On Fast Algorithm for Computing Even-Length DCT

TL;DR

This paper analyzes a recursive algorithm for computing even-length DCTs, demonstrating its efficiency and potential advantages over existing prime factor-based methods for certain lengths.

Contribution

It shows that C.W. Kok's recursive DCT algorithm has optimal multiplicative complexity for small m and introduces a scaled form with lower complexity for some lengths.

Findings

Same multiplicative complexity as prime factor decomposition for m ≤ 2

Simple conversion to scaled form

Lower multiplicative complexity for some lengths

Abstract

We study recursive algorithm for computing DCT of lengths $N=q 2^m$ ($m,q \in \mathbb{N}$, $q$ is odd) due to C.W.Kok. We show that this algorithm has the same multiplicative complexity as theoretically achievable by the prime factor decomposition, when $m \leqslant 2$. We also show that C.W.Kok's factorization allows a simple conversion to a scaled form. We analyze complexity of such a scaled factorization, and show that for some lengths it achieves lower multiplicative complexity than one of known prime factor-based scaled transforms.