how do you expect noise to be the same, not even through 2 system you expect to be the same, but even the same system at different moments?
time domain to study noise is like trying to study the hills of terrain in a dense forest, no way.
You'd better check the spectrum envelop, that would show you whether you are filtering or not, mean variance higher statistical moments
Bear in mind that by padding zeros you are actually interleaving noise (random) and deterministic (null) pulses.
Therefore the FFT of a square pulses (sinc?) should somehow show up.
And agreeing with David, if you want to add 3rd dimension, time, then why not using a waterfall with command waterfall() or with command spectrogram()?
example of spectrogram with a linear chirp:
t = 0:1/1e3:2;
y = chirp(t,0,1,250);
If you find my answer useful, would you please be so kind to mark it as accepted answer?
thanks in advance, awaiting answer