Irrational-Dilation Orthonormal Wavelet Basis and its Calculation Method

We have already proposed an orthonormal wavelet basis having an arbitrary real dilation. However, when its dilation is an irrational number, it is very difficult to calculate its transform and inverse transform because of its infinite number of wavelet shapes and its irrational distances between wavelets. In this paper, based on the decomposition and reconstruction algorithms, we propose a calculation method of its transform and inverse transform.