State Key Laboratory for Multispectral Information Processing Technologies, Institute of Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan 430074, P.R.China

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Abstract—Discrete Cosine transform (DCT) is an important tool in digital signal processing. In this paper, a novel algorithm to perform DCT multiplierlessly is proposed. First, by modular mapping and truncating Taylor series expansion, the DCT is expressed in the form of the product of the constants and discrete moments. Second, by performing appropriate bit operations and shift operations in binary system, the product can be transformed to some additions of integers. The proposed algorithm only involves integer additions and shifts because the discrete moments can be computed only by integer additions. An efficient and regular systolic array is designed to implement the proposed algorithm, and the complexity analysis is also given. Different to other fast Cosine transforms, our algorithm can deal with arbitrary length signals and get high precision. The approach is also applicable to multi-dimensional DCT and DCT inverses.

Index Terms—discrete Cosine transform, moments, multiplierless, systolic arrays

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Cite: Zhenbing Liu, Jianguo Liu, and Guoyou Wang, " An Arbitrary-length and Multiplierless DCT Algorithm and Systolic Implementation," Journal of Computers vol. 5, no. 5, pp. 725-732, 2010.