## Abstract

Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible integer cosine transformations on n input integers. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. The detailed structure of such a reversible design strongly depends on the odd prime factors of the determinant of the transform: whether those are of the form 2^{k} ± 1 or of the form 2^{k} ± 2^{l} ± 1 or neither of these forms.

Original language | English |
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Article number | 11 |

Journal | ACM Journal on Emerging Technologies in Computing Systems |

Volume | 11 |

Issue number | 2 |

ISSN | 1550-4832 |

DOIs | |

Publication status | Published - 1 Oct 2014 |

## Keywords

- Garbage-free multiplication
- Integer cosine transform
- Reversible computation