The probability density of spectral estimates based on modifiedperiodogram averages

Authors:
P.E. Johnson;D.G. Long
Affiliations:
Bell Aerosp. & Technol. Corp., Boulder, CO;-
Venue:
IEEE Transactions on Signal Processing
Year:
1999

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Abstract

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