A window metric called independent sample rate is given in a book that I recently read. It says that in spectral estimation, the variance of power-level estimates is inversely proportional to the number of independent samples in the analysis window, which is given by
where $\eta_w$ is the independent sample rate, $M$ is the data length and $N$ is the window length. For rectangular and Hamming window, $\eta_w=1.5$ and $\eta_w=1.91$, respectively.
If spectrally white noise is assumed in the band and a large analysis time, the independent sample rate is given by, as indicated by the book,
is the autocorrelation function of the window $w(n)$.
Concerning the above description, my question is
- why is the independent sample rate not related to the overlap percent of windows between successive data segments. By intuition, I think more independent data samples can be given if proper overlap is applied.
- How is the equation (*) derived?
P.S.: The equation (*) is derived in Albert IH. Nuttall - SIGNAL-TO-NOISE RATIOS REQUIRED FOR SHORT-TERM NARROWBAND DETECTION OF GAUSSIAN PROCESSES document.