Wavelet bases with a general integer dilation factor d⩾2 and better regularity properties

It is well known that by adding some extra zeros to a Daubechies low-pass wavelet filter, one gets new orthonormal wavelet basis with better regularity property. In this paper, we give a detailed study of this procedure in the general case of a wavelet filter associated with any integer dilation factor d⩾2. Moreover, we describe an algorithm for the construction of symmetric scaling functions with dilation factor d=4. Finally, we provide the reader with some numerical examples that illustrate the results of this work.