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RESEARCH PRODUCT

Biorthogonal Multiwavelets Originated from Hermite Splines

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This chapter presents multiwavelet transforms that manipulate discrete-time signals. The transforms are implemented in two phases: 1. Pre (post)-processing, which transforms a scalar signal into a vector signal (and back). 2. Wavelet transforms of the vector signal. Both phases are performed in a lifting way. The cubic interpolating Hermite splines are used as a predicting aggregate in the vector wavelet transform. Pre(post)-processing algorithms which do not degrade the approximation accuracy of the vector wavelet transforms are presented. A scheme of vector wavelet transforms and three pre(post)-processing algorithms are described. As a result, we get fast biorthogonal algorithms to transform discrete-time signals which are exact on sampled cubic polynomials. The transform results in the expansion of signals over biorthogonal bases consisting of translations of a few discrete-time wavelets which are symmetric and have short supports.