Forward and inverse transformations between Haar wavelet and arithmetic functions

Forward and inverse transformations between Haar wavelet and arithmetic functions

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Mutual conversions between Haar wavelet and arithmetic transforms are presented. The new relations allow direct calculation of an arithmetic spectrum from a Haar wavelet spectrum and vice versa without the need to obtain the original function. As both arithmetic and Haar wavelet transforms are used widely in many areas, these results should further increase the scope of their applications.


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