Prony's method and matrix pencil method performance on determining the complex natural resonance frequencies of a linear system

Characterization of a physical system is an important issue to approach some applied physics and engineering problems. The complex natural resonance frequencies of the system which are included in its impulsive response are characteristic of such system and are part of its description. Few works written in English language show a comparison among discrete methods that extract natural complex frequencies from a system impulsive response. Much less common is to find works written in Spanish language about this important research topic. Given this situation, important discrete numeric methods to estimate the complex natural resonance frequencies of a system through its impulsive response are described, tested and compared in different simulation scenarios in this document. According to the obtained results, the matrix pencil method with a SVD filter is the less sensitive method to the noise, while the Prony method and its different versions are the fastest ones. Scenarios that could be more suitable for each method are discussed.