Gaussian processes; correlation methods; probability; random processes; spectral analysis
Welch's (1967) method for spectral estimation of averaging modified periodograms has been widely used for decades. Because such an estimate relies on random data, the estimate is also a random variable with some probability density function. Here, the PDF of a power estimate is derived for an estimate based on an arbitrary number of frequency bins, overlapping data segments, amount of overlap, and type of data window, given a correlated Gaussian input sequence. The PDFs of several cases are plotted and found to be distinctly non-Gaussian (the asymptotic result of averaging frequency bins and/or data segments), using the Kullback-Leibler distance as a measure. For limited numbers of frequency bins or data segments, the precise PDF is considerably skewed and will be important in applications such as maximum likelihood tests.
(c) 1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.;