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.