Small-Size Algorithms for the Type-I Discrete Cosine Transform with Reduced Complexity

Abstract

Discrete cosine transforms (DCTs) are widely used in intelligent electronic systems for data storage, processing, and transmission. The popularity of using these transformations, on the one hand, is explained by their unique properties and, on the other hand, by the availability of fast algorithms that minimize the computational and hardware complexity of their implementation. The type-I DCT has so far been perhaps the least popular, and there have been practically no publications on fast algorithms for its implementation. However, at present the situation has changed; therefore, the development of effective methods for implementing this type of DCT becomes an urgent task. This article proposes several algorithmic solutions for implementing type-I DCTs. A set of type-I DCT algorithms for small lengths N=2,3,4,5,6,7,8 is presented. The effectiveness of the proposed solutions is due to the possibility of fortunate factorization of the small-size DCT-I matrices, which reduces the complexity of implementing transformations of this type.

The Development of Fast DST-II Algorithms for Short-Length Input Sequences

“…We plan to collect a library of fast short-length algorithms for all types of discrete trigonometric transforms. For some types of trigonometric transformations, such as DCT-I, DCT-II, and DCT-IV (as well as some others), such algorithms have already been developed [32,36,37]. The subject of our research is fast algorithms for small-sized DST-II transforms.…”

“…A fairly large number of works have been devoted to the development of small-sized DCT algorithms, and much less attention has been paid to similar algorithms for the DST. Among the other types of discrete trigonometric transforms, DCT-II/DST-II plays an important role [29,[32][33][34][35]. For small-sized DCT-II, the algorithms were shown in one of our previous papers [36].…”

Efficient Algorithms and Architectures for DSP Applications

“…In [6], Kolenderski and Cariow present new algorithms for type-I DCT, with reduced complexity. Type-I DCT is a less popular transform, but it has important applications in wireless communication systems.…”