Symmetric shifted gaussian pulse

Question

Consider this short code:

fc=2e9;
fs = 100e9;
for n=1:2
  tc = gmonopuls('cutoff',fc);
  t{n}  = -2*tc:1/fs:2*tc;
  y{n} = gmonopuls(t{n}+n*5e-11,fc);
  fc=fc+5e3;
end
plot(t{1},y{1},'r',t{2},y{2},'k')

It generates a two Gaussian mono-pulses shifted by a slight amount:

My problem is this: How do I make this symmetric? Note how the tails match up...they are zero for both the red and black pulse. I am new to the signal processing toolbox in matlab and want to modify the code below to have matched heads too.

SleuthEye SleuthEye · Accepted Answer · 2018-04-17T02:12:48

gmonopuls computes a Gaussian pulse which is centered at 0:

t = -2*tc:1/fs:2*tc;
y = gmonopuls(t,fc);
plot(t, y, 'k');

Evaluating this function at different time instants does not change the fundamental shape of the curve. It would only change which part of the curve you are sampling:

K = 2*tc;
for n=1:3
  t{n} = -2*tc:1/fs:2*tc + (n-2)*K;
  y{n} = gmonopuls(t{n},fc);
end
plot(t{1},y{1},'rx', t{2},y{2},'k', t{3},y{3},'bs');
legend('t-K','t','t+K');

To obtain a curve shifted along the time axis you simply need to add a time offset after you have computed your function:

for n=1:2
  tc = gmonopuls('cutoff',fc);
  t{n} = -2*tc:1/fs:2*tc;
  y{n} = gmonopuls(t{n},fc);
  t{n} = t{n} - n*5e-11;
  fc=fc+5e3;
end
plot(t{1},y{1},'r',t{2},y{2},'k')

Symmetric shifted gaussian pulse

1 Answers