Prony's Model

The Prony method is a linear combination of a set of Exponent items for fitting and equi-spacing sampling data. It can analyze the signal amplitude, phase, damping factor, frequency and other information.

As early as 1795, Prony proposed a linear combination of the complex exponent function to describe the mathematical model of the same interval sampling data, often known as the Prony model, and provided a linear approximate solution.Algorithm.

Under the background of interference noise, the strict solution of this model is a highly nonlinear optimization problem. For more than 200 years, people have provided approximation algorithms from various perspectives. These algorithms are not rigorous and optimal. This is because the Prony model is pathological in terms of numerical values. Non-strict and optimal algorithms are very sensitive to the noise impact, which greatly limits the application of the Prony model.

As an extension of the Fourier series, the Prony model is of great significance in both theory and application. As a linear spectral estimation method, it is widely used in signal processing in the fields of radar, underwater sound, earthquake, speech, photochemistry, and Optical Physics. If the model can be successfully applied to radar signal processing, it will fundamentally improve the radar target resolution.

 

You can learn about the Prony's model, which can be used in audio digital signal processing.