Half-Delay B-Spline Filter for Construction of Shift-Invariant Wavelet Transform
H. Olkkonen, Jaakko Olkkonen · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · 2007
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[n]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.