Volterra series

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

Identification of nonlinear physiological systems

Abstract: Preface. 1. Introduction. 1.1 Signals. 1.2 Systems and Models. 1.3 System Modeling. 1.4 System Identification. 1.5 How Common are Nonlinear Systems? 2. Background. 2.1 Vectors and Matrices. 2.2 Gaussian Random Variables. 2.3 Correlation Functions. 2.4 Mean-Square Parameter Estimation. 2.5 Polynomials. 2.6 Notes and References. 2.7 Problems. 2.8 Computer Exercises. 3. Models of Linear Systems. 3.1 Linear Systems. 3.2 Nonparametric Models. 3.3 Parametric Models. 3.4 State-Space Models. 3.5 Notes and References. 3.6 Theoretical Problems. 3.7 Computer Exercises. 4. Models of Nonlinear Systems. 4.1 The Volterra Series. 4.2 The Wiener Series. 4.3 Simple Block Structures. 4.4 Parallel Cascades. 4.5 The Wiener-Bose Model. 4.6 Notes and References. 4.7 Theoretical Problems. 4.8 Computer Exercises. 5. Identification of Linear Systems. 5.1 Introduction. 5.2 Nonparametric Time-Domain Models. 5.3 Frequency Response Estimation. 5.4 Parametric Methods. 5.5 Notes and References. 5.6 Computer Exercises. 6. Correlation-Based Methods. 6.1 Methods for Functional Expansions. 6.2 Block Structured Models. 6.3 Problems. 6.4 Computer Exercises. 7. Explicit Least-Squares Methods. 7.1 Introduction. 7.2 The Orthogonal Algorithms. 7.3 Expansion Bases. 7.4 Principal Dynamic Modes. 7.5 Problems. 7.6 Computer Exercises. 8. Iterative Least-Squares Methods. 8.1 Optimization Methods. 8.2 Parallel Cascade Methods. 8.3 Application: Visual Processing in the Light Adapted Fly Retina. 8.4 Problems 8.5 Computer Exercises. References. Index. IEEE Press Series in Biomedical Engineering.

Transistor distortion analysis using volterra series representation

Abstract: Intermodulation distortion due to nonlinear elements in transistors is analyzed using Volterra series representation. It is shown that this technique is well suited for the analysis of transistor distortion where the nonlinearities are small but frequency dependent. An ac transistor model incorporating four nonlinearities is briefly described. The nonlinear nodal equations of the model are successively solved by expressing nodal voltages in terms of the Volterra series expansion of the input voltage. Based on this analysis, a digital computer program has been developed which computes the second and the third harmonic distortion for a given set of input frequencies and transistor parameters. The results compare favorably with measured values. This method also enables the derivation of closed form ac expressions for a simplified model; these expressions show the dependence of distortion on frequency, load and source impedances, bias currents and voltages, and the parameters of the transistor. The technique is also extended to cascaded transistors, and simplified expressions for the overall distortion in terms of the distortion and gain of individual transistors are derived. Finally, a few pertinent practical applications are discussed.

Behavioral modeling of RF power amplifiers based on pruned volterra series

Abstract: Behavioral modeling techniques provide a convenient and efficient means to predict system-level performance without the computational complexity of full circuit simulation or physics-level analysis of nonlinear systems, thereby significantly speeding up the analysis process. General Volterra series based models have been successfully applied for radio frequency (RF) power amplifier (PA) behavioral modeling, but their high complexity tends to limit their applications to "weakly" nonlinear systems. To model a PA with strong nonlinearities and long memory effects, for example, the general Volterra model involves a great number of coefficients. In this letter, we propose a new simplified Volterra series based model for RF power amplifiers by employing a "near-diagonality" pruning algorithm to remove the coefficients which are very small, or else not sensitive to the output error, therefore dramatically reducing the complexity of the behavioral model.

Output Frequency Characteristics of Nonlinear Systems

Abstract: Some interesting properties of output frequencies of Volterra-type nonlinear systems are particularly investigated. These results provide a very novel and useful insight into the super-harmonic and inter-modulation phenomena in output frequency response of nonlinear systems, with consideration of the effects incurred by different nonlinear components in the system. The new properties theoretically demonstrate several fundamental output frequency characteristics and unveil clearly the mechanism of the interaction (or coupling effects) between different harmonic behaviors in system output frequency response incurred by different nonlinear components. These results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities. They can provide an important guidance to modeling, identification, control and signal processing by using the Volterra series theory in practice.

Statistical inference for time-varying ARCH processes

Abstract: In this paper the class of ARCH(oo) models is generalized to the nonstationary class of ARCH(oo) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation "locally stationary ARCH(oo) process." The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < oo) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.