A version of discrete Haar transform with nodes of $\Pi_0$-grids

Abstract

We propose a version of the two-dimensional discrete Haar transform with 2 nodes forming Π 0-grids associated with the triangular partial sums of Fourier-Haar series of a given function. Due to the structure of Π 0-grids, the computation of coefficients of this discrete transform is based on a cubature formula with 2 nodes being exact for Haar polynomials of degree at most , owing to that all the coefficients (1 , 2) 1 , 2 of the constructed transform coincide with the Fourier-Haar coefficients (1 , 2) 1 , 2 for Haar polynomials of degree at most −max{ 1 , 2 } (0 1 + 2 , where). The standard two-dimensional discrete Haar transform with 2 nodes does not possess this property.