Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials

Tapan K. Sarkar, Odilon Pereira

Research output: Contribution to journalArticlepeer-review

1062 Scopus citations


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 Appendix.

Original languageEnglish (US)
Pages (from-to)48-55
Number of pages8
JournalIEEE Antennas and Propagation Magazine
Issue number1
StatePublished - Feb 1995

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials'. Together they form a unique fingerprint.

Cite this