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CORR
2007
Springer

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

8 years 9 months ago
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
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 ∼ 2N log2 N to ∼ 17 9 N log2 N for a power-of-two transform size N. 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. Key words: discrete cosine transform; lapped transform; fast Fourier transform; arithmetic complexity
Xuancheng Shao, Steven G. Johnson
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where CORR
Authors Xuancheng Shao, Steven G. Johnson
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