Affiliation:
1. School of Mathematics and Physics, Jinggangshan University, Ji’an 343009, P. R. China
2. School of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243000, P. R. China
Abstract
Continuous wavelet transform (CWT) is a linear convolution of signal and wavelet function for a fixed scale. This paper studies the algorithm of CWT with Morlet wavelet as mother wavelet by using nonzero-padded linear convolution. The time domain filter, which is a non-causal filter, is the sample of wavelet function. By making generalized discrete Fourier transform (GDFT) and inverse transform for this filter, we can get a geometrically weighted periodic extension of the filter when evaluated outside its original support. From this extension of the time domain filter, we can get a causal filter. In this paper, GDFT-based algorithm for CWT, which has a more concise form than that of linear convolution proposed by Jorge Martinez, is constructed by using this causal filter. The analytic expression of the GDFT of this filter, which is essential for GDFT-based algorithm for CWT, is deduced in this paper. The numerical experiments show that the calculation results of GDFT-based algorithm are stable and reliable; the running speed of GDFT-based algorithm is faster than that of the other two algorithms studied in our previous work.
Funder
Natural Science Foundation of Jiangxi Province
National Natural Science Foundation of China
the Science and Technology Plan Project of Jiangxi Provincial Education Department
the Doctoral research startup project of Jinggangshan University
Natural Science Foundation of Anhui Province (CN)
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Information Systems,Signal Processing
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献