Applicability of Continuous, Stationary, and Discrete Wavelet Transforms in Engineering Signal Processing
Publication: Journal of Performance of Constructed Facilities
Volume 35, Issue 5
Abstract
Wavelet-based signal processing techniques are widely applied in multiple disciplines. However, few studies consider the applicability of different wavelet transforms in engineering signal processing fields. Based on the role of the wavelet transform, four engineering signal processing fields are classified, namely, singularity detection, denoising, time-frequency analysis, and sparse representation. Moreover, to clarify the confusion between wavelet transforms and the corresponding algorithms, this study compares the continuous, stationary, and discrete wavelet transforms and their corresponding algorithms, namely, the continuous wavelet convolution algorithm, á trous algorithm, and multiresolution algorithm, respectively. Both self-generated signals and engineering signals are applied to test the applicability of different wavelet-based algorithms in different engineering problems. The results show that all three wavelet-based algorithms could be applied in singularity detection; of these, the á trous algorithm was preferred for its translation invariance and filter property. Both the á trous and multiresolution algorithms could be applied in denoising due to their filter property together with decomposition and reconstruction algorithms. However, only the multiresolution algorithm could be applied in the time-frequency analysis and sparse representation due to its nonredundant property, filter property, and decomposition and reconstruction algorithms. These results provide references for engineers to select a proper wavelet-based algorithm in practice.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grant Nos. 51879203 and 52079099).
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Published In
Journal of Performance of Constructed Facilities
Volume 35 • Issue 5 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
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Received: Dec 23, 2020
Accepted: Jun 4, 2021
Published online: Jul 26, 2021
Published in print: Oct 1, 2021
Discussion open until: Dec 26, 2021
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