Using the matrix pencil method to estimate the parameters of a sum of complex exponentials
- 1 February 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Antennas and Propagation Magazine
- Vol. 37 (1) , 48-55
- https://doi.org/10.1109/74.370583
Abstract
The approximation of a function by a sum of complex exponentials is a problem that is at least two centuries old. Fundamentally, all techniques discussed in this article proceed from using the same sequence of data samples and vary only, but importantly, in how those samples are used in achieving the parameter estimation. All of these techniques, in other words, seek the same quantitative parameters to represent the sampled data, but use different routes to get there. The techniques for estimating the parameters are either linear or nonlinear. The linear techniques are emphasized in this presentation. In particular, the matrix pencil method is described, which is more robust to noise in the sampled data. The matrix pencil approach has a lower variance of the estimates of the parameters of interest than a polynomial-type method (Prony's method belongs to this category), and is also computationally more efficient. A bandpass version of the matrix pencil can be implemented in hardware, utilizing an AT&T DSP32C chip operating in real time. A copy of the computer program implementing the matrix pencil technique is given in the appendix.<>Keywords
This publication has 38 references indexed in Scilit:
- An improved pencil-of-functions method and comparisons with traditional methods of pole extractionIEEE Transactions on Antennas and Propagation, 1987
- Rational modeling by pencil-of-functions methodIEEE Transactions on Acoustics, Speech, and Signal Processing, 1983
- Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noiseIEEE Transactions on Acoustics, Speech, and Signal Processing, 1982
- Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihoodProceedings of the IEEE, 1982
- Suboptimal approximation/identification of transient waveforms from electromagnetic systems by pencil-of-function methodIEEE Transactions on Antennas and Propagation, 1980
- Problems and solutions associated with Prony's method for processing transient dataIEEE Transactions on Antennas and Propagation, 1978
- A technique for extracting the poles and residues of a system directly from its transient responseIEEE Transactions on Antennas and Propagation, 1975
- Filter analysis by use of pencil of functions: Part IIEEE Transactions on Circuits and Systems, 1974
- Filter analysis by Grammian methodIEEE Transactions on Audio and Electroacoustics, 1973
- Identification of linear systems through a Grammian technique†International Journal of Control, 1970