SDR FFT Averaging

Question

Say we have an SDR receiving some digital signal. The tuner will down convert the signal to be fed to the ADC, which digitizes the signal to be further processed by software.

The signal presents a non-repetitive waveform to the ADC which can't be analyzed with a standard Fourier transform. According to this article, to analyze a non-periodic waveform, several FFT blocks must be recorded and then averaged.

My concern is in demodulating the signal. If the end result is an average of the actual signal, then how do software programs correctly decode the signal? Do the number of samples in each FFT block matter, or the number of blocks averaged? Is it possible to recreate the signal with 100% accuracy?

Answer 1

The tuner will down convert the signal to be fed to the ADC, which digitizes the signal to be further processed by software.

So, an SDR based on a quadrature mixer or an IF mixer (superheterodyne/low IF).

The signal presents a non-repetitive waveform to the ADC which can't be analyzed with a standard Fourier transform.

Uff! That's quite a claim. Anyway, you're doing the processing not on the input, but on the output of the ADC, which is a discrete-time signal with a finite duration. So, "standard Fourier transform" doesn't apply, anyways. You need to consider your problem a bit more precisely!

According to this article, to analyze a non-periodic waveform, several FFT blocks must be recorded and then averaged.

That's one way to estimate a power spectrum. There's others! But this is the first time where you actually mention what you want to do with the signal: estimate a spectrum. You can use the Fourier transform for other things as well!

My concern is in demodulating the signal. If the end result is an average of the actual signal

it's not – you're not demodulating the power spectrum, you're demodulating the signal.

You don't always do FFTs and average them. That's simply not the case. It's the case if you are estimating the spectrum of your signal the way the article describes. In case you're trying to extract information from a time-modulated signal, you simply won't do that.