Showing papers on "Volterra series published in 1975"

Identification of nonlinear systems using random impulse train inputs

Abstract: Nonlinear systems that require discrete inputs can be characterized by using random impulse train (Poisson process) inputs. The method is analagous to the Wiener method for continuous input systems, where Gaussian white-noise is the input. In place of the Wiener functional expansion for the output of a continuous input system, a new series for discrete input systems is created by making certain restrictions on the integrals in a Volterra series. The kernels in the new series differ from the Wiener kernels, but also serve to identify a system and are simpler to compute. For systems whose impulse responses vary in amplitude but maintain a similar shape, one argument may be held fixed in each kernel. This simplifies the identification problem. As a test of the theory presented, the output of a hypothetical second order nonlinear system in response to a random impulse train stimulus was computer simulated. Kernels calculated from the simulated data agreed with theoretical predictions. The Poisson impulse train method is applicable to any system whose input can be delivered in discrete pulses. It is particularly suited to neuronal synaptic systems when the pattern of input nerve impulses can be made random.

Distortion in variable-capacitance diodes

Abstract: Distortion in variable-capacitance diodes is analyzed using the Volterra series approach. Closed-form expressions for intermodulation distortion produced by variable-capacitance diodes in series- and parallel-tuned circuits are derived and verified by experiment at frequencies up to 200 MHz. The choice of the diode capacitance law exponent for minimum distortion is investigated. Distortion in multiple-diode connections is analyzed and the advantages of the back-to-back connection is shown. Calculation shows the elimination of third-order distortion for n=0.5 in this connection.

Scattering analysis of nonlinearly loaded antennas

Abstract: A novel technique-Volterra series analysis-is applied to the analysis of a nonlinearly loaded antenna. The electromagnetic field problem is first reduced to a network problem by application of the method of moments. The nonlinear network problem is then solved using the Volterra technique. A procedure with sinusoidal inputs for obtaining a time domain solution from the frequency domain solution without using fast Fourier transform techniques is demonstrated. The i-v characteristic of the nonlinear load is approximated from scattered power measurements. The derived i-v characteristic is then used to predict scattered power levels at different intermodulation responses of the loaded antenna.

Estimation and analysis of nonlinear stochastic systems.

Abstract: The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

On discrete-time AGC amplifiers

Abstract: Continuous automatic gain control (AGC) amplifiers have received much attention in the past due to their widespread usage in radar, sonar, communications, and other electronic systems. A reexamination of the AGC problem for the discrete-time counterpart is presented in this paper. It is shown that the appealing notion of merely equating the response with the sampled response of an analogous continuous model is often not satisfactory, especially when the response time is of the order of the sampling time. A general solution to the large-signal response of the discrete AGC amplifier involves a nonlinear difference equation and is solved by using a discrete Volterra series representation. Several feedback functions that have received attention in the past for continuous AGC amplifiers are considered: exponential, p th-law, and linear. In addition, a new configuration called "geometric feedback" is introduced that has certain desirable properties, namely, the feedback function can be tailored to give the desired large-signal transient response while the small-signal bandwidth remains independent of input level.

High Frequency Distortion Analysis of a Semiconductor Diode for CATV Applications

Abstract: Intermodulation distortion generated in a semiconductor diode in series with a resistor is analysed using a Volterra series representation. The equivalent circuit of a diode includes the nonlinear junction conductance, nonlinear junction capacitance, series resistance and series inductance. Nonlinear terms up to and including the fifth order are considered. It is shown that for the VHF range of frequencies the diode capacitance can significantly affect the magnitude and phase of the total distortion at a given product frequency.

On the impossibility of a partial mass violation in surface runoff systems

Abstract: The class of nonnegative, initially relaxed, and nonanticipating systems has many applications in engineering. In this paper a proof is given to a theorem stating that in this class of systems, if the input total mass is equal to the output total mass, then for any nonnegative input-output pair, the system fulfills also a partial mass condition. In applying this theorem to systems expressed by the Volterra series it is concluded that the input functions must be bounded. Two such bounds on the input functions are considered: (1) bounds resulting from the requirement of a nonnegative output and (2) bounds resulting from the mass-conserving property of the system. The theorem mentioned above implies that the set of input functions causing nonnegative output functions is a subset of the set of input functions that do not violate the mass-conserving property of the system. It is therefore clear that the bounds of type 1 are the dominant among the two bounds for any nonnegative input function. In a system expressed by an Nth order Volterra series the bounds on the input can be evaluated by solving a polynomial inequality of order N - 1. An example is given for a system expressed by a third-order Volterra series in which the bounds on the input form two regions. Explicit equations for the bounds of type 1 and 2 are derived for a second-order system.

Volterra Series Synthesis of Nonlinear Stochastic Tracking Systems

Abstract: One of the most important objectives of a radar angle-tracking loop is to keep the target within the beamwidth of the radar antenna. Thus, the behavior of the antenna pointing error is of vital interest in determination of tracking performance. For a tracker with a general polynomial linearity (representing nonlinear receiver characteristics), subjected to constant line-of-sight rate inputs, random initial antenna pointing errors, and white Gaussian receiver noise, a method to obtain approximations to the transient mean and variance of the antenna pointing error as explicit functions of time is presented.

Reachability, observability, and realization theory for factorable Volterra systems

Abstract: A long standing approach to nonlinear system theory is the use of Volterra series to represent Input/output behavior. Techniques have been developed for determining the terms in the series from differential equation descriptions and from Input/output experiments. However the generality of this representation in a sense ignores structural features of the system under consideration, and this often precludes mathematical tractibility.

Volterra Series Synthesis ofNonlinear Stochastic Tracking Systems

Abstract: Oneofthemostimportant objectives ofaradar angle-tracking loop istokeepthetarget within thebeamwidth oftheradar antenna. Thus,thebehavior oftheantennapointing errorisofvital interest in determination oftracking performance. Foratracker withageneral polynomial linearity (representing nonlinear receiver characteristics), subjected toconstant line-of-sight rateinputs, randominitial antenna pointing errors, andwhiteGaussian receiver noise, amethodto obtain approximations tothetransient meanandvariance ofthe antenna pointing error asexplicit functions oftimeispresented. Avital function ofanangle-tracking loop istomaintain aninterceptor's radar antenna pointed atamoving target in space. Aninterceptor-target