4.7 Article

Higher-density dyadic wavelet transform and its application

Journal

MECHANICAL SYSTEMS AND SIGNAL PROCESSING
Volume 24, Issue 3, Pages 823-834

Publisher

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ymssp.2009.10.017

Keywords

Shift invariance; Dyadic wavelet transform; Perfect reconstruction; Intermediate scale; Denoising; Envelope analysis; Early fault

Funding

  1. National Natural Science Foundation of China [50905191, 50875272, 50735008]

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This paper proposes a higher-density dyadic wavelet transform with two generators, whose corresponding wavelet filters are band-pass and high-pass. The wavelet coefficients at each scale in this case have the same length as the signal. This leads to a new redundant dyadic wavelet transform, which is strictly shift invariant and further increases the sampling in the time dimension. We describe the definition of higher-density dyadic wavelet transform, and discuss the condition of perfect reconstruction of the signal from its wavelet coefficients. The fast implementation algorithm for the proposed transform is given as well. Compared with the higher-density discrete wavelet transform, the proposed transform is shift invariant. Applications into signal denoising indicate that the proposed wavelet transform has better denoising performance than other commonly used wavelet transforms. In the end, various typical wavelet transforms are applied to analyze the vibration signals of two faulty roller bearings, the results show that the proposed wavelet transform can more effectively extract the fault characteristics of the roller bearings than the other wavelet transforms. (C) 2009 Elsevier Ltd. All rights reserved.

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