Half-delay B-spline filter for construction of shift-invariant wavelet transform

H. Olkkonen, Juuso Olkkonen

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

We introduce a general framework for the shift-invariant biorthogonal wavelet transform. The method is based on the two parallel wavelet transforms, where the wavelets form a Hilbert transform pair. This condition requires that the impulse responses of the scaling filters are half-delayed versions of each other: ho and ho [n - 1/2]. The ideal half-delay operator is constructed by the interpolation and decimation procedure based on the polyphase decomposition of the two-scale B-spline equation. The present method yields linear phase and shift-invariant wavelet transform coefficients and can be adapted to any of the existing biorthogonal DWT filter bank.
Original languageEnglish
Pages (from-to)611-615
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Volume54
Issue number7
DOIs
Publication statusPublished - 2007
MoE publication typeA1 Journal article-refereed

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Splines
Wavelet transforms
Filter banks
Impulse response
Mathematical operators
Interpolation
Decomposition

Keywords

  • Discrete wavelet transform (DWT)
  • Fractional delay (FD) filters
  • Multirate signal processing
  • Shift invariance

Cite this

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abstract = "We introduce a general framework for the shift-invariant biorthogonal wavelet transform. The method is based on the two parallel wavelet transforms, where the wavelets form a Hilbert transform pair. This condition requires that the impulse responses of the scaling filters are half-delayed versions of each other: ho and ho [n - 1/2]. The ideal half-delay operator is constructed by the interpolation and decimation procedure based on the polyphase decomposition of the two-scale B-spline equation. The present method yields linear phase and shift-invariant wavelet transform coefficients and can be adapted to any of the existing biorthogonal DWT filter bank.",
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Half-delay B-spline filter for construction of shift-invariant wavelet transform. / Olkkonen, H.; Olkkonen, Juuso.

In: IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 54, No. 7, 2007, p. 611-615.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Olkkonen, Juuso

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AB - We introduce a general framework for the shift-invariant biorthogonal wavelet transform. The method is based on the two parallel wavelet transforms, where the wavelets form a Hilbert transform pair. This condition requires that the impulse responses of the scaling filters are half-delayed versions of each other: ho and ho [n - 1/2]. The ideal half-delay operator is constructed by the interpolation and decimation procedure based on the polyphase decomposition of the two-scale B-spline equation. The present method yields linear phase and shift-invariant wavelet transform coefficients and can be adapted to any of the existing biorthogonal DWT filter bank.

KW - Discrete wavelet transform (DWT)

KW - Fractional delay (FD) filters

KW - Multirate signal processing

KW - Shift invariance

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