ZHANG Shiqiang, ZHANG Shufang, WANG Yan. Biorthogonal Wavelet Construction Using Homotopy Method[J]. Chinese Journal of Electronics, 2015, 24(4): 772-775. doi: 10.1049/cje.2015.10.018
Citation: ZHANG Shiqiang, ZHANG Shufang, WANG Yan. Biorthogonal Wavelet Construction Using Homotopy Method[J]. Chinese Journal of Electronics, 2015, 24(4): 772-775. doi: 10.1049/cje.2015.10.018

Biorthogonal Wavelet Construction Using Homotopy Method

doi: 10.1049/cje.2015.10.018
Funds:  This work is supported by the Key Project of National Natural Science Foundation of China (No.61231006)
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  • Corresponding author: WANG Yan (corresponding author)was born in 1974, Shanxi Province.He received the Ph.D. degree in communicationand information systems fromDalian Maritime University in 2007.He is now a supervisor of postgraduate,associate professor of Dalian MaritimeUniversity. His research interests includesignal processing, image processingand wavelet analysis. (Email: dlmuwangyang@dlmu.edu.cn)
  • Received Date: 2015-02-03
  • Rev Recd Date: 2015-03-10
  • Publish Date: 2015-10-10
  • The biorthogonal wavelets families are used widely because they have compact support, complete symmetry and linear phase. According to Bézout's theorem, the biorthogonal wavelets available now are only some particular examples of total solutions. The quantity of solutions is decided jointly by the scaling function vanishing moment N and dual vanishing moment Ñ. The relationship of N, Ñ and solutions' quantity is discussed in detail. According to the constraint conditions which the compact biorthogonal wavelets satisfy, a number of biorthogonal wavelets are constructed in which the global convergent homotopy method is used for different N and Ñ. The filter coefficients and plots of scaling function, dual scaling function, wavelet function and dual wavelet function are given.
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