Calculating power spectral density from FFT

[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.

 

[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.

 

[GhostLoveScore]

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.

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?

 

[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).