Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.
Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.
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DOI：
10.1098/rspa.2016.0776
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发表时间：
2017-04
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影响因子：
--
通讯作者：
Lilly JM
中科院分区：
文献类型：
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作者：
Lilly JM
一种方法是由孤立的，时间本地化的“事件”的叠加组成的信号的定量分析。在这里，这些事件被视为广义莫尔斯小波，一个广泛的家庭连续解析函数的尺度和相位旋转的版本。使用另一个莫尔斯小波分析由这样的函数的复制组成的信号允许人们从小波变换在其自身的最大值处的值直接估计事件的属性。确定一般幂律噪声中事件的分布，以便基于预期的误检率建立显著性。最后，一个事件的“影响区域”内的小波变换的表达式允许形成一个标准，用于拒绝虚假的最大值，由于数值伪影或其他不合适的事件。然后可以基于时间/尺度平面上的少量孤立点来重建信号。这种方法，被称为元素分析，适用于识别的长寿命的涡流结构，在海洋流观测沿跟踪测量海面高程从卫星测高。
A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized ‘events’. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event’s ‘region of influence’ within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis, is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry.