Fast DCT-VIII Algorithms for Short-Length Input Sequences

Discrete cosine transforms (DCTs) are widely used in intelligent electronic systems for storing, processing, and transmitting data. Their popularity stems, on the one hand, from their unique properties and, on the other hand, from the availability of fast algorithms that minimize the computational and hardware complexity of their implementation. Until recently, the Type VIII DCT had been one of the least studied variants, with virtually no publications addressing fast algorithms for its implementation. However, this situation has changed, making the development of efficient implementation methods for this transform a timely and important research problem. In this paper, several algorithmic solutions for implementing the Type VIII DCT are proposed. A set of Type VIII DCT algorithms for small lengths N = 3, 4, 5, 6, 7 is presented. The effectiveness of the proposed solutions is due to the possibility of successful factorization of small-sized DCT-VIII matrices, leading to a reduction in the computational complexity of implementing transforms of this type. Compared with direct matrix–vector computation, the proposed algorithms achieve an approximate 53% reduction in the number of multiplications, at the cost of an increase of about 21% in the number of additions. This work continues a series of previously published studies aimed at creating a library of small-sized algorithms for discrete trigonometric transforms.