulse repetition frequency is 1 kHz, the sample rate is 50 kHz, and the pulse train length is 25 ms. The gain factor is a sinusoid of frequency 0.1 Hz.

ts = 0:1/50e3:0.025;
d = [0:1/1e3:0.025;sin(2*pi*0.1*(0:25))]';
y = pulstran(ts,d,x,fs);

Plot the periodic Gaussian pulse train.

plot(ts,y)
xlim([0 0.01])
xlabel('Time (s)')
ylabel('Waveform')

Write a function that generates custom pulses consisting of a sinusoid damped by an exponential. The pulse is an odd function of time. The generating function has a second input argument that specifies a single value for the sinusoid frequency and the damping factor. Display a generated pulse, sampled at 1 kHz for 1 second, with a frequency and damping value, both equal to 30.

fnx = @(x,fn) sin(2*pi*fn*x).*exp(-fn*abs(x));

ffs = 1000;
tp = 0:1/ffs:1;

pp = fnx(tp,30);

plot(tp,pp)
xlabel('Time (s)')
ylabel('Waveform')

Use the pulstran function to generate a train of custom pulses. The train is sampled at 2 kHz for 1.2 seconds. The pulses occur every third of a second and have exponentially decreasing amplitudes.

Initially specify the generated pulse as a prototype. Include the prototype sample rate in the function call. In this case, pulstran replicates the pulses at the specified locations.

fs = 2e3;
t = 0:1/fs:1.2;

d = 0:1/3:1;
dd = [d;4.^-d]';

z = pulstran(t,dd,pp,ffs);

plot(t,z)
xlabel('Time (s)')
ylabel('Waveform')

Generate the pulse train again, but now use the generating function as an input argument. Include the frequency and damping parameter in the function call. In this case, pulstran generates the pulse so that it is centered about zero.

y = pulstran(t,dd,fnx,30);

plot(t,y)
xlabel('Time (s)')
ylabel('Waveform')

Write a function that generates a custom exponentially decaying sawtooth waveform of frequency 0.25 Hz. The generating function has a second input argument that specifies a single value for the sawtooth frequency and the damping factor. Display a generated pulse, sampled at 0.1 kHz for 1 second, with a frequency and damping value equal to 50.

fnx = @(x,fn) sawtooth(2*pi*fn*0.25*x).*exp(-2*fn*x.^2);

fs = 100;
t = 0:1/fs:1;

pp = fnx(t,50);

plot(t,pp)

Use the pulstran function to generate a train of custom pulses. The train is sampled at 0.1 kHz for 125 seconds. The pulses occur every 25 seconds and have exponentially decreasing amplitudes.

Specify the generated pulse as a prototype. Generate three pulse trains using the default linear interpolation method, nearest neighbor interpolation and piecewise cubic interpolation. Compare the pulse trains on a single plot.

d = [0:25:125; exp(-0.015*(0:25:125))]';
ffs = 100;
tp = 0:1/ffs:125;

r = pulstran(tp,d,pp);
y = pulstran(tp,d,pp,'nearest');
q = pulstran(tp,d,pp,'pchip');


plot(tp,r)
hold on
plot(tp,y)
plot(tp,q)
xlim([0 125])
legend('Linear interpolation','Nearest neighbor interpolation','Piecewise cubic interpolation')
hold off