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arXiv · 0708.4399

Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

Xuancheng Shao·Steven G. Johnson
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Abstract

We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact count is strictly lowered for all N > 4. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.

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Xuancheng Shao, Steven G. Johnson. 2007-08-31. Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations. https://doi.org/10.1016/j.sigpro.2007.11.024

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