Wavelet periodicity detection algorithms

John J. Benedetto; Goetz E. Pfander

doi:10.1117/12.328148

19 October 1998 Wavelet periodicity detection algorithms

John J. Benedetto, Goetz E. Pfander

Proceedings Volume 3458, Wavelet Applications in Signal and Imaging Processing VI; (1998) https://doi.org/10.1117/12.328148
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

This paper deals with the analysis of time series with respect to certain known periodicities. In particular, we shall present a fast method aimed at detecting periodic behavior inherent in noise data. The method is composed of three steps: (1) Non-noisy data are analyzed through spectral and wavelet methods to extract specific periodic patterns of interest. (2) Using these patterns, we construct an optimal piecewise constant wavelet designed to detect the underlying periodicities. (3) We introduce a fast discretized version of the continuous wavelet transform, as well as waveletgram averaging techniques, to detect occurrence and period of these periodicities. The algorithm is formulated to provide real time implementation. Our procedure is generally applicable to detect locally periodic components in signals s which can be modeled as s(t) equals A(t)F(h(t)) + N(t) for t in I, where F is a periodic signal, A is a non-negative slowly varying function, and h is strictly increasing with h' slowly varying, N denotes background activity. For example, the method can be applied in the context of epileptic seizure detection. In this case, we try to detect seizure periodics in EEG and ECoG data. In the case of ECoG data, N is essentially 1/f noise. In the case of EEG data and for t in I,N includes noise due to cranial geometry and densities. In both cases N also includes standard low frequency rhythms. Periodicity detection has other applications including ocean wave prediction, cockpit motion sickness prediction, and minefield detection.

Citation Download Citation

John J. Benedetto and Goetz E. Pfander "Wavelet periodicity detection algorithms", Proc. SPIE 3458, Wavelet Applications in Signal and Imaging Processing VI, (19 October 1998); https://doi.org/10.1117/12.328148

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