A novel interpretation of Prony's method

Article Abstract:

A new interpretation of Prony's method enables its connection to the theory of orthogonal polynomials for the solution of minimization problems. The first two steps in Prony's method are interpreted as approximation problems. A non-homogeneous, constant coefficient, linear difference equation is fitted so that the non-homogeneous part is minimized in the least squares sense for measured samples. A homogeneous solution to the equation is developed that minimizes the particular solution and approximates the general solution.

Polynomials, Product introduction, Applications, New Technique, Minimization, Difference Equations

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Comments on 'An exponential second-order probability-density function.' (comments) (technical)

Article Abstract:

The exponential function proposed by Pyati for probability density is not superior to the joint probability density function (JPDF ) used by Barrick for the same application. Barrick's JPDF is valid for small point separations but unrealistic when the limit of r approaches infinity. Pyati's JPDF is an infinite sum and extremely difficult to manipulate. In situations with close point spacing, it is a gross failure.

Mathematical models, Probability, Functions, Functions (Mathematics)

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A Prony Method for Noisy Data: Choosing the Signal Components and Selecting the Order in Exponential Signal Models

Article Abstract:

Improvements on Prony's method for determining values of parameters of a linear combination of exponential functions are based on low-rank approximations to data matrices. A simple procedure is presented for estimation of signal parameters in the presense of noise. Data are illustrated in a table and in a graph.

Numerical analysis, Noise (Sound), Signal processing, Noise, Applied Mathematics

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