Rationalized Hadamard-Haar transform

摘要

A hybrid version of Haar transforms (HT) and Walsh-Hadamard transforms (WHT), called the Hadamard-Haar transform (HHT), has been developed, which effectively combines the advantages of both the transforms. Recently the HT has been rationalized so that the powers of √2 are replaced by integer powers of 2 [11-13]. In addition, the rationalized HT(RHT) retains also the properties of the HT. Similarly to the RHT, the (HHT), is now rationalized. Fast algorithms for efficient implementation of rationalized HHT [(RHHT)], based on sparse matrix factors, have now been developed. Also by using pipeline structure real-time digital processors have now been designed. These hardware utilize only adders subtractors and delay units.