Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.

ABSTRACT: 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 sp

SUBMITTER: Lilly JM 

PROVIDER: S-EPMC5415685 | biostudies-literature | 2017 Apr

REPOSITORIES: biostudies-literature