Analysis of time-invariant systems in the time and frequency domain by associated linear equations (ALEs)

Previous work has demonstrated that if a system possesses a Volterra series representation, it can be described by a series of associated linear equations (ALEs). Each ALE produces a particular Volterra operator. The versatility of this methodology allows the independent observation of each harmonic order component in the system response. In the frequency domain the associated frequency response functions (AFRFs) are shown to be easier to analyse and interpret than the more complicated higher-order frequency response functions (HFRFs). Based on a single bi-dimensional graph a full analysis of the system's harmonic behaviour is carried out for the single degree of freedom (sdof) case.