### Abstract

This paper deals with the pole zero identification of a linear system from a measured input-output record. One objective is to show that the pencil-of-function method minimizes a weighted version of the Kalman equation error. It follows that the pencil-of-function method is capable of yielding robust estimates for poles located in a given region of the complex s plane. The second objective of this paper is to illustrate that identical sets of equations arise in three supposedly different analytical techniques for obtaining the impulse response of a system. The techniques investigated are 1) the least squares technique based on the discrete Wiener-Hopf equation, 2) Pisarenko's eigenvalue method, and 3) Jain's pencil-of-function method. The proof of equivalence is valid only for the noise-free case when the system order is known. Instead of using the conventional differential equation formulation, equivalence is shown with the integral form utilized in the pencil-of-function method.

Original language | English (US) |
---|---|

Pages (from-to) | 654-656 |

Number of pages | 3 |

Journal | IEEE Transactions on Acoustics, Speech, and Signal Processing |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1984 |

### ASJC Scopus subject areas

- Signal Processing

## Fingerprint Dive into the research topics of 'A Discussion of Various Approaches to the Linear System Identification Problem'. Together they form a unique fingerprint.

## Cite this

*IEEE Transactions on Acoustics, Speech, and Signal Processing*,

*32*(3), 654-656. https://doi.org/10.1109/TASSP.1984.1164338