High-Precision and Fixed-Point Discrete Cosine Transform without Multiplications

Discrete cosine transform (DCT) is an important tool in digital signal processing. In this paper, based on our previous work of performing DCT via linear sums of discrete moments, we have made development to eliminate multiplications in discrete cosine transforms by performing appropriate bit operations and shift in binary system, which can be implemented by integer additions of fixed points. An efficient and regular systolic array is designed to implement it, 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.