Abstract
In this paper, we propose an orthonormal wavelet basis having a dilation factor (R + 1)/ R with an arbitrary real number R > 0. This orthonormal wavelet basis requires an infinite number of wavelet shapes when the dilation factor (R + 1)/ R is ir-rational, and (R + 1)/ R can be taken an arbitrary real number greater than 1 with the appropriate real number R > 0.
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