In wavelet theory the two-scale dilation equation has a central role. B-splines serve as good candidates for wavelet analysis, since they obey the two-scale dilation equation. This work describes the B-spline wavelet transform, which is based on the polyphase decomposition of the two-scale dilation equation. We construct a linear quadrature mirror filter (QMF) B-spline wavelet filter bank, which can be effectively implemented by the polyphase filters. The interpolating property of the two-scale dilation equation is applied for constructing the shift-invariant complex QMF B-spline wavelets. The validity of the B-spline wavelet transform is warranted in multi-scale analysis of neuroelectric signal waveforms.
Olkkonen, H., & Olkkonen, J. T. (2010). Shift-invariant B-spline wavelet transform for multi-scale analysis of neuroelectric signals. IET Signal Processing, 4(6), 603-609. https://doi.org/10.1049/iet-spr.2009.0109