Wavelet Frames Generated by Spline Based p-Filter Banks

  • Amir Z. Averbuch
  • Pekka Neittaanmaki
  • Valery A. Zheludev
Chapter

Abstract

This chapter presents a design scheme to generate tight and so-called semi-tight frames in the space of discrete-time periodic signals. The frames originate from three- and four-channel perfect reconstruction periodic filter banks. The filter banks are derived from interpolating and quasi-interpolating polynomial splines and from discrete splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) and one high-pass filter, whose magnitude’s response mirrors that of a low-pass filter. In addition, these filter banks comprise one or two band-pass filters. In the semi-tight frames case, all the filters have linear phase and (anti)symmetric impulse response, while in the tight frame case, some of band-pass filters are slightly asymmetric. The design scheme enables to design framelets with any number of LDVMs.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Amir Z. Averbuch
    • 1
  • Pekka Neittaanmaki
    • 2
  • Valery A. Zheludev
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  2. 2.Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland

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