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

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Xuancheng Shao, Steven G. Johnson
• Keywords: Algorithms, CORR 2007, Discrete Cosine Transform, Education, Power-of-two Transform Size