- #1
Malamala
- 348
- 28
Hello! I have some time series from a self-heterodyne measurement. Basically i have a laser and I combine it with a delayed version of itself, shifted by ##\Omega = 2\pi \times 80## MHz. The delay is ##\tau = 100##ns. I remove the DC so the signal from the beat note is:
$$V(t) = V_0\cos(\Omega t + \phi(t+\tau)-\phi(t))$$
where ##V## is the oscilloscope signal (in V), and ##\phi(t)## is the phase noise of the laser. What I am interested in, is getting the power spectral density (PSD) of this ##\phi(t+\tau)-\phi(t)## term. I have the data on my laptop (it was recorded for ##2## ms, with a sampling rate of ##500## mega sample per second). I understand that, ideally, I just need to multiply this by ##sin(\Omega)## and ##cos(\Omega)## and get the in-phase (I) and quadrature (Q) signal, then compute ##arctan(Q/I)##, and then what I need is just the FFT of this. But after reading online more there seems to be other things that I might need to do, like windowings, applying a hilbert transform, detrending, welch transforms and doing some and not the others change the result. And I am not sure which transformations I need to include (or how can I figure out which I should include). I've never done this in practice before and it's a bit overwhelming. Can someone guide me a bit on how to proceed?
$$V(t) = V_0\cos(\Omega t + \phi(t+\tau)-\phi(t))$$
where ##V## is the oscilloscope signal (in V), and ##\phi(t)## is the phase noise of the laser. What I am interested in, is getting the power spectral density (PSD) of this ##\phi(t+\tau)-\phi(t)## term. I have the data on my laptop (it was recorded for ##2## ms, with a sampling rate of ##500## mega sample per second). I understand that, ideally, I just need to multiply this by ##sin(\Omega)## and ##cos(\Omega)## and get the in-phase (I) and quadrature (Q) signal, then compute ##arctan(Q/I)##, and then what I need is just the FFT of this. But after reading online more there seems to be other things that I might need to do, like windowings, applying a hilbert transform, detrending, welch transforms and doing some and not the others change the result. And I am not sure which transformations I need to include (or how can I figure out which I should include). I've never done this in practice before and it's a bit overwhelming. Can someone guide me a bit on how to proceed?