Non-separable Haar-type wavelets and canonical number systems

In this work the method of construction of Haar-type orthonormal wavelet basis of L-2(R-n) from characteristic functions chi(Q) of fundamental tiles of number systems suggested by Mendivil and Piche [1] is generalized. In the prototype work construction of Haar-type wavelet basis was built upon existence of positional number system with the complex base in the ring of Gaussian integers. In this paper the construction of Haar-type wavelet basis of L-2 (R-n) associated with canonical binary number systems in other fields is considered.