Topic
Volterra series
About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.
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TL;DR: The second-order analysis of the output of a discrete-time nonlinear system described by a truncated Volterra series whose input consists of a sequence of independent random variables (white noise) is considered, and the computational aspects of the analysis are discussed with the aim of showing that in several situations closed-form results can be obtained.
Abstract: The second-order analysis of the output of a discrete-time nonlinear system described by a truncated Volterra series whose input consists of a sequence of independent random variables (white noise)is considered The main result consists of an explicit formula for the mean value of the output process in terms of the cumulants of the input and of Volterra kernels This formula, with suitable modifications, allows the calculation of the output correlation as well as of the continuous and discrete components of the spectral distribution Several applications are considered, and in particular the Gaussian white noise case is worked out in detail Finally, the computational aspects of the analysis are discussed with the aim of showing that in several situations closed-form results can be obtained
13 citations
TL;DR: In this paper, the truncation of Volterra series expansions is studied using the output frequency characteristics of nonlinear systems to develop a new algorithm for determining the terms to include in a VOLTERRA series expansion, and the results show the influence of both the generalized frequency response functions and properties of the input spectra on the significance of individual terms in the series.
Abstract: The truncation of Volterra series expansions is studied using the output frequency characteristics of nonlinear systems to develop a new algorithm for determining the terms to include in a Volterra series expansion. The results show the influence of both the generalized frequency response functions and properties of the input spectra on the significance of individual terms in the series. The effectiveness of the proposed method is demonstrated using simulation studies including the analysis of a single degree of freedom mechanical oscillator. Nonlinear system analyses using Volterra series theory must always be based on a truncated Volterra series description. The present study provides an effective strategy for determining which terms to include in the analysis of practical nonlinear systems based on Volterra series models.
13 citations
TL;DR: In this paper, the effects of weak nonlinearities of operational transconductance amplifiers (OTAs) on the performance of continuous-time OTA-capacitor (OTA-C) filters are investigated.
Abstract: Effects caused by weak nonlinearities of operational transconductance amplifiers (OTAs) on the performance of continuous-time OTA-capacitor (OTA-C) filters are investigated. Nonlinear phenomena, such as compression/expansion and desensitization, are examined and the resulting distortion of the transfer function shape of high-order OTA-C filters with sinusoidal inputs is discussed. The Volterra series method is used to represent filters by their nonlinear transfer function for computer analysis and simulation. Using this approach, distortion and interference criteria are established for predicting analytically the onset of nonlinear behavior in the frequency responses of OTA-C filters. Finally, representative calculation results are presented and verified via SPICE simulations.
13 citations
TL;DR: It is shown that the MLS used does enable the higher order kernels to be measured and the problems of selecting the correct sequences are discussed and the necessary system checks described.
Abstract: Previous work from this group (IHR, Southampton) has shown the feasibility of using maximum length sequence (MLS) stimulation to obtain evoked otoacoustic emissions (OAE). Because an MLS is one of a set of inputs that enables the Volterra series to be computed, we investigated its use with OAE. We wanted to see if the Volterra series could model the system and if we could extract the higher order kernels. In order to realise a practicable MLS system, a variant of the MLS has been used which permits real time recovery of the response and so enables the rejection of noisy epochs. This paper shows that the MLS used does enable the higher order kernels to be measured. The problems of selecting the correct sequences are discussed and the necessary system checks described.
13 citations
TL;DR: The second-and third-order distortion buildup in a CATV repeater system is analyzed by means of the Volterra series expansion of the output signal in terms of the input signal to see that the low-frequency phase intercepts are the dominant factors in determining the cascaded distortion.
Abstract: The second-and third-order distortion buildup in a CATV repeater system is analyzed by means of the Volterra series expansion of the output signal in terms of the input signal. Expressions for cascaded distortion products are given in terms of the single amplifier distortion product and the low frequency phase intercepts of the amplifier, cable equalizer, and cable itself. From these expressions it is also seen that the low-frequency phase intercepts are the dominant factors in determining the cascaded distortion. Conditions for cancellation of either the second-or third-order distortion products are then given.
13 citations