IDENTIFICATION OF IMPULSE RESPONSE BY USE OF SMOOTH INPUT SIGNALS.

Shuichi Adachi, Masahiro Ibaragi, Akira Sano

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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 languageEnglish
Pages (from-to)36-44
Number of pages9
JournalElectronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)
Volume69
Issue number12
Publication statusPublished - 1986 Dec

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Impulse response
Autocorrelation
Mean square error

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering

Cite this

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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.",
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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.

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