Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 3 , pp. 524-544

A MODIFIED PRONY ALGORITHM FOR SUM OF DAMPED OR UNDAMPED EXPONENTIAL SIGNALS

By

DEBASIS KUNDU, *Indian Institute of Technology*

SUMMARY. Osborne (1975) introduces a modified Prony algorithm for fitting sum of exponential to the real data sets. Smyth (1985) and Osborne and Smyth (1990) investigate the stability of the algorithm. They show by numerical comparison that the modifed Prony algorithm works better than any other standard non-linear regression algorithm. In this paper we generalize the concept of Osborne (1975) to the complex parameters case, which is very important in signal processing. We investigate its stability and show by numerical experiments that the modified Prony algorithm works very well for complex exponentials in complex noise also.

*AMS (1980) subject classification.* 62J02, 65D10, 65U05.

*Key words and phrases.* Prony's method, non-linear least squares, asymptotic stability, circulant matrix, consistent estimates, separable regression, normal equation, convergence matrix, discrete Fourier transform.

This paper in Mathematical Reviews.