解析波的高阶性质
Higher-Order Properties of Analytic Wavelets
摘要：
研究了高阶小波性质对解析小波变换行为的影响，确定了具有优越性能的小波函数。这是通过详细的调查广义莫尔斯小波，一个两个参数的家庭，完全解析连续小波。时间/频率局部化的程度，尺度和频率之间的映射的存在，以及调制振荡信号的估计属性中所涉及的偏差，提出了重要的考虑因素。小波的行为被发现是强烈的影响，在频率和时间域的小波的不对称程度，量化的第三中心时刻。一个特定的子集的广义莫尔斯小波，公认为来自非齐次艾里函数，出现具有特别理想的性能。这些“艾里小波”大大优于只有近似解析Morlet小波高时间本地化。特殊情况下的广义Morse小波的检查，揭示了广泛的行为，可以匹配的信号的特征。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
