An Arbitrary-length and Multiplierless DCT Algorithm and Systolic Implementation

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.