LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequency-domain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. This technique extracts values of the Volterra nonlinear transfer functions and stores these values in binary files. Using these files, the modeled substem can be simulated for an arbitrary periodic input expressed as a finite sum of sines and cosines. Furthermore, the extraction can be based on any circuit simulator that is capable of steady state simulation. Thus a large system can be divided into smaller subsystems, each of which is characterized by circuit level simulations or lab measurements. The total system can then be simulated using the subsystem characterization stored as tables in binary files.

In this contribution we present a novel algorithm for the efficient computation of the output of Volterra filters in diagonal coordinate representation (DCR), while allowing for different memory length for each kernel. This is achieved by extending partitioned block filtering methods for fast convolution in the discrete Fourier transform (DFT) domain to Volterra filters. It is shown that the DCR is particularly favorable for modeling the cascade of a Volterra filter followed by a linear filter, as required for applications such as nonlinear acoustic echo cancellation. To obtain a corresponding adaptive structure of the proposed approach, we introduce a generalization of a known DFT-domain adaptive algorithm for linear systems to Volterra filters.

In this thesis, the mapping capability of the Gabor polynomial is reviewed and the nonlinear mapping capability of Multi-layer perceptron(MLP) is discussed in terms of the number of parameters used to represent them. It is shown that the pattern storage capability of multi-variate polynomial is much higher than the commonly used lower bound on multilayer perceptron pattern storage. It is also shown that multi-layer perceptron networks having second and third degree polynomial activations can be constructed which implement Gabor polynomials and therefore have the same high pattern storage capability. The polynomial networks are mapped to a conventional sigmoidal MLP resulting in highly efficient network. It is shown clearly that albeit techniques like output weight optimization and con...