Rationalized Hadamard-haar Transform

A hybrid version of Haar (HT) and Walsh-Hadamard transforms (WHT) called Hadamard-Haar trans form (HHT)r which effectively combines the advantages of both the transforms has been developed. Recently HT has beet rationalized such that the Powers of Y'2 are replaced by integer powers of 2 [11-131. Besides, the rationalized HT (RHT) retains all the properties of HT. Similar to (RHT), the (HHT)r 'IS now rationalized. Fast algorithms for efficient implementation of rationalized HHT (RHHT)r based on sparse matrix factors are now developed. Also by using pipeline structure, realrtime digital processors are now designed. These hardware utilize only adders, subtractors and delay units.