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

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