  The power-spectrum subband energy ratio (PSER) has been applied in a variety
of fields, but reports on its statistical properties have been limited. As
such, this study investigates these characteristics in the presence of additive
Gaussian white noise for both pure noise and mixed signals. By analyzing the
probability and independence of power spectrum bins, and the relationship
between the F and beta distributions, we develop a probability distribution for
the PSER. Results showed that in the case of pure noise, the PSER follows a
beta distribution. In addition, the probability density function and the
quantile exhibited no relationship with the noise variance, only with the
number of lines in the power spectrum, that is, PSER is not affected by noise.
When Gaussian white noise was mixed with the known signal, the resulting PSER
followed a doubly non-central beta distribution. In this case, it was difficult
to identify the quantile, as the probability density and cumulative
distribution functions were represented by infinite series. However, when a
spectral bin did not contain the power spectrum of the known signal, an
approximated quantile was found. This quantile is strictly proved to be in
agreement with the quantile in the case of pure noise and offers a convenient
methodology for identifying valid signals.
