Title :
The probability density of spectral estimates based on modified periodogram averages
Author :
Johnson, Paul E. ; Long, David G.
Author_Institution :
Bell Aerosp. & Technol. Corp., Boulder, CO, USA
fDate :
5/1/1999 12:00:00 AM
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
Keywords :
Gaussian processes; correlation methods; probability; random processes; spectral analysis; Kullback-Leibler distance; correlated Gaussian input sequence; data window; frequency bins; maximum likelihood tests; modified periodogram averages; nonGaussian PDF; overlapping data segments; power estimate; probability density; probability density function; random data; random variable; spectral estimates; Covariance matrix; Density functional theory; Frequency estimation; Frequency measurement; Maximum likelihood estimation; Probability density function; Random variables; Spectral analysis; Statistical analysis; Testing;
Journal_Title :
Signal Processing, IEEE Transactions on
