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Alfredo Restrepo, Universidad de los Andes (Colombia)
Luis F. Zuluaga, Universidad de los Andes (Colombia)
Luis E. Pino, Universidad de los Andes (Colombia)
In a stochastic resonance system, additive noise and a nonlinear component system permit the amplification of a weak periodic signal, whenever the strength of the noise is within a certain interval. For one such a system with a nonlinearity consisting of a threshold function, we define a measure of goodness and, for the case of Gaussian noise, we derive required intervals of noise variance for stochastic resonance.
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Cristian Emanuel Savin, Concordia University (Canada)
M. Omair Ahmad, Concordia University (Canada)
M.N. Srikanta Swamy, Concordia University (Canada)
This paper addresses the problem of designing weighted order statistic (WOS) filters by employing an objective function given as the Lp norm of the error between the desired signal and the estimated one. The conventional design of WOS filters uses a mean absolute error (MAE) objective function, and as such, it is a special case of the general, Lp norm based design, developed here. In this paper, it is shown that in stack filtering, the Lp norm can be expressed as a linear combination of the decision errors incurred by the Boolean operators at each level of the stack filter architecture. Based on this formulation of the Lp norm, both nonadaptive and adaptive algorithms for the design of Lp WOS filters are developed. A design example is considered, to illustrate the performance of the designed Lp WOS filters with different values of p. The simulation results show that the Lp WOS filters with p>=2 are capable of removing more impulsive noise compared with the conventional MAE WOS filters.
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Tania Stathaki, Imperial College (U.K.)
Anne Scohyers, Imperial College (U.K.)
A novel approach is taken for the estimation of the parameters of a Volterra model, which is based on constrained optimisation. The equations required for the determination of the Volterra kernels are formed entirely from the second and higher order statistical properties of the "output" signal to be modelled and can therefore be classed as blind in nature. These equations are highly nonlinear and their solution is achieved through a judicious use of reliably measured statistical features of the signal to be modelled, in conjunction with appropriate constraints and penalty functions. Examples are given to illustrate the method and it is evident from those that this novel approach is producing useful results in contexts that have been hitherto unattainable.
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Olufemi Adeyemi, University of Rhode Island (U.S.A.)
Faye G. Boudreaux-Bartels, University of Rhode Island (U.S.A.)
Existing algorithms for accurately estimating the f((alpha)) singularity spectrum from the samples of generalized dimensions D_q of a multifractal chaotic time series use either linear interpolation of the known D_q values or finely sample the D_q curve. Also, the derivative in the expression for Legendre transform necessary to go from D_q to f((alpha)) is approximated using first order centered difference equation. Finely sampling the D_q is computationally intensive and the crude linear approximations to interpolation and differentiation give erroneous end points in the f((alpha)) curve. We propose using standard min-max filter design methods to more accurately interpolate between known samples of the D_q values and evaluate the Legendre transform. We use optimum (min-max) interpolators and differentiators designed with the Parks-McClellan algorithm. The new min-max approach exhibits computational reduction and improved accuracy. Examples are provided that show improved accuracy for attractors that contain multifractal behavior.
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Hans Schurer, University of Twente (The Netherlands)
Cornelis H. Slump, University of Twente (The Netherlands)
Otto E. Herrmann, University of Twente (The Netherlands)
Alex G.J. Nijmeijer, AEMICS B.V. (The Netherlands)
Mark A. Boer, AEMICS B.V. (The Netherlands)
Based on a simplified nonlinear lumped element model of the electrodynamic loudspeaker in either a closed or a vented cabinet, a new nonlinear controller is derived, simulated and implemented on a DSP. The Volterra series expansion, a well known functional expansion to model nonlinear systems, is used to estimate the nonlinear parameters from distortion measurements. The controller is directly based on the nonlinear differential equation, and is tested for the case of a low frequency electrodynamic loudspeaker in a closed cabinet. Digital implementation is realized on a general purpose TMS320C30 DSP development board, using the automatic code generation from schematic entry of the Alta-Group SPW software.
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Robert Nowak, Michigan State University (U.S.A.)
Richard Baraniuk, Rice University (U.S.A.)
Nonlinearities are often encountered in the analysis and processing of real-world signals. This paper develops new transformations for nonlinear signal processing. The theory of tensor norms is employed to show that wavelets provide an optimal basis for the new transformations. The results are applied to Volterra kernel identification.
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Elena Stringa, University of Genova (Italy)
Carlo S. Regazzoni, University of Genova (Italy)
A new set of non linear signal and image processing operators is presented. Their definition is based on the introduction of the statistical properties of Bayesian reconstruction in soft morphological operators. Statistical soft operators represent a trade-off between the noise cleaning properties of statistical morphology and the shape preservation properties of soft morphology. The main characteristic of these operators is the individualization of two parts within each structuring element (SE) according to soft morphology (i.e. "hard" and "soft" SEs), and to define on this basis a probabilistic estimation model which is a generalization of the Statistical Morphology model. Results are presented to show that the statistical soft morphological operators can be considered robust to structured noise, i.e. noise showing both statistical (e.g. additive Gaussian noise) and morphological (e.g. noise with a particular shape) structure.
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Ted W. Frison, Randle, Inc. (U.S.A.)
Henry D.I. Abarbanel, INLS, UCSD (U.S.A.)
Nonstationary chaotic behavior is not an oxymoron. We present two methods for capturing nonstationary chaos, then present a few examples including biological signals, ocean waves and traffic flow. The issue is of practical interest because it is often useful to capture when nonstationary events take place and it is desirable to know over what periods a signal is stationary.
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Jean-Pierre Costa, University of Nice (France)
Thierry Pitarque, University of Nice (France)
Eric Thierry, University of Nice (France)
The miniaturization of GSM handsets creates nonlinear acoustical echoes between the microphone and the loudspeaker when signal level is high. Nonlinear adaptive filtering can tackle this problem but the computational complexity has to be reduced by restricting the number of coefficients introduced by nonlinear models. This paper compares performances of different nonlinear models. In a first training stage we use the OLS (Orthogonal Least Squares) identification method to find models using the fewest coefficients along with a good fitting accuracy. In a second filtering stage these parsimonious models are used to adaptively filter the GSM signal
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Daniel Homm, University of Erlangen (Germany)
Rudolf Rabenstein, University of Erlangen (Germany)
The suitability of methods from multidimensional systems theory and digital signal processing for the efficient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial differential equation into a transfer function description of a multidimensional continuous system. It serves as the starting point for the derivation of a discrete system which closely models the behaviour of the given continuous system and which is suitable for computer implementation. This concept is extended here to the simulation of nonlinear multidimensional systems. The essence of the presented method is a systematic way to turn a nonlinear partial differential equation into a set of ordinary differential equations, for which standard methods for the numerical integration exist. This paper reviews briefly the linear case, points out the various difficulties arising from nonlinearity and shows how to overcome them. Numerical results demonstrate the effectiveness of the method.
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Panos Koukoulas, University of Athens (Greece)
Nicholas Kalouptsidis, University of Athens (Greece)
This paper is concerned with third order Volterra system identification. It is shown that crosscumulant information can be converted into a Fredholm integral equation. Closed form expressions for the Volterra kernels are derived using the determinant theory. Finally, special emphasis is focused on IID inputs.
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Balasubramaniam Santhanam, Georgia Institute of Technology (U.S.A.)
Petros Maragos, Georgia Institute of Technology (U.S.A.)
Existing multicomponent AM--FM demodulation algorithms either assume spectrally distinct components or components separable via linear filtering and break down when the components overlap spectrally or if one of the components is stronger than the other. In this paper, we present a nonlinear algorithm for multicomponent AM--FM demodulation which avoids the above shortcomings and works well even for extremely small spectral separation of the components. The proposed algorithm separates the multicomponent demodulation problem into two tasks: periodicity-based algebraic separation of the components and then monocomponent demodulation via energy--based methods.
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Subhash Challa, SPRC, Queensland University of Technology (Australia)
Farhan A. Faruqi, SPRC, Queensland University of Technology (Australia)
The classical approach to designing filters for systems where system equations are linear and measurement equations are nonlinear is to linearise measurement equations, and apply an Extended Kalman Filter (EKF). This results in suboptimal, biased, and often divergent filters. Many schemes proposed to improve the performance of the EKF concentrated on better linearisation techniques, iterative techniques and adaptive schemes. The improvements achieved were marginal and often reduced the bias and divergence problems but were far from optimal unbiased estimators. In this paper, we present a new approach to Optimal Nonlinear filtering in linear system - nonlinear measurements case. It is based on approximation of evolved probability density functions using quasi-moments followed by numerical evaluation of Bayes' conditional density equation.
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Murali Tummla, Naval Postgrad. School (U.S.A.)
Michael T. Donovan, Naval Postgrad. School (U.S.A.)
Bruce E. Watkins, NCCOSC (U.S.A.)
Richard North, NCCOSC (U.S.A.)
Demands for higher data rates coupled with increased competition for the available RF bandwidth demand communications systems with greater bandwidth efficiency. Bandwidth efficient modulation techniques, such as QAM, require highly linear amplifier performance to achieve acceptable bit error rates. The nonlinear distortion which results when an amplifier is operated near saturation may preclude their use. One attractive option is to predistort the signal by placing a nonlinear filter in the signal path which compensates for the distortion introduced by the amplifier. In this paper, we present a predistortion technique which uses an inverse amplifier model based on a Volterra series approach. The input-output data from the amplifier is used to develop the parameters for a discrete Volterra series. The RLS adaptive filter technique is utilized to provide periodic updates to the inverse filter which allows tracking of amplifier variations. Results are presented for the case of 64 QAM modulation using a TWT amplifier operated at saturation.
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