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Markus Püschel (Proc. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vol. 2, pp. 501-504, 2003)
Cooley-Tukey FFT like Algorithms for the DCT
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Published paper (link to publisher)
The Cooley-Tukey FFT algorithm decomposes a discrete Fourier transform (DFT) of size n = km into smaller DFT of size k and m. In this paper we present a theorem that decomposes a polynomial transform into smaller polynomial transforms, and show that the FFT is obtained as a special case. Then we use this theorem to derive a new class of recursive algorithms for the discrete cosine transforms (DCT) of type II and type III. In contrast to other approaches, we manipulate polynomial algebras instead of transform matrix entries, which makes the derivation transparent, concise, and gives insight into the algorithms' structure. The derived algorithms have a regular structure and, for 2-power size, minimal arithmetic cost (among known DCT algorithms).Keywords: Algorithm theory and analysis, Algebraic signal processing theory, Fast algorithms, Discrete/fast cosine transforms