FAST COMPUTATION OF THE DISCRETE WALSH AND HADAMARD TRANSFORMS

The discrete Walsh and Hadamard transforms are often used in image pro cessing tasks such as image coding, pattern recognition, and sequency filtering. In this correspondence, a new discrete Walsh transform (DWT ) algorithm is derived in which a modified form of the DWT relation is decomposed into smaller-sized transforms using vectorized quantities. A new sequency-ordered discrete Hadamard transform (DHAT) algorithm i s also presented. The proposed approach results in more regular algori thms requiring no independent data swapping and fewer array-index upda ting and bit-reversal operations. An analysis of the computational com plexity and the execution time performance are provided. The results a re compared with those of the existing algorithms.