Higher-Order Properties of Analytic Wavelets
Higher-Order Properties of Analytic Wavelets
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DOI：
10.1109/tsp.2008.2007607
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发表时间：
2009-01-01
影响因子：
5.4
通讯作者：
Olhede, Sofia C.
中科院分区：
文献类型：
--
作者：
Lilly, Jonathan M.;Olhede, Sofia C.
研究了高阶小波特性对解析小波变换行为的影响，确定了具有良好性能的小波函数。这是通过对广义莫尔斯小波的详细研究来实现的，广义莫尔斯小波是一种双参数精确解析连续小波族。时间/频率的局部化程度，尺度和频率之间的映射的存在，以及估计调制振荡信号特性所涉及的偏差，被认为是重要的考虑因素。小波行为被发现受到小波在频率和时域的不对称程度的强烈影响，由第三个中心矩量化。广义莫尔斯小波的一个特殊子集，被认为是从非齐次艾里函数派生出来的，具有特别理想的性质。这些“Airy小波”在高时间定位方面大大优于仅有的近似解析Morlet小波。研究了广义莫尔斯小波的特殊情况，揭示了可以与信号特征相匹配的广泛行为。
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.