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Wavelet Frames Generated by Spline Based p-Filter Banks

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Spline and Spline Wavelet Methods with Applications to Signal and Image Processing

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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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Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amir Z. Averbuch & Valery A. Zheludev

  2. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmaki

Authors
  1. Amir Z. Averbuch
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  2. Pekka Neittaanmaki
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  3. Valery A. Zheludev
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Correspondence to Amir Z. Averbuch .

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Averbuch, A.Z., Neittaanmaki, P., Zheludev, V.A. (2014). Wavelet Frames Generated by Spline Based p-Filter Banks. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8926-4_17

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  • DOI: https://doi.org/10.1007/978-94-017-8926-4_17

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8925-7

  • Online ISBN: 978-94-017-8926-4

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