摘要翻译：
研究了高阶小波性质对解析小波变换行为的影响，识别出具有良好性能的小波函数。这是通过对广义Morse小波的详细研究来实现的，广义Morse小波是一个精确解析连续小波的双参数族。时/频局部化程度、标度与频率之间映射的存在性以及估计调制振荡信号性质时所涉及的偏差被认为是重要的考虑因素。研究发现，小波在频率域和时间域上的不对称程度对小波的行为有很大的影响，如用三阶中心矩量化的那样。广义Morse小波的一个特殊子集被认为是由非齐次Airy函数导出的，它具有特别理想的性质。这些“Airy小波”在高时间局域性方面明显优于仅有的近似解析Morlet小波。研究了广义Morse小波的特殊情况，揭示了与信号特征相匹配的广泛行为。
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英文标题：
《Higher-Order Properties of Analytic Wavelets》
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作者：
J. M. Lilly and S. C. Olhede
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最新提交年份：
2009
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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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.
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PDF链接：
https://arxiv.org/pdf/802.2377