Half-Delay B-Spline Filter for Construction of Shift-Invariant Wavelet Transform

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 54; no. 7; pp. 611 - 615
• Main Authors: Olkkonen, H., Olkkonen, J.T.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Circuits; Construction; Discrete wavelet transform (DWT); Discrete wavelet transforms; Equations; Filter bank; Filter banks; fractional delay (FD) filters; Interpolation; Linear phase; Mathematical analysis; multirate signal processing; Propagation delay; shift invariance; Signal analysis; Signal processing; Spline; Transforms; Wavelet coefficients; Wavelet transforms
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2007.895327

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:h o [n ] and h o [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.