UCL logo

UCL Discovery

UCL home » Library Services » Electronic resources » UCL Discovery

Higher-Order Properties of Analytic Wavelets

Lilly, JM; Olhede, SC; (2009) Higher-Order Properties of Analytic Wavelets. IEEE T SIGNAL PROCES , 57 (1) 146 - 160. 10.1109/TSP.2008.2007607.

Full text not available from this repository.

Abstract

The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a two-parameter family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a mapping between scale and frequency, and the bias involved in estimating properties of modulated oscillatory signals, are proposed as important considerations. Wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain, as quantified by the third central moments. A particular subset of the generalized Morse wavelets, recognized as deriving from an inhomogeneous Airy function, emerge as having particularly desirable properties. These "Airy wavelets" substantially outperform the only approximately analytic Morlet wavelets for high time localization. Special cases of the generalized Morse wavelets are examined, revealing a broad range of behaviors which can be matched to the characteristics of a signal.

Type: Article
Title: Higher-Order Properties of Analytic Wavelets
DOI: 10.1109/TSP.2008.2007607
Keywords: Hilbert transform, instantaneous frequency, ridge analysis, time-frequency analysis, wavelet transform, MULTIPLE MORSE WAVELETS, POLARIZATION PHASE-RELATIONSHIPS, SIGNALS, FUNDAMENTALS, FREQUENCY, EDDY
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/168521
Downloads since deposit
0Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item