A Discussion of Various Approaches to the Linear System Identification Problem

Tapan K. Sarkar, Soheil A. Dianat

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageEnglish (US)
Pages (from-to)654-656
Number of pages3
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
Issue number3
StatePublished - Jun 1984
Externally publishedYes

ASJC Scopus subject areas

  • Signal Processing


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