### Abstract

The CORDIC algorithm for the calculation of trigonometric functions has traditionally suffered from two problems; speed, and the necessity to pre-scale the inputs. The speed problem is overcome to a large extent by the introduction of redundant number systems which have been shown by others. Here we show a new CORDIC system which has a unit scale factor that can be ignored. The unit scale factor is achieved by rotating the vector in 3 dimensional space in a manner which scales its projection onto the X-Y plane by the reciprocal of the overall scale factor. This new technique takes the same number of cycles as the standard CORDIC algorithm, with only marginally slower cycle times than the redundant system of Takagi. The system is shown to be entirely compatible with redundant number system implementations of the CORDIC algorithm.

Original language | English |
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Title of host publication | Mathematics in Signal Processing III |

Editors | J G McWirter |

Place of Publication | Oxford |

Publisher | Oxford University Press |

Pages | 63-73 |

Number of pages | 11 |

ISBN (Print) | 0198534809 |

Publication status | Published - Aug 1994 |

Event | Mathematics in Signal Processing III - Warwick, UK United Kingdom Duration: 1 Aug 1994 → … |

### Conference

Conference | Mathematics in Signal Processing III |
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Country | UK United Kingdom |

City | Warwick |

Period | 1/08/94 → … |

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## Cite this

Clarke, C. T., & Nudd, G. R. (1994). Redundant Arithmetic CORDIC System with a Unit Scale Factor. In J. G. McWirter (Ed.),

*Mathematics in Signal Processing III*(pp. 63-73). Oxford University Press.