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Journal of Inforamtion Science and Engineering, Vol.5 No.1, pp.17-33 (January 1989)
Block Diagonal Structure in Discrete Transforms*

Ja-Ling Wu, Yuh-Ming Huang, J. Shiu
and Shyh-Huei Hsu
Department of Computer Science and Information Engineering
National Taiwan University
Taipei, Taiwan 10764, Republic of China

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.

Keywords: block diagonal structure, discrete transforms, running discrete transform, walsh-hadamard transform, discrete hartley transform, two-stage discrete transforms

Received July 29, 1988; revised February 20, 1989.
Communicated by Jun S. Huang.
*This work was supported by the National Science Council.