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

H. Olkkonen, Juuso Olkkonen

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


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
Issue number7
Publication statusPublished - 2007
MoE publication typeA1 Journal article-refereed


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

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