Efficient Split-Radix and Radix-4 DCT Algorithms and Applications

Abstract

This paper proposes efficient split-radix and radix-4 Discrete Cosine Transform (DCT) of types II/III algorithms. The proposed fast split-radix and radix-4 algorithms extend the previous work on the lowest multiplication complexity, self-recursive, radix-2 DCT II/III algorithms. The paper also addresses the self-recursive and stable aspects of split-radix and radix-4 DCT II/III algorithms having simple, sparse, and scaled orthogonal factors. Moreover, the proposed split-radix and radix-4 algorithms attain the lowest theoretical multiplication complexity and arithmetic complexity for 8-point DCT II/III matrices. The factorization corresponding to the proposed DCT algorithms contains sparse and scaled orthogonal matrices. Numerical results are presented for the arithmetic complexity comparison of the proposed algorithms with the known fast and stable DCT algorithms. Execution time of the proposed algorithms is presented while verifying the connection to the order of the arithmetic complexity. Moreover, we will show that the execution time of the proposed split-radix and radix-4 algorithms are more efficient than the radix-2 DCT algorithms. Finally, the implementations of the proposed DCT algorithms are stated using signal-flow graphs.