https://www.dtc.umn.edu/s/resources/gg-se.pdf

A bibliography on nonlinear system identification

In this study, digital higher-order spectral analysis and frequency-domain Volterra system models are utilized to yield a practical methodology for the identification of weakly nonlinear time-invariant systems up to third order. The primary focus is on consideration of random excitation of nonlinear systems and, thus, the approach makes extensive use of higher-order spectral analysis to determine the frequency-domain Volterra kernels, which correspond to linear, quadratic, and cubic transfer functions. Although the Volterra model is nonlinear in terms of its input, it is linear in terms of its unknown transfer functions. Thus, a least squares approach is used to determine the optimal (in a least squares sense) set of linear, quadratic, and cubic transfer functions. Of particular practical note, is the fact that the approach of this paper is valid for non-Gaussian, as well as Gaussian, random excitation. It may also be utilized for multitone inputs. The complexity of the problem addressed in this paper arises from two principal causes: (1) the necessity to work in a 3D frequency space to describe cubically nonlinear systems, and (2) the necessity to characterize the non-Gaussian random excitation by computing higher-order spectral moments up to sixth order. A detailed description of the approach used to determine the nonlinear transfer functions, including considerations necessary for digital implementation, is presented. >

Application of higher order spectral analysis to cubically nonlinear system identification

A frequency-domain block recursive least-square adaptive algorithm is presented for the identification of nonlinear systems which can be modeled by a third-order Volterra series. The identification algorithm is based on the application of the Volterra theory and adaptive signal-processing techniques. The approach does not assume any particular statistics of the input. Moreover, the adaptive algorithm can be used, with a little modification, for the identification of a second-order Volterra system driven by stationary random inputs. >

On the identification of a third-order Volterra nonlinear system using a frequency-domain block RLS adaptive algorithm

A nonlinearity compensation approach in the digital frequency domain which is based on the concept and theory of pth-order (here, p=3) inverses of Volterra nonlinear systems (i.e. linearizing a given nonlinear system) is presented. Since the pth-order postinverse of a system is identical to the pth-order preinverse, only the preinverse of a given system is considered. The third-order inverse operation is derived. It is based upon a discrete Volterra series representation. A simple example is given to demonstrate the validity of the digital frequency-domain approach for the compensation of some unwanted nonlinearities. >

On the linearization of Volterra nonlinear systems using third-order inverses in the digital frequency-domain

A hierarchical alternative updated adaptive Volterra filter with pipelined architecture

A new approach to FM distortion equalization is suggested and a nonlinear equalizer operating in the baseband frequency range is presented. It is shown that, using analog multipliers and differentiators, a baseband equalizer can be designed which eliminates all types of distortion products. The synthesis of the FM distortion equalizer is given with minimum number of multipliers. Using the synthesis procedure an equalizer circuit was designed for 1800 channel microwave FM systems. Experimental results obtained with the equalizer are discussed.

A. Baranyi

Papers

Nonlinear FM Distortion Equalizer