Fast algorithm of discrete Walsh-Haar transformation
Li Lü, Baochang Shi, Jinwen Tian, Jian Liu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
Walsh-Haar function system that was first intruoduced by us is a new kind of function systems, and has a good global/local property. This function system is called Walsh ordering function system since its generation kernel functions belong to Walsh ordering Walsh function system. We worked out a recursive property of the matrix corresponding to the first Walsh-Haar functions in Walsh-Haar function system, and we also proved that Walsh-Haar function system is perfect and orthogonal similar to Walsh function system and Haar function system. Thus, discrete Walsh-Haar transformation (DW-HT) is an orthogonal transformation that can be widely used in signal processing. In this paper, using the recursive property of the matrix and the fast algorithm of discrete Walsh transformation (DWT) in Walsh ordering, we have designed a fast algorithm of Walsh ordering DW-HT based on the bisection technique. The idea and method used in this paper can be used for designing fast algorithms of other ordering DW-HTs and other discrete orthogonal transformations.