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From Blackman-Tukey pilot estimators to wavelet packet estimators: A modern perspective on an old spectrum estimation idea. (English) Zbl 1009.94519

Summary: The ubiquitous problem of good spectrum estimation has been researched for many years, and in their seminal 1958 book R. B. Blackman and J. W. Tukey [The measurement of power spectra, Unabridged and corrected republication (Dover, New York) (1959; Zbl 0084.21703)] describe a ‘pilot spectrum’, a ‘simple and cheap preliminary estimate’ of the spectral density function. They also define a modification to the simple pilot estimator, the ‘complete version’. Remarkably, both these estimators are in fact wavelet-based estimators, using the Haar wavelet filter. In this paper we update and extend the ‘complete’ pilot estimator of Blackman and Tukey by firstly utilising the discrete wavelet packet transform rather than the discrete wavelet transform previously implicitly used in the basic pilot estimator, thus enabling uniform frequency resolution, and secondly by using the maximal overlap, or undecimated, version (MODWPT), the equivalent of a ‘complete’ estimator. Both equiripple and maximally flat wavelet filter designs are considered. For rapidly varying or high dynamic range power spectra, the technique of rejection filtration, also discussed in the same book, is implemented, but again using the MODWPT. The result is a spectrum estimator that is easily derivable from wavelet software and that is extremely competitive with other existing spectrum estimation approaches.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65T60 Numerical methods for wavelets

Citations:

Zbl 0084.21703
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