### Abstract

When a delay of even one iteration is introduced in the coefficient update loop, the projection properties of the NLMS (normed least mean square) algorithm are lost, allowing the error vector to increase as well as decrease in any given update. This makes the analysis of the algorithm with delay much more difficult. An exact analysis of the delayed update algorithm, on a sample function basis, is developed. It is shown that for any delay, the gain parameter, can be chosen sufficiently small to guarantee exponential convergence, assuming only that the input satisfies the standard mixing condition.

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

Publisher | Publ by IEEE |

Pages | 2129-2132 |

Number of pages | 4 |

Volume | 3 |

ISBN (Print) | 078030033 |

State | Published - 1991 |

Event | Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91 - Toronto, Ont, Can Duration: May 14 1991 → May 17 1991 |

### Other

Other | Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91 |
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City | Toronto, Ont, Can |

Period | 5/14/91 → 5/17/91 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing*(Vol. 3, pp. 2129-2132). Publ by IEEE.

**Sample convergence of the normed LMS algorithm with feedback delay.** / Voltz, Peter.

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

*Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing.*vol. 3, Publ by IEEE, pp. 2129-2132, Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 91, Toronto, Ont, Can, 5/14/91.

}

TY - GEN

T1 - Sample convergence of the normed LMS algorithm with feedback delay

AU - Voltz, Peter

PY - 1991

Y1 - 1991

N2 - When a delay of even one iteration is introduced in the coefficient update loop, the projection properties of the NLMS (normed least mean square) algorithm are lost, allowing the error vector to increase as well as decrease in any given update. This makes the analysis of the algorithm with delay much more difficult. An exact analysis of the delayed update algorithm, on a sample function basis, is developed. It is shown that for any delay, the gain parameter, can be chosen sufficiently small to guarantee exponential convergence, assuming only that the input satisfies the standard mixing condition.

AB - When a delay of even one iteration is introduced in the coefficient update loop, the projection properties of the NLMS (normed least mean square) algorithm are lost, allowing the error vector to increase as well as decrease in any given update. This makes the analysis of the algorithm with delay much more difficult. An exact analysis of the delayed update algorithm, on a sample function basis, is developed. It is shown that for any delay, the gain parameter, can be chosen sufficiently small to guarantee exponential convergence, assuming only that the input satisfies the standard mixing condition.

UR - http://www.scopus.com/inward/record.url?scp=0026287622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026287622&partnerID=8YFLogxK

M3 - Conference contribution

SN - 078030033

VL - 3

SP - 2129

EP - 2132

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

PB - Publ by IEEE

ER -