## 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 2 N log_{2} N + O (N) to frac(17, 9) N log_{2} N + O (N) for a power-of-two transform size N, and the exact count is strictly lowered for all N ≥ 8. These results are derived by considering the DCT to be a special case of a DFT of length 8 N, 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.

Original language | English |
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Pages (from-to) | 1313-1326 |

Number of pages | 14 |

Journal | Signal Processing |

Volume | 88 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2008 |

## Keywords

- Arithmetic complexity
- Discrete cosine transform
- Fast Fourier transform
- Lapped transform

## ASJC Scopus subject areas

- Control and Systems Engineering
- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering