Rationalized Hadamard-Haar transform

A family of discrete Haar transforms

Family of discrete haar transforms.

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.

Rationalized Hadamard-haar Transform

A hybrid version of the slant (ST) and Haar Transforms (HT) called slant-Haar transform (SHT) is developed. Its properties and fast algorithms are also developed. Based on some standard performance criteria its utility and effectiveness are compared with other discrete transforms in applications such as feature selection, Wiener filtering and data compression.

M. A. Narasimhan

Papers

Image data compression by hadamard-haar transform.