While studying spectrum analyzers I ran into the concept of RMS averaging as a mean to reduce dispersion of data without affecting power spectral density (PSD).
What is not really clear to me is how this is achieved: as per the calculation, I found that it is obtained by averaging the magnitude of the squared values of each FFT's frequency bin over a certain number of acquired traces. However, while the definition itself is not the problem and it is obvious that the dispersion of data will be reduced (it's an average), I don't see how the PSD can stay the same without being affected by such a computation.
Here follows all I found on the subject (professor's online notes):
`` • Change of point of view: now we want to measure the power spectral density of noise without reducing it
• Since we processed the input signal by truncating and sampling, also white noise trace is displayed with a «noisy» spectrum
• In order to quantify the noise power density, it is useful to introduce the RMS averaging, that is the average on the magnitude of the square value of each frequency bin of the FFT performed on Np traces
• This technique reduces the dispersion of data displayed without changing the PSD''