A Modified Prony Algorithm for Exponential Function Fitting
نویسندگان
چکیده
A modification of the classical technique of Prony for fitting sums of exponential functions to data is considered. The method maximizes the likelihood for the problem (unlike the usual implementation of Prony’s method, which is not even consistent for transient signals), proves to be remarkably effective in practice, and is supported by an asymptotic stability result. Novel features include a discussion of the problem parametrization and its implications for consistency. The asymptotic convergence proofs are made possible by an expression for the algorithm in terms of circulant divided difference operators.
منابع مشابه
A Modified Prony Algorithm for Fitting Functions Defined by Difference Equations
This paper reformulates, generalizes and investigates the stability of the modified Prony algorithm introduced by Osborne (1975), with special reference to rational and exponential fitting. The algorithm, originally for exponential functions, is generalized to the least squares fitting of any function which satisfies a linear homogeneous difference equation. Using the difference equation formul...
متن کاملImproving the Performance of the Prony Method Using a Wavelet Domain Filter for MRI Denoising
The Prony methods are used for exponential fitting. We use a variant of the Prony method for abnormal brain tissue detection in sequences of T 2 weighted magnetic resonance images. Here, MR images are considered to be affected only by Rician noise, and a new wavelet domain bilateral filtering process is implemented to reduce the noise in the images. This filter is a modification of Kazubek's al...
متن کاملA Modified Prony Algorithm for Estimating Sinusoidal Frequencies
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...
متن کاملModification of exponential based hyperelastic strain energy to consider free stress initial configuration and Constitutive modeling
In this research, the exponential stretched based hyperelastic strain energy was modified to provide the unstressed initial configuration. To this end, as the first step, the model was calibrated by the experimental data to find the best material parameters. The fitting results indicated material stability in large deformations and basic loading modes. In the second step, the initial pseudo str...
متن کاملParameter estimation for nonincreasing exponential sums by Prony–like methods
Let zj := e fj with fj ∈ (−∞, 0] + i [−π, π) be distinct nodes for j = 1, . . . ,M . With complex coefficients cj 6= 0, we consider a nonincreasing exponential sum h(x) := c1 e f1 x + . . . + cM e fM x (x ≥ 0). Many applications in electrical engineering, signal processing, and mathematical physics lead to the following problem: Determine all parameters of h, if 2N sampled values h(k) (k = 0, ....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 16 شماره
صفحات -
تاریخ انتشار 1995