Calculate phase from time-domain response

Hi all,

I have following sinusoidal waveform as my system's input:

And following signal as my system's time-domain response:

Putting both of above diagrams into one (steady-state region) is depicted below:

Now the question is how can I calculate the phase shift caused by system? i.e. phase shift from blue line to red lines.

Answer 1

[Adam]

You should be able to just find the peaks of each and take the shifts between the two or use the hilbert transform to give complex signals, find the 0-phase points of both curves and calculate the shift from those, which will amount to pretty much the same thing.

doc hilbert

[Hasan Ghorbani]

Thanks for the reply. I think I just did what you mentioned in the first line of your response i.e. finding the peaks of each using cursor and take the shifts between the two