Applicability of Continuous, Stationary, and Discrete Wavelet Transforms in Engineering Signal Processing

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.