### Abstract

In this paper, an algorithm that can be utilized to determine the presence or absence of limit cycles in fixed-point implementation of digital filters is given. It is applicable for filters in state-space formulation (and hence, application to the corresponding direct form follows as a special case), and is independent of the order, type of quantization, and whether the accumulator is single- or double-length. Bounds on the amplitude and period of possible limit cycles are presented. The robustness of the algorithm in terms of limit cycle performance with respect to filter coefficient perturbations is verified. The algorithm is then used to obtain regions in the coefficient space where a filter of given order is limit cycle free. In this process, we have obtained limit cycle free regions that were previously unknown for the Two's complement case.

Original language | English (US) |
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Title of host publication | Proceedings - IEEE International Symposium on Circuits and Systems |

Editors | Anon |

Publisher | IEEE |

Pages | 2035-2038 |

Number of pages | 4 |

Volume | 3 |

State | Published - 1995 |

Event | Proceedings of the 1995 IEEE International Symposium on Circuits and Systems-ISCAS 95. Part 3 (of 3) - Seattle, WA, USA Duration: Apr 30 1995 → May 3 1995 |

### Other

Other | Proceedings of the 1995 IEEE International Symposium on Circuits and Systems-ISCAS 95. Part 3 (of 3) |
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City | Seattle, WA, USA |

Period | 4/30/95 → 5/3/95 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*(Vol. 3, pp. 2035-2038). IEEE.

**Exhaustive search algorithm for checking limit cycle behavior of digital filters.** / Premaratne, Kamal; Kulasekere, E. C.; Bauer, P. H.; Leclerc, L. J.

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

*Proceedings - IEEE International Symposium on Circuits and Systems.*vol. 3, IEEE, pp. 2035-2038, Proceedings of the 1995 IEEE International Symposium on Circuits and Systems-ISCAS 95. Part 3 (of 3), Seattle, WA, USA, 4/30/95.

}

TY - GEN

T1 - Exhaustive search algorithm for checking limit cycle behavior of digital filters

AU - Premaratne, Kamal

AU - Kulasekere, E. C.

AU - Bauer, P. H.

AU - Leclerc, L. J.

PY - 1995

Y1 - 1995

N2 - In this paper, an algorithm that can be utilized to determine the presence or absence of limit cycles in fixed-point implementation of digital filters is given. It is applicable for filters in state-space formulation (and hence, application to the corresponding direct form follows as a special case), and is independent of the order, type of quantization, and whether the accumulator is single- or double-length. Bounds on the amplitude and period of possible limit cycles are presented. The robustness of the algorithm in terms of limit cycle performance with respect to filter coefficient perturbations is verified. The algorithm is then used to obtain regions in the coefficient space where a filter of given order is limit cycle free. In this process, we have obtained limit cycle free regions that were previously unknown for the Two's complement case.

AB - In this paper, an algorithm that can be utilized to determine the presence or absence of limit cycles in fixed-point implementation of digital filters is given. It is applicable for filters in state-space formulation (and hence, application to the corresponding direct form follows as a special case), and is independent of the order, type of quantization, and whether the accumulator is single- or double-length. Bounds on the amplitude and period of possible limit cycles are presented. The robustness of the algorithm in terms of limit cycle performance with respect to filter coefficient perturbations is verified. The algorithm is then used to obtain regions in the coefficient space where a filter of given order is limit cycle free. In this process, we have obtained limit cycle free regions that were previously unknown for the Two's complement case.

UR - http://www.scopus.com/inward/record.url?scp=0029179785&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029179785&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3

SP - 2035

EP - 2038

BT - Proceedings - IEEE International Symposium on Circuits and Systems

A2 - Anon, null

PB - IEEE

ER -