Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

Application of the Volterra Series to the Analysis and Design of an Angle Track Loop

Abstract: A typical function of an angle tracking loop is to keep a radar antenna pointed at a target. The error in pointing is directly related to successful operation of the tracking device; therefore, its behavior is of interest. For a tracker with a general polynomial nonlinearity, an arbitrary initial pointing error, and a bounded deterministic input, a method is developed for finding upper bounds on the magnitude of the tracking error using Volterra series techniques. Convergence regions of the Volterra series are also obtained. Applications of these results are made to a second-order tracking device.

A model-order reduction method based on krylov subspaces for mimo bilinear dynamical systems

Abstract: In this paper, we present a Krylov subspace based projection method for reduced-order modeling of large scale bilinear multi-input multioutput (MIMO) systems. The reduced-order bilinear system is constructed in such a way that it can match a desired number of moments of multivariable transfer functions corresponding to the kernels of Volterra series representation of the original system. Numerical examples report the effectiveness of this method.

Volterra-system identification using adaptive real-coded genetic algorithm

Abstract: In this paper, a floating-point genetic algorithm (GA) for Volterra-system identification is presented. The adaptive GA method suggested here addresses the problem of determining the proper Volterra candidates, which leads to the smallest error between the identified nonlinear system and the Volterra model. This is achieved by using variable-length GA chromosomes, which encode the coefficients of the selected candidates. The algorithm relies on sorting all candidates according to their correlation with the output. A certain number of candidates with the highest correlation with the output are selected to undergo the first evolution "era". During the process of evolution the candidates with the least significant contribution in the error-reduction process is removed. Then, the next set of candidates are applied into the next era. The process continues until a solution is found. The proposed GA method handles the issues of detecting the proper Volterra candidates and calculating the associated coefficients as a nonseparable process. The fitness function employed by the algorithm prevents irrelevant candidates from taking part in the final solution. Genetic operators are chosen to suit the floating-point representation of the genetic data. As the evolution process improves and the method reaches a near-global solution, a local search is implicitly applied by zooming in on the search interval of each gene by adaptively changing the boundaries of those intervals. The proposed algorithms have produced excellent results in modeling different nonlinear systems with white and colored Gaussian inputs with/without white Gaussian measurement noise

Quadratic-linear filters for signal detection

Abstract: The second-order Volterra series (quadratic-linear) filter was synthesized under three different optimization criteria for signal detection The performance of the filters is shown to exceed that of quadratic-only or linear-only filters when the noise process is characterized by both separation in the mean and separation in variance The applications are in object detection and image segmentation, especially in model-drive approaches to these problems For 2-D applications, the mapping order of pixels into the signal vector is shown to have no effect on the optimality of the filters, regardless of nonlinearity >

Identifying the main nonlinear contributions: use of multisine excitations during circuit design

Abstract: Modeling and understanding the nonlinear behavior of analog and RF circuits is essential for good design of telecommunication systems. Classical Volterra series give the designer this necessary insight, but they are only valid for weakly nonlinear systems and they are difficult to edit. To overcome these limitations, we developed a technique to identify, quantify and qualify the sources of nonlinear behavior in analog and RF circuits by combining the information obtained by a set of simulations that use periodic excitation signals with a given power spectrum and arbitrary phases. The paper describes and demonstrates this approach by the analysis of the cascade of a BiCMOS power preamplifier and power amplifier with adaptive biasing for 5 GHz wireless local area networks (WLAN). The approach is applicable to weakly and strongly nonlinear systems, which is demonstrated by pushing the amplifier into compression. Furthermore, it provides useful design information, such as the contribution of each subcircuit to the overall nonlinear behavior.