Relationship between arithmetic and Haar wavelet transforms in the form of layered Kronecker matrices

The relationship between the arithmetic and Haar wavelet transforms is investigated. An interesting connection in the form of layered vertical and horizontal Kronecker matrices between the two transforms is revealed. The new relations apply to an arbitrary dimension of the transform matrices and enable the arithmetic spectrum to be calculated directly from the Haar wavelet spectrum, and vice versa, without the necessity of reobtaining the original function