We investigate the modified Prony algorithm of Osborne and Smyth (1991, 1993) applied to the estimation of the frequency of oscillation of a sinusoidal signal with added white noise, and compare it with the algorithms usually associated with the names of Prony and Pisarenko. We show that the Pisarenko algorithm returns O(N− 1 2 ) consistent estimates, and that the modified Prony algorithm retur...

Systems of Prony type appear in various signal reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. We propose a novel approach for solving Prony-type systems, which requires sampling the signal at arithmetic progressions. By keeping the number of equations small and fixed, we demonstrate that such “decimation” can lead ...

In this paper, signals measured by phasor measurement units (PMUs) are used to monitor power system small signal stability. In the proposed method, proper signals selected based on the modes observability and Prony analysis is employed to extract signal damping information (amplitude and frequency of participated modes) in real-time. The proposed method is simulated using a test signal in ideal...

Vortex induced vibrations (VIV) of long flexible risers subjected to ocean currents exhibit a strongly nonlinear phenomenon. Although significant efforts have been done for the frequency or time-frequency analysis of this complicated phenomenon, an effective method is still lacking. The objective of this paper is to provide a new method — a Prony-based method — for analyzing the time-varying fr...

We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in “near-colliding” situations. We consider a case when the structure of the system is a-priori fixed. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recentl...

Waveforms obtained from a superconducting Fault Current Limiter are investigated using the Prony modelling technique. Comparable measurements with the use of standard tools of spectral analysis (like FFT) fail because of short data available and low levels of higher spectral components. Streszczenie. W pracy przedstawiono wyniki analizy widmowej prądów i napięć zarejestrowanych w obwodach z nad...

This paper extends the Prony method to the identification of a class of fuzzy systems parameterized by a set of time-varying parameters. The Prony formulation is an optimal solution minimizing the fluctuation effects while accurately estimating the time-varying system parameters. A closed-form and efficient algorithm for adaptively calculating the time-varying parameters is derived. This soluti...

We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in “near-colliding” situations. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recently discovered “decimation” technique, we present an algorithm which appl...