Abstract-Volterra series have been in the engineering literature for some time now, and yet there have been few attempts to measure Volterra kernels. This paper discusses techniques for measuring the Volterra kernels of weakly nonlinear systems. We introduce a new quick method for measuring the second Volterra kernel which is analogous to pseudo-noise testing of a linear device. To illustrate the discussion we present an experimental example, an electro-acoustic transducer. Throughout the paper we emphasize the practical aspects of kernel measurement. V I. INTRODUCTION:PURPOSEAND POINTOFVIEW OLTERRA SERIES have appeared in the engineering literature for 40 years now. There have been many articles devoted to theoretical issues such as existence of Volterra series (e.g., [ l]-[3]) computation of Volterra kernels

In this paper we carefully study the analysis involved with Volterra series. We address system-theoretic issues ranging from bounds on the gain and incremental gain of Volterra series operators to the existence of Volterra series operator inverses, and mathematical topics such as the relation between Volterra series operators and Taylor series. The proofs are complete, and use only the basic facts of analysis. We prove a general Steady-state theorem for Volterra series operators, and then establish a general formula for the spectrum of the output of a Volterra series operator in terms of the spectrum of a periodic input. This paper is meant to complement recent work on Volterra series expansions for dynamical systems.

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.