The probability density of spectral estimates based on modified periodogram averages

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Permanent URL	http://hdl.lib.byu.edu/1877/1123
Title	The probability density of spectral estimates based on modified periodogram averages
BYU Creator	Long, David G.
Creator	Johnson, Paul E.
Keywords	Gaussian processes; correlation methods; probability; random processes; spectral analysis
Description/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.
Source	Johnson, P. E., and D. G. Long. "The Probability Density of Spectral Estimates Based on Modified Periodogram Averages." Signal Processing, IEEE Transactions on 47.5 (1999): 1255-61;
Publisher	IEEE
Date Original	1999-05
Language	English eng en
Publication Type	Peer-Reviewed Articles
Type	Text
Format	application/pdf
Owning Institution	Brigham Young University
BYU College	Ira A. Fulton College of Engineering and Technology
BYU Department	Electrical and Computer Engineering
Copyright Status	(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.;
Copyright Use Information	http://www.lib.byu.edu/generic_copyright.html

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The probability density of spectral estimates based on modified periodogram averages

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