Volterra series

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

Applications of Multilinear and Waveform Relaxation Methods for Efficient Simulation of Interconnect-Dominated Nonlinear Networks

Abstract: Applications of multilinear and waveform relaxation methods are presented for efficient transient analysis of interconnect-dominated nonlinear networks. In this paper, two procedures that realize these well-known and fundamental theories in conventional circuit simulation tools are developed by taking advantage of the unique characteristics of interconnect networks. The multilinear theory uses the Volterra functional series to decompose the nonlinear network into multiple linear networks. Then, the solutions of the mildly nonlinear network are obtained from the linear combinations of sequences of responses of the decomposed linear networks. On the other hand, the waveform relaxation technique is used to solve networks with strong nonlinearity. The networks are partitioned into linear and nonlinear subnetworks and each subnetwork is solved iteratively using the waveform relaxation technique. Simplified analysis steps that give good insight into these techniques are also derived analytically. Finally, the accuracy and efficiency of the methods are verified with two examples.

Pseudorandom Test for Nonlinear Circuits Based on a Simplified Volterra Series Model

Abstract: Pseudorandom test of analog and mixed-signal circuits provides a low-cost test solution; however, its application has been restricted to linear circuit testing. This paper presents an efficient pseudorandom test method for nonlinear circuits. The method uses a simplified Volterra series model to characterize nonlinear behaviors of devices under test (DUTs) accurately with a low complexity algorithm. A multilevel pseudorandom sequence is used to excite DUTs over a wide range of frequencies and generate a spread-spectrum output response. The cross spectral density of the input test pattern and output response is computed to estimate the parameters of Volterra series and predict the performance of DUTs. In addition, the method can be used to compensate nonlinear errors of DUTs and improve performance. The mathematical background and simulation results are presented to validate the proposed method

Nonlinear multichannel active noise control using partial updates [acoustic noise control]

Abstract: We consider in this paper a model for nonlinear multichannel active noise controllers based on truncated Volterra filters. A previously proposed approximate affine projection (AP) adaptation algorithm is revisited with the aim of reducing its implementation complexity by applying suitable partial update strategies. The experimental results confirm that remarkable computational reductions are achieved with limited degradations of the convergence behavior.

Nonlinear Aspects of Telecommunications: Discrete Volterra Series and Nonlinear Echo Cancellation

Abstract: The discrete Volterra series holds particular value in the analysis of nonlinear systems in telecommunications. However, most books on the Volterra series either do not address this application or only offer a partial discussion. Nonlinear Aspects of Telecommunications provides an in-depth treatment of the Volterra series and the benefits it offers as a representation of nonlinear problems, particularly in echo cancellation in digital telecommunications systems.Beginning with the fundamentals of the discrete Volterra series, the author presents its basic definition, notions, conditions for convergence and stability, and its matrix representation for multiple-input and multiple-output nonlinear digital systems. He pays significant attention to the important problem of approximating a nonlinear digital system using the discrete Volterra series and offers new results in this area--results not yet available in other texts.The second part of the book uses the background of Part I to show the Volterra series' application to echo cancellation. It provides introductory material regarding the basics of adaptive cancellers, and analyzes structures for nonlinear echo cancellers using nonlinear transversal filters for baseband transmission. The last section covers nonlinear echo cancellers for voiceband transmission and interleaved structures.Full of illustrations, examples, and new results, Nonlinear Aspects of Telecommunications is your first and best resource for understanding and applying the discrete Volterra series to nonlinear echo cancellation problems.Features