In this paper, local cubic quasi-interpolating splines on non-uniform gridsare described. The splines are designed by fast computational algorithms that utilizethe relation between splines and cubic interpolation polynomials. These splines providean efficient tool for real-time signal processing. As an input, the splines use eitherclean or noised arbitrarily-spaced samples. Formulas for the spline’s extrapolationbeyond the sampling interval are established. Sharp estimations of the approximationerrors are presented. The capability to adapt the grid to the structure of an objectand to have minimal requirements to the operating memory are of great advantagesfor offline processing of signals and multidimensional data arrays. The designedsplines serve as a source for generating real-time wavelet transforms to apply to signalsin scenarios where the signal’s samples subsequently arrive one after the otherat random times. The wavelet transforms are executed by six-tap weighted movingaverages of the signal’s samples without delay. On arrival of new samples, only a coupleof adjacent transform coefficients are updated in a way that no boundary effectsarise.
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