The properties of output frequencies of nonlinear volterra systems

Nonlinear systems usually have complicated output frequencies in the frequency domain. For the class of nonlinear Volterra systems, some interesting properties for system output frequencies are studied in this paper. These properties provide a novel insight into the output frequencies of Volterra systems, i.e., the periodicity of the output frequencies. They also demonstrate several novel frequency characteristics of system output spectrum such as the opposite property, and reveal clearly the nonlinear effects on system output spectrum from different nonlinearities. These new results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities, and provide an important guidance to applications of Volterra system theory in practices for analysis and design of nonlinear systems. Examples and discussions are given to illustrate these new results.