Haar wavelet-based technique for sharp jumps classification

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Abstract

A wavelet-based technique is proposed for analysing localized significant changes in observed data, in the presence of noise. The main tasks of the proposed technique are

  • 1.

    (a) denoising the observed data without removing localized significant changes,

  • 2.

    (b) classifying the detected sharp jumps (spikes), and

  • 3.

    (c) obtaining a smooth trend (deterministic function) to represent the time-series evolution.

By using the Haar discrete wavelet transform, the sequence of data is transformed into a sequence of wavelet coefficients. The Haar wavelet coefficients together with their rate of change, represent local changes and local correlation of data, therefore, their analysis gives rise to multi-dimensional thresholds and constraints which allow both the denoising and the sorting of data in a suitable space.

Keywords

Wavelets
Jumps
Classification
Haar

Cited by (0)

1

The author wishes to thank N. Bellomo for his many suggestions and comments on a preliminary draft of this paper.