In this paper, We investigate and summarize some computational tasks of discrete transforms in which the block diagonal structure (BDS) plays a dominant role. The topics discussed here are:
(1) Block Diagonal Structure in Walsh-Hadamard based discrete transforms.
(2) Block Diagonal Structure in Running Discrete Transforms.
(3) Block Diagonal Structure in the transform conversions between DHT and DCT.
(4) Block Diagonal Structure in Two Stage DHTs.
From the view point of VLSI system design, two important factors are most important: the regularity of the processor cells and the local communication between processors. The hardware implementation of block diagonal algorithms, for moderate N, just meets the above requirements. An example of WHT/DHT is also included in this paper.