Time series denoising with wavelet transform

Abstract

This paper concerns the possibilities of applying wavelet analysis to discovering and reducing distortions occurring in time series.Wavelet analysis basics are briefly reviewed. WaveShrink method including three most common shrinking variants (hard, soft, and non-negative garrote shrinkage functions) is described. Another wavelet-based filtering method, with parameters depending on the length of wavelets, is introduced. Sample results of filtering follow the descriptions of both methods. Additionally the results of the use of both filtering methods are compared. Examples in this paper deal only with the simplest “mother” wavelet function – Haar basic wavelet function.

Keywords

• wavelet transform
• WaveShrink
• filtration
• noise reduction
• Haar basic wavelet function