A multi-virtual-output approach to frequency domain analysis of exponential-type nonlinear systems

Nonlinear systems with exponential-type nonlinearity can be widely seen in system modeling (e.g., neural networks with Gaussian basis function). Understanding of this kind of nonlinearity in the frequency domain would be of significance for the analysis and design of corresponding nonlinear systems. To this aim, a systematic method is proposed for calculating the generalized frequency response functions (GFRFs) of exponential-type nonlinear systems. By assigning several intermediate states regarded as virtual outputs, the proposed method can effectively produce the GFRFs of the nonlinear system and thus the nonlinear characteristic output spectrum (nCOS) can be obtained readily which is shown very useful for the analysis and design of nonlinear systems in the frequency domain. Two examples, i.e., nonlinear distortion of an amplifier and a simple radial basis function neural network, are presented to illustrate the theoretical results. It is demonstrated that the proposed frequency-domain method provides a unique frequency-domain insight into the nonlinear influence incurred by exponential-type nonlinearity (e.g., the Gaussian basis function) on system output response (e.g., nonlinear circuit distortion, neural networks).