A discussion of various approaches to the linear system identification problem
- 1 June 1984
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Acoustics, Speech, and Signal Processing
- Vol. 32 (3) , 654-656
- https://doi.org/10.1109/tassp.1984.1164338
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.Keywords
This publication has 10 references indexed in Scilit:
- Factorial linear modelling, algorithms and applicationsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Rational modeling by pencil-of-functions methodIEEE Transactions on Acoustics, Speech, and Signal Processing, 1983
- Approximation by a Sum of Complex Exponentials Utilizing the Pencil of Function MethodPublished by Springer Nature ,1983
- A discussion of various approaches to the identification/approximation problemIEEE Transactions on Antennas and Propagation, 1982
- Suboptimal approximation/identification of transient waveforms from electromagnetic systems by pencil-of-function methodIEEE Transactions on Antennas and Propagation, 1980
- On the simultaneous estimation of poles and zeros in speech analysisIEEE Transactions on Acoustics, Speech, and Signal Processing, 1977
- Linear Prediction of SpeechPublished by Springer Nature ,1976
- Linear prediction: A tutorial reviewProceedings of the IEEE, 1975
- Filter analysis by use of pencil of functions: Part IIEEE Transactions on Circuits and Systems, 1974
- The Retrieval of Harmonics from a Covariance FunctionGeophysical Journal International, 1973