2
$\begingroup$

I am using software to produce power spectral density (PSD) plots of time-series (voltage versus time). Unfortunately, the units of the produced plots are alien to me. I'm used to reading and interpreting PSD's in more common, "tangible" units like dBm/Hz or W/Hz, however these plots are described as:

Returns a PSD in $dB$ units that is normalized and divided by frequency bin width (i.e. it is normalized to the time-integral squared amplitude of the time domain and then divided by frequency bin width).

How is a PSD in units of dB to be interpreted, and what is the purpose of "normalizing to the time-integral squared amplitude of the time domain"? No further context is provided.

$\endgroup$
1
  • $\begingroup$ What library are you using? $\endgroup$
    – DanielSank
    Mar 29, 2021 at 22:20

1 Answer 1

1
$\begingroup$

You can interpret the PSD in units of dB the same way as you interpret it in more common units of dBm/Hz.

The time integral squared amplitude of the voltage signal in the time domain can be thought of as the total "energy" in the signal (area under the curve). This energy is not physical and need not make sense. Now if you divide the signal with that quantity, you are normalizing the signal so that the total "energy" is now 1. When you fourier transform this signal to get the PSD, you preserve this total energy and therefore your PSD can have units of dB. The reference is not 1mW or 1uW but just 1. The additional benefit of dividing out by the frequency bin width is that now your calculated quantity is now free of the choice of bin width. All this is done to focus on the qualitative nature of the PSD and not the quantitative values themselves. Hope this helps

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.