A new theoretical approach for Prony’s method. (English) Zbl 0711.62082
The authors present two new results about R. Prony’s method [J. École Polytech. Paris 1(2), 24-96 (1975)] including an extension of the geometric method of T. L. Henderson [IEEE Trans. Acoust. Speech Signal Process. 29, 982-988 (1981)] to the case of multiple poles, and the development of a new method for eliminating known poles from a time series in order to compute the remaining poles.
Reviewer: V.V.Krakhotko
MSC:
| 62M15 | Inference from stochastic processes and spectral analysis |
| 93E12 | Identification in stochastic control theory |
References:
| [1] | Auton, J. R.; Van Blaricum, M. L., Investigation of Procedures for Automatic Resonance Extraction from Noisy Transient Electromagnetics Data, AFWL Math. Note 79, Vols. I, II, III (1981), General Research Corp: General Research Corp Santa Barbara, Calif |
| [2] | Fuhrman, P. A., On the partial realization problem and the recursive inversion of Hankel and Toeplitz matrices, (Contemporary Mathematics: Linear Algebra and Its Role in System Theory (1985), Amer. Math. Soc: Amer. Math. Soc Providence) |
| [3] | Heinig, G.; Rost, K., Algebraic Methods for Toeplitz-like Matrices and Operators (1984), Birkhaüser: Birkhaüser Boston · Zbl 0549.15013 |
| [4] | Henderson, T. L., Geometric methods for determining system poles from transient response, IEEE Trans. Acoust. Speech Signal Process, ASSP-29 (1981) |
| [5] | T.L. Henderson, Irregularly spaced samples and the theory of generalized aliasing in spectral pole identification, personal communication.; T.L. Henderson, Irregularly spaced samples and the theory of generalized aliasing in spectral pole identification, personal communication. |
| [6] | Karlin, S.; Studden, W. J., Tchebycheff Systems: With Applications in Analysis and Statistics (1966), Wiley-Interscience: Wiley-Interscience New York · Zbl 0153.38902 |
| [7] | Kulp, R. W., An optimum sampling procedure for use with the Prony method, IEEE Trans. Electromagnetic Compatibility, EMC-23, 2, 67-71 (1981) |
| [8] | Poggio, A. J.; Van Blaricum, M. L.; Miller, E. K.; Mittra, R., Evaluation of a processing technique for transient data, IEEE Trans. Antennas and Propagation, AP-26, 167-173 (1978) |
| [9] | Pólya, G.; Szegö, G., Aufgaben und Lehrsätze aus der Analysis, Band II (1925), Springer-Verlag: Springer-Verlag Berlin · JFM 51.0173.01 |
| [10] | Prony, R., Essai Experimental et Analytique…, J. École Polytech. Paris, 1, 2, 24-96 (1795) |
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