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Estimation of generalized frequency response functions for quadratically and cubically nonlinear systems

The results in this paper are an important step towards routinely analysing nonlinear systems in the frequency domain and formed a foundation for part of EPSRC grant EP/F017715/1 £378K. The paper introduces new methods to estimate Volterra kernels which are one of the fundamental descriptors for nonlinear dynamic systems. The results have significant advantages compared to traditional methods because the new algorithms are based directly on time domain measurements and avoid all the problems of windowing and smoothing in multi dimensions which are a part of the old frequency domain methods.