# I Calculating power spectral density from FFT

1. Dec 9, 2016

### GhostLoveScore

EDIT: Sorry. It's FFT - Fast Fourier Transform, not FTT.
I am interested in doing some amateur radio astronomy. Mainly at 1420MHz, hydrogen line. I have a RTL SDR stick. For those who don't know what that is, it's USB DVB-T receiver that can receive anything between 24 – 1766 MHz.

Now, there is a finished program for what I am asking, but I don't like using something that I don't know how it works. This is the source for finished program https://github.com/mariocannistra/radio-astronomy-fftw

SDR stick outputs I/Q data. I/Q data is just amplitude data but the amplitude is sampled at the same time 90 degrees away from the other sample. Amplitude of the signal is sqrt(I^2+Q^2). (I don't know how to insert equation, sorry). No problem so far.

I can record a sample of the signal and there is a library for Raspberry PI for doing Fast Fourier Transform on that sample. This is where I got stuck. How to find power spectral density from the Fast Fourier Transform?

I got the impression that it's just amplitude squared - I^2+Q^2? Can it be that simple?

I apologize for any nonsense that I may have said here. And of course I wrote FTT instead of FFT in the thread title. If I wrote everything correctly that would be weird. Moderators, please correct that.

2. Dec 9, 2016

### olivermsun

The FFT gives a complex output which is basically Z = I + Qi. So to generate the power spectrum you take Z * conj(Z) = abs(Z).^2 = I^2 + Q^2.
If you're taking the FFT of a real input signal, then the positive and negative frequency parts have equal power, so you can just plot the positive frequency power spectrum and multiply by 2.

3. Dec 10, 2016

### GhostLoveScore

I assume that in Z=I + Qi, I and Q are not the same variables as I, Q in raw data received from SDR? In this case Z= I + Qi, I and Q are just real and imaginary components of FFT output?

4. Dec 10, 2016

### olivermsun

Sorry for the bad notation. Yes, I and Q are real and imaginary components of the FFT output, but they are basically just the coefficients (not the full oscillating signals as in the raw I/Q data outputs).