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Showing papers on "Volterra series published in 1973"


Journal ArticleDOI
TL;DR: A general characterization of multi-input movement detection models is given in terms of the Volterra series formalism, when nonlinearities of order higher than the second are negligible and an n-input system can be decomposed into a set of 2-input systems, summing linearly.
Abstract: A general characterization of multi-input movement detection models is given in terms of the Volterra series formalism. When nonlinearities of order higher than the second are negligible, an n-input system can be decomposed into a set of 2-input systems, summing linearly. For a (symmetrical) 2-input system which has significant nonlinearities only up to the second order, the correlation model is its most general expression, if the infinite time average of the output is taken. Specific observations from optomotor experiments (e.g. phase invariance and contrast frequency dependence) can be interpreted in a general way in terms of properties of the Volterra representation.

213 citations


Journal ArticleDOI
TL;DR: A new analysis approach to understand and minimize nonlinear distortion in bipolar transistors is presented, employing a recently developed nonlinear device model, known as the integral charge control model, and a powerful analysis tool: the Volterra series representation.
Abstract: A new analysis approach to understand and minimize nonlinear distortion in bipolar transistors is presented. It employs a recently developed nonlinear device model, known as the integral charge control model, and a powerful analysis tool: the Volterra series representation. The salient analytical features of this paper are: a simple representation of the Volterra transfer functions of the transistor, compact expressions for frequency-dependent distortion coefficients, and physically meaningful asymptotic low- and high-frequency distortion coefficients. The analytical results have been experimentally verified. Finally, specific design examples are furnished to illustrate the powerful nature of the above analytical expressions.

42 citations


Journal ArticleDOI
TL;DR: A numerical example based on an eight-storm record is included, where the objective function for the optimization procedure is the sum of squared deviations between observed and predicted output ordinates for all storms included in the record.
Abstract: Adopting a discretization scheme for input, output, and kernel functions of second-order Volterra series representation of the surface runoff system leads to a set of linear equations for the unknown ordinates of the two-kernel functions. The equations are solved by an iterative descent optimization procedure taking into account also additional constraining equations derived from the properties of the kernel functions and the definition of the system adopted. The objective function for the optimization procedure is the sum of squared deviations between observed and predicted output ordinates for all storms included in the record. The inclusion of the constraining equations is done by an iterative scheme based on the penalty function method. The algorithm adopted for the solution converges to the optimal solution in a finite number of iterations, and its rate of convergence is independent of initial values adopted for the unknowns. A numerical example based on an eight-storm record is included.

37 citations


Journal ArticleDOI
Tomaso Poggio1
TL;DR: By means of the Volterra series an extension of the association properties of holography is proposed and the significance of non-linearities embedded within the formal structure of a holographic-like associative memory is pointed out.
Abstract: By means of the Volterra series an extension of the association properties of holography is proposed. Also, the significance of non-linearities embedded within the formal structure of a holographic-like associative memory is pointed out.

22 citations


Journal ArticleDOI
TL;DR: In this paper, a nonlinear system with memory and two input ports and one output port is considered, and it is assumed that the system can be represented by a double Volterra series.
Abstract: Consider a nonlinear system, with memory, which has two input ports and one output port. It is assumed that the system can be represented by a double Volterra series. Two results for such a system are stated in Part I. The first is a general expression for the sinusoidal components of the output y (t) when the two inputs x u (t) and x v (t) are sums of sinusoidal terms. The second result is an expression for the power spectrum of y (t) when x u (t) is a stationary Gaussian process and x v (t) = P cos pt. Part II is concerned with using results from the theory of Volterra series for multi-input systems to calculate the third-order distortion in an idealized frequency converter.

21 citations


Journal ArticleDOI
TL;DR: In this paper, the problem of determining the kernels in the discrete Volterra-series representation of a time-invariant non-linear discrete-time system is considered, and the identification problem is transformed to an optimal control problem, which is then solved using dynamic-programming formulation.
Abstract: The problem of determining the kernels in the discrete Volterra-series representation of a time-invariant non-linear discrete-time system is considered. The identification problem is transformed to an optimal control problem, which is then solved using dynamic-programming formulation. Examples illustrating the use of the techniques are presented.

16 citations


Journal ArticleDOI
TL;DR: In this paper, a general description of interchannel and intra-channel crosstalk interference created in a communications system is given in the form of a Volterra series expansion of the interference signal in terms of the signal which produced the interference.
Abstract: This paper studies a general description of interchannel and intra-channel crosstalk interference created in a communications system. This description is in the form of a Volterra series expansion of the interference signal in terms of the signal which produced the interference. From it we are able to precisely define the “intelligible” part of the crosstalk. This description also provides us with quantitative measures of the amount of crosstalk created in some communications channel by signals in another channel, as well as a measure (intelligible crosstalk ratio) of the amount of intelligible crosstalk produced. We then consider a particular model for the generation of intelligible crosstalk [or direct adjacent channel interference (DACI)] between two neighboring angle-modulated channels in which the signal in one channel adds to the signal of the second channel, the sum is filtered, and the filter output then passes through an AM-PM conversion device. Using our definition, a simple expression for the intelligible crosstalk ratio for this model is derived in terms of the filter characteristic. We observe that this crosstalk ratio exhibits a number of properties usually associated with DACI.

6 citations


Journal ArticleDOI
TL;DR: In this article, the Volterra kernels that characterize the various terms representing the free and forced response components are defined, and a convolution-type relationship between these kernels is developed.
Abstract: The discrete form of the Volterra series is used to evaluate the response of non-linear discrete-time systems. The Volterra kernels that characterize the various terms representing the free and forced response components are defined, and a convolution-type relationship between these kernels is developed.

5 citations


Journal ArticleDOI
TL;DR: The discrete form of the Volterra series is used to evaluate the response of a class of non-linear discrete-time systems described by an ordinary nonlinear difference equation with zero initial conditions.
Abstract: The discrete form of the Volterra series is used to evaluate the response of a class of non-linear discrete-time systems described by an ordinary nonlinear difference equation with zero initial conditions. Recurrence relations for the Volterra kernels are developed in the time domain and in the transform domain as well.

3 citations


01 Jan 1973
TL;DR: In this paper, a new analysis approach to understand and minimize non-linear distortion in bipolar transistors is presented, which employs a recently developed honlinear device model, known as the integral charge control model, and a powerful analysis tool: the Volterra series representation.
Abstract: A new analysis appioach to understand and minimize non- linear distortion in bipolar transistors is presented. It employs a recently developed honlinear device model, known as the integral charge control model, and a powerful analysis tool: the Volterra series representation. The salient analytical features of this paper are: a simple representation of the Volterra transfer functions of the transis- tor, Compact expressions for frequency-dependent distortion coef- ficients, and physically meaningful asymptotic low- and high-frequency distortion coefficients. The analytical results have been experimentally verified. Finally, specific design examples are furnished to illustrate.the powerful nature of the above analytical expressions.