Generalized morse wavelets
Generalized morse wavelets
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DOI：
10.1109/tsp.2002.804066
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发表时间：
2002-11-01
影响因子：
5.4
通讯作者：
Walden, AT
中科院分区：
文献类型：
--
作者：
Olhede, SC;Walden, AT
本文研究了一类广义莫尔斯小波，这是适用于时变谱估计的特征函数小波，通过平均的时间尺度特征。广义莫尔斯小波的阶k（相应的特征值阶）取决于一个参数（β，γ）的双峰，我们扩展的结果，得出的特殊情况β = γ = 1，并包括证明“的分辨率的身份。“小波很容易使用离散傅里叶变换（DFT）计算，对于（beta，gamma）=（2 m，2），可以精确计算。修正了以前发表的本征值公式。结果表明，当gamma > 1时，广义莫尔斯小波的能量集中性优于Hermites小波;对于复信号，必须同时使用解析复小波和反解析复小波或奇偶真实的小波进行尺度图分析，而对于真实的信号，解析复小波就足够了.
This paper examines the class of generalized Morse wavelets, which are eigenfunction wavelets suitable for use in time-varying spectrum estimation via averaging of time-scale eigenscalograms. Generalized Morse wavelets of order k (the corresponding eigenvalue order) depend on a doublet of parameters (beta, gamma); we extend results derived for the special case beta = gamma = 1 and include a proof of "the resolution of identity." The wavelets are easy to compute using the discrete Fourier transform (DFT) and, for (beta, gamma) = (2m, 2), can be computed exactly. A correction of a previously published eigenvalue formula is given. This shows that for gamma > 1, generalized Morse wavelets can outperform the Hermites in energy concentration, contrary to a conclusion based on the gamma = 1 case.For complex signals, scalogram analyses must be carried out using both the analytic and anti-analytic complex wavelets or odd and even real wavelets, whereas for real signals, the analytic complex wavelet is sufficient.