Tree-structured Haar transforms (Q1851096)

Classical Haar functions are defined by the dyadic splitting of the interval. In this paper, the authors generalize the idea to an arbitrary time and scale splitting. To a given binary tree is associated an orthogonal system of Haar-type functions, which are called tree-structured Haar functions (TSH). A general background is introduced to design fast TSH transforms. The authors show that the algorithm requires \(2(N-1)\) additions and \(3N-2\) multiplications, where \(N\) designates the number of leaves of the binary tree.