On Fast Algorithm for Computing Even-Length DCT

We study recursive algorithm for computing DCT of lengths N = q 2m (m, q ∈ N, q is odd) due to C. W. Kok [16]. We show that this algorithm has the same multiplicative complexity as theoretically achievable by the prime factor decomposition, when m 6 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 [14]. Index Terms Discrete cosine transform, DCT, scaled transform, factorization, multiplicative complexity.