How to work out the noise power and SNR in the systems output?

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Jared Joselowitz
Jared Joselowitz 2020-9-9
I have this 2nd order underdamped system with the following equation:
damp = 0.15;
natural_freq = 5;
theta = acos(damp);
wd = natural_freq*sqrt(1-damp^2);
t = 0:0.0251:6
% fitted model
y = 1 - (1/sqrt(1-damp^2))*exp(-damp*natural_freq*t).*sin(wd*t + theta);
How do you obtain an estimate of the noise power as well as signal-to-noise ratio (dB) present at the system’s output.

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