A New Class of Hilbert Pairs of Almost Symmetric Orthogonal Wavelet Bases

• WANG Daiwei

  Department of Communication Engineering and Informatics, The University of Electro-Communications

• ZHANG Xi

  Department of Communication Engineering and Informatics, The University of Electro-Communications

Abstract

This paper proposes a new class of Hilbert pairs of almost symmetric orthogonal wavelet bases. For two wavelet bases to form a Hilbert pair, the corresponding scaling lowpass filters are required to satisfy the half-sample delay condition. In this paper, we design simultaneously two scaling lowpass filters with the arbitrarily specified flat group delay responses at ω=0, which satisfy the half-sample delay condition. In addition to specifying the number of vanishing moments, we apply the Remez exchange algorithm to minimize the difference of frequency responses between two scaling lowpass filters, in order to improve the analyticity of complex wavelets. The equiripple behavior of the error function can be obtained through a few iterations. Therefore, the resulting complex wavelets are orthogonal and almost symmetric, and have the improved analyticity. Finally, some examples are presented to demonstrate the effectiveness of the proposed design method.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E99.A (5), 884-891, 2016

  The Institute of Electronics, Information and Communication Engineers

Keywords

• DT<i>C</i>WT
• Hilbert transform pair
• almost symmetric orthogonal wavelets
• FIR filter
• Remez exchange algorithm

Details

• CRID: 1390282681288332416
• NII Article ID: 130005148588
• DOI: 10.1587/transfun.e99.a.884
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E99.A/5/E99.A_884/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed