The geometric mean of power (amplitude) spectra has a much smaller bias than the classical arithmetic (RMS) averaging
Rik Pintelon, Johan Schoukens, Jean Renneboog · IEEE Transactions on Instrumentation and Measurement · 1988
The statistical properties of the geometric mean of power (amplitude) spectra resulting from a discrete Fourier transform (DFT) are compared with those of arithmetic (RMS) averaging. The statistical properties are verified by means of frequency-domain and time-domain simulations. It is shown that the asymptotic bias of the geometric mean is a function of the fourth-order moments of the measurement noise.>