pulse train with gaussian pulses in an irregular interval

Hello, I would like to generate a pulse train using Gaussian pulses where the time interval between each pulse is a random variable vector, say X. I know how to do the fixed time interval using pulstran.m and after specifying the prototype pulse using gauspuls.m. However, the irregular seems to be not that straightforward. Any help will be appreciated.

Answer 1

[Mathieu NOE]

hello

a quick and dirty demo , not using gauspuls but that could be easily done also

clc
clearvars

f0 = 50; % pulse frequency
Var_Sq = 1; % pulse variance (squared)

Fs = 20*f0;
dt = 1/Fs;
samples = Fs;
t = dt*(0:samples-1)';
t_mid = max(t)/2;

signal_all = [];

N = 25; % number of pulses generated 

offset = 1.75*t_mid*(rand(N,1)-0.5); % random delay (spanned to the 75% of the max t value)

for ci =1:N
    signal2 = exp(-(((t-t_mid-offset(ci)).^2).*((f0)^2))./(Var_Sq));
    signal_all = [signal_all;signal2];
    
    figure(1), % just to show the individual gaussian pulses with different time offsets 
    hold on 
    plot(t,signal2);

end
% now all samples are concatenated to make one signal with random delta t
% between pulses
figure(2),
plot(signal_all)
    

[Ioannis Matthaiou]

neat solution, thanks!

[Mathieu NOE]

my pleasure !

Answer 2

[Paul]

Can't the d input to pulstran be set to whatever offsets you want, random or otherwise? Taking the example from the pulstran docpage

fnx = @(x,fn) sin(2*pi*fn*x).*exp(-fn*abs(x));
ffs = 1000;
tp = 0:1/ffs:1;
pp = fnx(tp,30);
fs = 2e3;
t = 0:1/fs:1.2;
d = sort(rand(1,4))   % random offsets

d = 1×4

0.0035 0.5865 0.6244 0.9692

z = pulstran(t,d,pp,ffs);
plot(t,z)
xlabel('Time (s)')
ylabel('Waveform')

[Ioannis Matthaiou]

Thanks for that. It looks like the pulses you produced, using the pulstran function and the random offset, vary in magnitude too.

[Paul]

That's just the effect of how the pulses interact with each other when one pulse starts before the previous one damps out. We can see from the first pulse that the fundamental pulse takes about 0.2 seconds to damp out. But the leading edge of pulses 2 and 3 are only about 0.04 seconds part, so they will interefere with each other, either constructively or destructively as the case may be. Think of the limiting case where two pulses start at the exact same time. The fourth pulse is spearated enough in time such that it looks just like the first.

[Ioannis Matthaiou]

Thanks for clarifying that.