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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01 May 2000
TL;DR: In this paper, the problem of symbolic analysis of nonlinear dynamical behavior in the design of analogue circuits and systems is addressed, where classical circuit and system level simulators rely on numerical simulations for that analysis, a symbolical method is considered here.
Abstract: The problem of the symbolic analysis of nonlinear dynamical behaviour in the design of analogue circuits and systems is addressed in this paper. Where classical circuit and system level simulators basically rely on numerical simulations for that analysis, a symbolical method is considered here. This method is based on the Volterra Series (VS). A short introduction on the use of VS in system analysis is given. An implementation of a symbolic system analysis tool in its first stages based on VS is described. Complexity and efficiency of the implemented methods are discussed. An example is given where the implemented analysis tool is used optimise a simple circuit. The results are verified with Spice. Finally, an outlook on the open problems of the current implementation is given.
9 citations
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TL;DR: A perturbation theoretic technique has been used to analyze an Ebers–Moll modeled transistor amplifier circuit and expressions derived can be used to derive corrections to the behavior of the amplifier when the input swing is not small enough.
Abstract: In this paper, a perturbation theoretic technique has been used to analyze an Ebers–Moll modeled transistor amplifier circuit. The main advantage of the proposed method is that the use of the perturbation technique helps to obtain more accurate closed form Volterra series. These expressions can be used to derive corrections to the behavior of the amplifier when the input swing is not small enough. The expressions derived in this paper can also be used for transistor parameter estimation, as variations in transistor parameters affect the circuit performance critically.
9 citations
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TL;DR: The evaluation results show that the CS algorithms can efficiently construct a sparse Volterra model for the super-RENS read- out channel and that observable nonlinear interactions take place among restricted components in the read-out channel.
Abstract: In this paper, we investigate the compressed sensing (CS) algorithms for modeling a super-resolution near-field structure (super-RENS) disc system with a sparse Volterra filter. It is well known that the super-RENS disc system has severe nonlinear inter-symbol interference (ISI). A nonlinear system with memory can be well described with the Volterra series. Furthermore, CS can restore sparse or compressed signals from measurements. For these reasons, we employ the CS algorithms to estimate a sparse super-RENS read-out channel. The evaluation results show that the CS algorithms can efficiently construct a sparse Volterra model for the super-RENS read-out channel and that observable nonlinear interactions take place among restricted components in the read-out channel.
9 citations
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TL;DR: A novel method to estimate the frequency-domain baseband equivalent Volterra kernels of cubically nonlinear bandpass channels in orthogonal frequencydivision multiplexing (OFDM) systems using the higher-order auto-moment spectra of the random multisine signal is proposed.
Abstract: Modeling and compensation of nonlinear communication channels has long been an important research topic in digital communications. A nonlinear bandpass channel is commonly modeled by a baseband equivalent Volterra series which relates the complex envelopes of the channel input and output. In this paper, we propose a novel method to estimate the frequency-domain baseband equivalent Volterra kernels of cubically nonlinear bandpass channels in orthogonal frequencydivision multiplexing (OFDM) systems. We recognize that the input signal for an OFDM system employing QAM or PSK modulations satisfies the properties of a kind of random multisine signal. By exploring the higher-order auto-moment spectra of the random multisine signal, a computationally efficient algorithm for determining the frequency-domain baseband equivalent Volterra kernels is derived. The obtained kernel estimates are optimal in the minimum mean square error (MMSE) sense. The proposed method can be used to estimate nonlinear bandpass channels for OFDM systems employing pure QAMs, pure PSKs, or a mixture of QAMs and PSKs. The effectiveness of the proposed method is demonstrated by applying it to estimate the nonlinear bandpass channel of an example OFDM system. Nonlinear channel compensators based on the Volterra model can benefit from the proposed method.
9 citations
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TL;DR: This paper provides a full realization of off-repetitive discrete-time Volterra series (ORDVS) by departure from a traditional approach in favor of choosing a hierarchical structure and enables researchers to use high-order kernels and consequently covers high- order nonlinearities with the lowest possible computational load.
Abstract: Full realization of all versions of Volterra series like pure, truncated, and doubly finite Volterra series, and especially, the realization of their high orders is an intractable problem. Hence, practical implementation of Volterra series for high-order nonlinearities is not feasible with reasonable computational cost. For this reason, mathematicians, neuroscientists, and especially, biomedical and electrical engineers are forced to use only the low-order Volterra series. In this paper, we provide a full realization of off-repetitive discrete-time Volterra series (ORDVS) by departure from a traditional approach in favor of choosing a hierarchical structure. The proposed method is named fast full tantamount of off-repetitive discrete-time Volterra series (FFT-ORDVS). We have proven that the proposed off-repetitive discrete-time Volterra series approximates the basic discrete-time Volterra series very well and with much less computational complexity. In a conventional method, if $${M} +1$$ is considered as the memory length of the ORDVS, around $$2^{M}$$ math operations are needed for the full realization of it. In most cases, M is a large number and consequently, $$2^{M}$$ is too large. To solve this problem, we have proposed a simple polynomial time solution and using the proposed method, the same task is done only by 6M math operations. It means that we have found a shortcut to change an intractable problem ($${O}(2^{M}))$$ to a simple P problem (O(M)). This achievement enables researchers to use high-order kernels and consequently covers high-order nonlinearities with the lowest possible computational load. We have proven our claims mathematically and validated the performance of the proposed method using two numerical examples and a real problem.
9 citations