### Abstract

This paper introduces a new set of exchange rules for a Remez-like algorithm for the Chebyshev design of IIR digital filters. It is explained that the essential difficulty, in applying the Remez algorithm to rational functions, is that on some iteration, there may be no solution to the interpolation problem for which the denominator is strictly non-zero in the interval of approximation. Then the usual procedure for updating the interpolation points can not be applied. The new rules for updating the interpolation points address precisely this problem for the two-pole case. It is shown with examples that, when the Remez-like algorithm of Hofstetter et al. is applied to rational functions, there is a way to update the interpolation points so that the algorithm converges rapidly even when poles arise in the interval of approximation.

Original language | English (US) |
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Title of host publication | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |

Editors | Anon |

Publisher | IEEE |

Pages | 2209-2212 |

Number of pages | 4 |

Volume | 3 |

State | Published - 1997 |

Event | Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP. Part 1 (of 5) - Munich, Ger Duration: Apr 21 1997 → Apr 24 1997 |

### Other

Other | Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP. Part 1 (of 5) |
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City | Munich, Ger |

Period | 4/21/97 → 4/24/97 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering
- Acoustics and Ultrasonics

### Cite this

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings*(Vol. 3, pp. 2209-2212). IEEE.

**New exchange rules for IIR filter design.** / Selesnick, Ivan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings.*vol. 3, IEEE, pp. 2209-2212, Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP. Part 1 (of 5), Munich, Ger, 4/21/97.

}

TY - GEN

T1 - New exchange rules for IIR filter design

AU - Selesnick, Ivan

PY - 1997

Y1 - 1997

N2 - This paper introduces a new set of exchange rules for a Remez-like algorithm for the Chebyshev design of IIR digital filters. It is explained that the essential difficulty, in applying the Remez algorithm to rational functions, is that on some iteration, there may be no solution to the interpolation problem for which the denominator is strictly non-zero in the interval of approximation. Then the usual procedure for updating the interpolation points can not be applied. The new rules for updating the interpolation points address precisely this problem for the two-pole case. It is shown with examples that, when the Remez-like algorithm of Hofstetter et al. is applied to rational functions, there is a way to update the interpolation points so that the algorithm converges rapidly even when poles arise in the interval of approximation.

AB - This paper introduces a new set of exchange rules for a Remez-like algorithm for the Chebyshev design of IIR digital filters. It is explained that the essential difficulty, in applying the Remez algorithm to rational functions, is that on some iteration, there may be no solution to the interpolation problem for which the denominator is strictly non-zero in the interval of approximation. Then the usual procedure for updating the interpolation points can not be applied. The new rules for updating the interpolation points address precisely this problem for the two-pole case. It is shown with examples that, when the Remez-like algorithm of Hofstetter et al. is applied to rational functions, there is a way to update the interpolation points so that the algorithm converges rapidly even when poles arise in the interval of approximation.

UR - http://www.scopus.com/inward/record.url?scp=0030673248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030673248&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3

SP - 2209

EP - 2212

BT - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

A2 - Anon, null

PB - IEEE

ER -