Higher-Order Properties of Analytic Wavelets
By Jonathan M. Lilly, Sofia Charlotta Olhede. IEEE Transactions on Signal Processing, 2008
301 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Media Technology
View Paper: https://www.semanticscholar.org/paper/441ad6a2ef7bfc5ab841eedf85b7b815cb24c96a
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In Applied Mathematics
In Computer Vision and Pattern Recognition
In Media Technology
Citations in the corpus
- The continuous wavelet transform : a primer (2011, unknown): “s` = s0 2 ` nV ; ` = 0; 1; : : : ; nV nO; (47)”
- Generalized Morse Wavelets as a Superfamily of Analytic Wavelets (2012, methodology): “derivative of with respect to vanishes, see [9].”
- THE CONTINUOUS WAVELET TRANSFORM: MOVING BEYOND UNI‐ AND BIVARIATE ANALYSIS (2014, unknown): “I are all meaningful ( although in di¤erent senses ) we refer the reader to the mentioned paper by Lilly and Olhede ( 2009 ) .”