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Spline and Spline Wavelet Methods with Applications to Signal and Image Processing pp 393–407Cite as

Multiwavelet Frames Originated From Hermite Splines

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Abstract

The chapter presents a method for the construction of multiwavelet frame transform for manipulation of discrete-time signals. The frames are generated by three-channel perfect reconstruction oversampled multifilter banks. The design of the multifilter bank starts from a pair of interpolating multifilters, which originate from the cubic Hermite splines. The remaining multifilters are designed by factoring polyphase matrices. Input to the oversampled analysis multifilter bank is a vector-signal, which is derived from an initial scalar signal by one out of three pre-processing algorithms. The post-processing algorithms convert the vector output from the synthesis multifilter banks into a scalar signal. The discrete-time framelets, generated by the designed filter banks, are (anti)symmetric and have short support.

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Notes

  1. 1.

    See Sect. 15.4.

References

  1. A. Averbuch, V. Zheludev, T. Cohen, Multiwavelet frames in signal space originated from Hermite splines. IEEE Trans. Signal Process. 55(3), 797–808 (2007)

    Article  MathSciNet  Google Scholar 

  2. Z. Cvetković, M. Vetterli, Oversampled filter banks. IEEE Trans. Signal Process. 46(5), 1245–1255 (1998)

    Article  Google Scholar 

  3. B. Han, Dual multiwavelet frames with high balancing order and compact fast frame transform. Appl. Comput. Harmon. Anal. 26(1), 14–42 (2008)

    Article  Google Scholar 

  4. B. Han, Q. Mo, Multiwavelet frames from refinable function vectors. Adv. Comput. Math. 18(2–4), 211–245 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. H.O. Kim, R.Y. Kim, J.K. Lim, New look at the constructions of multiwavelet frames. Bull. Korean Math. Soc. 47(3), 563–573 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Pekka Neittaanmäki

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

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© 2016 Springer International Publishing Switzerland

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Averbuch, A.Z., Neittaanmäki, P., Zheludev, V.A. (2016). Multiwavelet Frames Originated From Hermite Splines. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-22303-2_16

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  • DOI: https://doi.org/10.1007/978-3-319-22303-2_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22302-5

  • Online ISBN: 978-3-319-22303-2

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