### Prony's Method

There are several variations on equation-error minimization, and some confusion in terminology exists. We use the definition of*Prony's method*given by Markel and Gray [48]. It is equivalent to ``Shank's method'' [9]. In this method, one first computes the denominator by minimizing

*ratio error*(as used in

*linear prediction*) for the all-pole part , with the first terms of the time-domain error sum discarded (to get past the influence of the zeros on the impulse response). When , it coincides with the covariance method of linear prediction [48,47]. This idea for finding the poles by ``skipping'' the influence of the zeros on the impulse-response shows up in the stochastic case under the name of

*modified Yule-Walker equations*[11]. Now, Prony's method consists of next minimizing output error with the pre-assigned poles given by . In other words, the numerator is found by minimizing

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The Padé-Prony Method

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An FFT-Based Equation-Error Method