Adaptation of the Short Time Fourier Transform for Analysis of Nonlinear Time-Varying Continuous Systems

Guillermo Manuel Flores Figueroa, Juan Alejandro Vazquez Feijoo, Guillermo Urriolagoitia Sosa

Abstract: The most commonly used tool for system analysis is the Fourier Transform, which can be applied to linear continuous systems. If a linear system is time-varying, the Short-Time Fourier Transform can be used. In another hand, the Volterra transform can consider an extension of the Fourier transform that is applied basically to continuous nonlinear systems. By the use of the Associated Linear Equations that are parametric models of Volterra operators, the present work obtains the Short-Time Fourier Transform for continuous nonlinear systems. The Short-Time Higher-Order Frequency Response Function is also defined

Keywords: Nonlinear systems, time-invariant systems, Frequency Response Function, Associated Linear Equations, Short-Time Fourier Transform, Volterra series