Ten lectures on wavelets
Simple regularity criteria for subdivision schemes
SIAM Journal on Mathematical Analysis
Multirate systems and filter banks
Multirate systems and filter banks
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
Detection of precursory signals in front of impulsive P-waves
Digital Signal Processing
Two-dimensional wavelet variance estimation with application to sea ice SAR images
Computers & Geosciences
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The ubiquitous problem of good spectrum estimation has been researched for many years, and in their seminal 1958 book Blackman and Tukey 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 easily derivable from wavelet software, and which is extremely competitive with other existing spectrum estimation approaches.