A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
The homomorphic analytic signal
IEEE Transactions on Signal Processing
On instantaneous amplitude and phase of signals
IEEE Transactions on Signal Processing
Analysis of singularities from modulus maxima of complex wavelets
IEEE Transactions on Information Theory
The monogenic wavelet transform
IEEE Transactions on Signal Processing
Bivariate instantaneous frequency and bandwidth
IEEE Transactions on Signal Processing
Improved wavelet feature extraction using kernel analysis for text independent speaker recognition
Digital Signal Processing
Wavelet ridge estimation of jointly modulated multivariate oscillations
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
On the analytic wavelet transform
IEEE Transactions on Information Theory
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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.