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IEEE Transactions on Signal Processing, 1997 This paper is composed of two parts. The first part surveys the literature regarding optimum nonlinear filtering from the (continuous-time) stochastic analysis point of view, and the other part explores the impact of recent applications of neural networks (in a discrete-time context) to nonlinear filtering.
Simon Haykin 0001, Paul Yee, Eric Derbez
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Filtering by nonlinear systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.
Campos Cantón, E. +2 more
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Signal Processing, 2014
In this paper, two new sub-classes of linear-in-the-parameters nonlinear discrete-time filters, derived from the truncation of multidimensional generalized Fourier series, are presented. The filters, called Fourier nonlinear filters and even mirror Fourier nonlinear filters, are universal approximators for causal, time-invariant, finite-memory ...
Alberto Carini, Giovanni L. Sicuranza
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In this paper, two new sub-classes of linear-in-the-parameters nonlinear discrete-time filters, derived from the truncation of multidimensional generalized Fourier series, are presented. The filters, called Fourier nonlinear filters and even mirror Fourier nonlinear filters, are universal approximators for causal, time-invariant, finite-memory ...
Alberto Carini, Giovanni L. Sicuranza
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Optics Letters, 1996
We demonstrate a nonlinear Christiansen filter in both the steady state and the transient regimes and in both the self- and the cross-modulation modes. Experiments in which a thermal nonlinearity was used agree well with predictions based on a modified scattering theory model.
S D, Vartak, N M, Lawandy
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We demonstrate a nonlinear Christiansen filter in both the steady state and the transient regimes and in both the self- and the cross-modulation modes. Experiments in which a thermal nonlinearity was used agree well with predictions based on a modified scattering theory model.
S D, Vartak, N M, Lawandy
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Journal of Nonlinear Science, 1997
It is shown how it is possible to combine Fourier projections with local nonlinear prediction to provide a methodology which can, in principle, recognize independent dynamical signals. That methodology is applied to a variety of chaotic signals with superimposed the sine waves. Moreover, it is shown how sine wave frequency can be recognized dynamically
Kember, G., Fowler, A. C., Evans, H. B.
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It is shown how it is possible to combine Fourier projections with local nonlinear prediction to provide a methodology which can, in principle, recognize independent dynamical signals. That methodology is applied to a variety of chaotic signals with superimposed the sine waves. Moreover, it is shown how sine wave frequency can be recognized dynamically
Kember, G., Fowler, A. C., Evans, H. B.
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Characterising auditory filter nonlinearity
Hearing Research, 1994An important aspect of auditory nonlinearity is that psychoacoustically measured auditory filters broaden as the level at which they are measured increases. However, it is not yet clear whether the change in filter shape is controlled primarily by the level of the probe or that of the masker.
Rosen, Stuart, Baker, Richard
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Neural Systems as Nonlinear Filters
Neural Computation, 2000Experimental data show that biological synapses behave quite differently from the symbolic synapses in all common artificial neural network models. Biological synapses are dynamic; their “weight” changes on a short timescale by several hundred percent in dependence of the past input to the synapse.
Wolfgang Maass 0001, Eduardo D. Sontag
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Journal of Applied Physics, 1953
The theory of optimum nonlinear filters outlined in this paper is based on the consideration of a sequence of classes of nonlinear filters, designated as 𝔑1, 𝔑2, 𝔑3, …, such that each class in the sequence includes all the preceding classes and, furthermore, the class of linear filters is a subclass of every class in the sequence.
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The theory of optimum nonlinear filters outlined in this paper is based on the consideration of a sequence of classes of nonlinear filters, designated as 𝔑1, 𝔑2, 𝔑3, …, such that each class in the sequence includes all the preceding classes and, furthermore, the class of linear filters is a subclass of every class in the sequence.
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Introducing Legendre nonlinear filters
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014This paper introduces a novel sub-class of linear-in-the-parameters nonlinear filters, the Legendre nonlinear filters. Their basis functions are polynomials, specifically, products of Legendre polynomial expansions of the input signal samples. Legendre nonlinear filters share many of the properties of the recently introduced classes of Fourier ...
Alberto Carini +3 more
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IEEE Transactions on Signal Processing, 1991
A nonlinear filter is introduced whose output is nearest in distance to the output of a FIR (finite impulse response) linear phase filter; hence it is called the NFIR filter. After choosing the impulse response of the FIR filter properly, the NFIR filter can clean impulsive noise and preserve edges of signals.
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A nonlinear filter is introduced whose output is nearest in distance to the output of a FIR (finite impulse response) linear phase filter; hence it is called the NFIR filter. After choosing the impulse response of the FIR filter properly, the NFIR filter can clean impulsive noise and preserve edges of signals.
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