Higher-Order Properties of Analytic Wavelets

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 exactl...

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Vydáno v:	IEEE transactions on signal processing Ročník 57; číslo 1; s. 146 - 160
Hlavní autoři:	Lilly, J.M., Olhede, S.C.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.01.2009 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Amplitude estimation Amplitude modulation Applied sciences Asymmetry Behavior Continuous wavelet transforms Earth Exact sciences and technology Frequency estimation Hilbert transform Information, signal and communications theory instantaneous frequency Localization Mathematical analysis Miscellaneous Morlet wavelet Position (location) ridge analysis Signal analysis Signal processing Studies Telecommunications and information theory time-frequency analysis Wavelet Wavelet analysis Wavelet domain wavelet transform Wavelet transforms Performance evaluation Time-frequency analysis Modulated signal wavelet transform Mapping Hilbert transformation ridge analysis Wavelets Hilbert transform Time domain method Asymmetry Wavelet transformation Signal processing Instantaneous frequency Localization
ISSN:	1053-587X, 1941-0476
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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 ldquoAiry waveletsrdquo 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.
AbstractList	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 ldquoAiry waveletsrdquo 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. 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. 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.
Author	Olhede, S.C. Lilly, J.M.
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Snippet	The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous... 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...
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SubjectTerms	Amplitude estimation Amplitude modulation Applied sciences Asymmetry Behavior Continuous wavelet transforms Earth Exact sciences and technology Frequency estimation Hilbert transform Information, signal and communications theory instantaneous frequency Localization Mathematical analysis Miscellaneous Morlet wavelet Position (location) ridge analysis Signal analysis Signal processing Studies Telecommunications and information theory time-frequency analysis Wavelet Wavelet analysis Wavelet domain wavelet transform Wavelet transforms
Title	Higher-Order Properties of Analytic Wavelets
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