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

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.