A Class of Algorithms for Continuous Wavelet Transform Based on the Circulant Matrix
Department of Mathematics, Jinggangshan University, Ji’an 343009, Jiangxi Province, China
Department of Mathematics, Tongji University, Shanghai 200092, China
Author to whom correspondence should be addressed.
Received: 20 November 2017 / Revised: 6 February 2018 / Accepted: 22 February 2018 / Published: 27 February 2018
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The Continuous Wavelet Transform (CWT) is an important mathematical tool in signal processing, which is a linear time-invariant operator with causality and stability for a fixed scale and real-life application. A novel and simple proof of the FFT-based fast method of linear convolution is presented by exploiting the structures of circulant matrix. After introducing Equivalent Condition of Time-domain and Frequency-domain Algorithms of CWT, a class of algorithms for continuous wavelet transform are proposed and analyzed in this paper, which can cover the algorithms in JLAB and WaveLab, as well as the other existing methods such as the
function in the toolbox of MATLAB. In this framework, two theoretical issues for the computation of CWT are analyzed. Firstly, edge effect is easily handled by using Equivalent Condition of Time-domain and Frequency-domain Algorithms of CWT and higher precision is expected. Secondly, due to the fact that linear convolution expands the support of the signal, which parts of the linear convolution are just the coefficients of CWT is analyzed by exploring the relationship of the filters of Frequency-domain and Time-domain algorithms, and some generalizations are given. Numerical experiments are presented to further demonstrate our analyses.
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MDPI and ACS Style
Yi, H.; Xin, S.-Y.; Yin, J.-F. A Class of Algorithms for Continuous Wavelet Transform Based on the Circulant Matrix. Algorithms 2018, 11, 24.
Yi H, Xin S-Y, Yin J-F. A Class of Algorithms for Continuous Wavelet Transform Based on the Circulant Matrix. Algorithms. 2018; 11(3):24.
Yi, Hua; Xin, Shi-You; Yin, Jun-Feng. 2018. "A Class of Algorithms for Continuous Wavelet Transform Based on the Circulant Matrix." Algorithms 11, no. 3: 24.
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