Getting the power spectral density from a plot

[Malamala]

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?

 

[osilmag]

Hi. The Welch method computes the PSD. You will need to consider your window length. Depending on the software you are using, it can be a rather quick and easy command. What computational software do you have?

 

[Malamala]

Hi. The Welch method computes the PSD. You will need to consider your window length. Depending on the software you are using, it can be a rather quick and easy command. What computational software do you have?

I am using python. Welch method is built it, but it has this parameter which defines how many points I have in each segment and the obtained PSD changes visually based on that. And it only looks like what I would expect, based on other papers, only when I include all the points in my data set in the segment (i.e. I have only one segment). So I am not sure if that is correct.

 

[osilmag]

You could try the FFT with a typical 256 pt window and then square the value of each frequency. That is kind of the original way of finding it. Compare how that looks with the welch method.