Study of arbitrary real dilation factor of orthonormal wavelet basis

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 irrational, and (R + 1)/R can be taken an arbitrary real number greater than 1 with the appropriate real number R > 0.