Abstract

Abstract. Characterization of the smoothness of signals (or functions) by using interpolatory wavelets is studied in this paper. The dual of an interpolatory wavelet, also called a distributional analyzing wavelet, plays an important role in interpolatory wavelet decomposition. The coefficients of the interpolatory wavelet series expansion are values of some functionals induced by this dual. In addition, while this series representation of a given signal models the so−called waveform of the signal, the vanishing moment property of the dual, rather than the interpolatory wavelet itself, gives rise to localized time information of the changes of the signal.

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