### Abstract

Among the many identification methods of impulse response of linear discrete system, the recursive least squares method is well known because of its ease of handling and excellent convergency. This paper analyzes why the least squares estimates of an impulse response sequence degrade in convergency when one utilizes smooth input signals for identification and the number of data is finite. It also presents an effective identification method even under such a condition. The magnitude of the eigenvalue of the correlation matrix of input signal is adopted as a quantitative index of input signal smoothness and it is demonstrated that small valued eigenvalues increase the mean squares error of least squares estimate. Using the idea of eigenvalue expansion, we present a new online identification method which truncates small eigenvalues associated with the input autocorrelation matrix.

Original language | English |
---|---|

Pages (from-to) | 36-44 |

Number of pages | 9 |

Journal | Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi) |

Volume | 69 |

Issue number | 12 |

Publication status | Published - 1986 Dec |

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### ASJC Scopus subject areas

- Computer Networks and Communications
- Electrical and Electronic Engineering

### Cite this

*Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)*,

*69*(12), 36-44.

**IDENTIFICATION OF IMPULSE RESPONSE BY USE OF SMOOTH INPUT SIGNALS.** / Adachi, Shuichi; Ibaragi, Masahiro; Sano, Akira.

Research output: Contribution to journal › Article

*Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)*, vol. 69, no. 12, pp. 36-44.

}

TY - JOUR

T1 - IDENTIFICATION OF IMPULSE RESPONSE BY USE OF SMOOTH INPUT SIGNALS.

AU - Adachi, Shuichi

AU - Ibaragi, Masahiro

AU - Sano, Akira

PY - 1986/12

Y1 - 1986/12

N2 - Among the many identification methods of impulse response of linear discrete system, the recursive least squares method is well known because of its ease of handling and excellent convergency. This paper analyzes why the least squares estimates of an impulse response sequence degrade in convergency when one utilizes smooth input signals for identification and the number of data is finite. It also presents an effective identification method even under such a condition. The magnitude of the eigenvalue of the correlation matrix of input signal is adopted as a quantitative index of input signal smoothness and it is demonstrated that small valued eigenvalues increase the mean squares error of least squares estimate. Using the idea of eigenvalue expansion, we present a new online identification method which truncates small eigenvalues associated with the input autocorrelation matrix.

AB - Among the many identification methods of impulse response of linear discrete system, the recursive least squares method is well known because of its ease of handling and excellent convergency. This paper analyzes why the least squares estimates of an impulse response sequence degrade in convergency when one utilizes smooth input signals for identification and the number of data is finite. It also presents an effective identification method even under such a condition. The magnitude of the eigenvalue of the correlation matrix of input signal is adopted as a quantitative index of input signal smoothness and it is demonstrated that small valued eigenvalues increase the mean squares error of least squares estimate. Using the idea of eigenvalue expansion, we present a new online identification method which truncates small eigenvalues associated with the input autocorrelation matrix.

UR - http://www.scopus.com/inward/record.url?scp=0022910819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022910819&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022910819

VL - 69

SP - 36

EP - 44

JO - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 8756-6621

IS - 12

ER -