a theory of nonsubtractive dither a detailed mathematical investigation of multibit quantizing systems using nonsubtractive dither is presented it is shown that by the use of dither having a suitably chosen probability density function moments of the total error can be made independent of the system input signal but that statistical independence of the error and the input signals is not achievable similarly it is demonstrated that values of the total error signal cannot generally be rendered statistically independent of one another but that their joint moments can be controlled and that in particular the error sequence can be rendered spectrally white the properties of some practical dither signals are explored and recommendations are made for dithering in audio video and measurement applications the paper collects all of the important results on the subject of nonsubtractive dithering and introduces important new ones with the goal of alleviating persistent and widespread misunderstandings regarding the technique

a method for the analysis of plates on a two parameter foundation in this study an iterative method is developed in order to analyze the plates on a two parameter elastic foundation based on the study by vallabhan et al 1991 where the material properties of the soil are used in order to compute the coefficients of subgrade reactions for the layered soil medium in the analysis the finite element method is used both plate and surrounding soil area divided into finite elements the plate finite element is considered by including the effects of subgrade reactions by means of the method suggested herein it is possible to examine the interaction between the separate plates close to each other and to assume the plate of arbitrary shape

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

enhancement of signal to noise ratio it is shown that the ratio of signal to noise ratio at the output to that at the input can be made larger than unity when a nonlinear system is subjected to a weak periodic perturbation and a harmonic noise this theoretical result is in conformity with the experimental observation published recently by r liet al

general measures for signal noise separation in nonlinear dynamical systems in every living cell millions of different types of molecules constantly interact and react chemically in a complex system that can adapt to fluctuating environments and extreme conditions living to survive and reproduce itself the information required to produce these components is stored in the genome which is copied in each cell division and transferred and mixed with another genome from parent to child the regulatory mechanisms that control biological systems for instance the regulation of expression levels for each gene has evolved so that global robustness and ability to survive under harsh conditions is a strength at the same time as biological tasks on a detailed molecular level must be carried out with good precision and without failures this has resulted in systems that can be described as a hierarchy of levels of complexity from the lowest level where molecular mechanisms control other components at the same level to pathways of coordinated interactions between components formed to carry out particular biological tasks and up to large scale systems consisting of all components connected in a network with a topology that makes the system robust and flexible this thesis reports on work that model and analyze complex biological systems and the signals and noise that regulate them at all different levels of complexity also it shows how signals are transduced vertically from one level to another as when a single mutation can cause errors in low level mechanisms disrupting pathways and create systemwide imbalances such as in type 2 diabetes the advancement of our knowledge of biological systems requires both that we go deeper and towards more detail of single molecules in single cells as well as taking a step back to understand the organisation and dynamics in the large networks of all components and unite the different levels of complexity

optimal noise benefits in neyman pearson and inequality constrained statistical signal detection we present theorems and an algorithm to find optimal or near optimal ldquostochastic resonancerdquo sr noise benefits for neyman pearson hypothesis testing and for more general inequality constrained signal detection problems the optimal sr noise distribution is just the randomization of two noise realizations when the optimal noise exists for a single inequality constraint on the average cost the theorems give necessary and sufficient conditions for the existence of such optimal sr noise in inequality constrained signal detectors there exists a sequence of noise variables whose detection performance limit is optimal when such noise does not exist another theorem gives sufficient conditions for sr noise benefits in neyman pearson and other signal detection problems with inequality cost constraints an upper bound limits the number of iterations that the algorithm requires to find near optimal noise the appendix presents the proofs of the main results

a refined model for beams on elastic foundations abstract the concept of a beam or slab on an elastic foundation has been one of the convenient tools for obtaining solutions to several geotechnical engineering problems while it is easy to establish quite accurately the stiffness characteristics of the beam or the slab the parameters which govern the behavior of the subsoil or the elastic foundation are indeed hard to model this difficulty remains true even if one assumes that the soil has linear isotropic and homogeneous properties using the vlasov model vallabhan and das 1988 j engng mech div asce 114 2 2072 2082 have developed an effective iterative technique to solve the beam on elastic foundation problem where the soil is assumed to have a uniform depth with a rigid base at the bottom geotechnical engineers usually encounter subsoil of finite depth and normally the elastic properties are considered to remain constant or vary linearly with depth in this paper the authors have extended their model to incorporate numerically this physical characteristic of the soil even though the derivations may look laborious the numerical model is quite simple and can be programmed on a desktop computer

stochastic resonance in extended bistable systems the role of potential symmetry we study the role of potential symmetry in a three field reaction diffusion system presenting bistability by means of a two state theory for stochastic resonance in general asymmetric systems by analyzing the influence of different parameters in the optimization of the signal to noise ratio we observe that this magnitude always increases with the symmetry of the system s potential indicating that it is this feature which governs the optimization of the system s response to periodic signals

noise enhanced parameter estimation this paper investigates the phenomenon of noise enhanced systems for a general parameter estimation problem when the estimator is fixed and known the estimation performance before and after the addition of noise are evaluated performance comparisons are made between the original estimators and noise enhanced estimators based on different criteria the form of the optimal noise probability density function pdf is determined the results are further extended to the general case where the noise is introduced to the system via a transformation for the case where the estimator is fixed and unknown approaches are also proposed to find the optimum noise finally two illustrative examples are presented where the performance comparison is made between the optimal noise modified estimator and gaussian noise modified estimator

stochastic resonance and generalized information measures abstract we use tsallis information measure and the recently advanced escort tsallis one in order to investigate the stochastic resonance sr phenomenon in particular on the basis of these generalized information measures gim both characterized by a non extensivity parameter q we study the effect of modifying the type of noise the gim are used to measure sr phenomenon comparing the input and output probability distributions finding that for the range of noise intensities enhancing sr q 0 gives the optimum measure an important advantage of using gim instead of shannon s measure is the possibility of detecting smaller signal amplitudes with the former than with the latter one

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

stochastic resonance in a trapping overdamped monostable system the response of a trapping overdamped monostable system to a harmonic perturbation is analyzed in the context of stochastic resonance phenomenon we consider the dynamics of a brownian particle moving in a piecewise linear potential with a white gaussian noise source based on linear response theory and laplace transform technique analytical expressions of signal to noise ratio snr and signal power amplification spa are obtained we find that the snr is a nonmonotonic function of the noise intensity while the spa is monotonic theoretical results are compared with numerical simulations

stochastic resonance in locally optimal detectors the aim of the paper is to show that the nonlinear effect known as stochastic resonance which corresponds to the improvement of the processing of information by noise occurs naturally in some detection problems we illustrate this by studying the problem of detecting a small amplitude sinusoid in non gaussian noise we show that in some cases the nonlinearity that appears in locally optimal detectors can be viewed as a stochastic resonator if the parameters of the locally optimal detector lod are not well tuned the performance can be improved by the addition of noise

noise enhancement in robust estimation of location in this paper we investigate the noise benefits to maximum likelihood type estimators m estimator for the robust estimation of a location parameter two distinct noise benefits are shown to be accessible under these conditions with symmetric heavy tailed noise distributions the asymptotic efficiency of the estimation can be enhanced by injecting extra noise into the m estimators with an asymmetric contaminated noise model having a convex cumulative distribution function we demonstrate that addition of noise can reduce the maximum bias of the median estimator these findings extend the analysis of stochastic resonance effects for noise enhanced signal and information processing

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

evaluation of stochastic resonance based detectors of weak harmonic signals in additive white gaussian noise a thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector the pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive monte carlo simulations parameter optimization and computational budget aspects are discussed

oversampled sigma delta modulation oversampled sigma delta modulation has been proposed as a practical implementation for high rate analog to digital conversion because of its simplicity and its robustness against circuit imperfections to date mathematical developments of the basic properties of such systems have been based either on simplified continuous time approximate models or on linearized discrete time models where the quantizer is replaced by an additive white uniform noise source in this paper we rigorously derive several basic properties of a simple discrete time single integrator loop sigma delta modulator with an accumulate and dump demodulator the derivation does not require any assumptions on the correlation or distribution of the quantizer error and hence involves no linearization of the nonlinear system but it does show that when the input is constant the state sequence of the integrator in the encoder loop can be modeled exactly as a linear system in an appropriate space two basic properties are developed 1 the behavior of the sigma delta quantizer when driven by a constant input and its relation to uniform quantization and 2 the rate distortion tradeoffs between the oversampling ratio and the average mean squared quantization error

stochastic resonance in an activator inhibitor system through adiabatic and quasi variational approaches abstract we study the phenomenon of stochastic resonance in a spatially extended system an activator inhibitor reaction diffusion model is analyzed through two different approximations an adiabatic one leading to a known form of the graham s nonequilibrium potential and a quasi variational approach that allows to obtain an approximated form of graham s potential for a different parameter region those potentials have been exploited to obtain firstly the probability for the decay of the metastable extended states and secondly expressions for the correlation function and for the signal to noise ratio within the framework of a two state description the analytical results show how this ratio depends on both local and nonlocal coupling parameters

exact analysis of beams on two parameter elastic foundations abstract efficient beams on two parameter elastic foundation finite elements have recently been developed the stiffness matrix and nodal loud vector of these elements have been derived on the basis of the exact displacement function obtained from the solution of the governing differential equation most of the existing elements are however either limited to certain combinations of beam and foundation parameters or provide only the solution of the homogeneous form of the governing equation in this paper a new finite element is derived which eliminates these limitations the stiffness matrix nodal load vector and shape function of the clement are derived using the differential equation of a beam on a two parameter elastic foundation the complete solution of the equation corresponding to the most common types of load is also presented this permits the determination of the deflections and internal forces anywhere along a simple or continuous beam on two parameter foundations

on some inverse eigenvalue problems for hermitian and generalized hamiltonian skew hamiltonian matrices abstract some inverse eigenvalue problems for hermitian and generalized hamiltonian skew hamiltonian matrices are discussed including best approximation problems and eigenvalue updating problems based on the spectral decomposition theory on hermitian and hamiltonian skew hamiltonian matrices simpler parametric expressions of solutions to the general inverse eigenvalue problems are given and then the best approximation problems and eigenvalue updating problems are solved by using these parametric expressions

a matrix inverse eigenvalue problem and its application the problem of generating a matrix a with specified eigenvalues which maps a given set of vectors of another given set is presented an existence theorem is given and proved a stable algorithm for producing the matrix a is discussed the relation between this problem and the pole assignment problem in control theory is investigated the application of this problem in the design of neural networks is discussed

stochastic resonance in discrete time nonlinear ar 1 models this paper deals with stochastic resonance this nonlinear physical phenomenon generally occurs in bistable systems excited by random input noise plus a sinusoid through its internal dynamics such a system forces cooperation between the input noise and the input sine provided the existence of fine tuning between the power noise and the dynamics the system reacts periodically at the frequency of the sine of particular interest is the fact that the local output signal to noise ratio presents a maximum when plotted against the input noise power the system resounds stochastically continuous time systems have already been studied we study the ability of intrinsically discrete time systems general nonlinear ar 1 models to produce stochastic resonance it is then suggested that such discrete systems can be used in signal processing

noise benefits in quantizer array correlation detection and watermark decoding quantizer noise can improve statistical signal detection in array based nonlinear correlators in neyman pearson and maximum likelihood ml detection this holds even for infinite variance symmetric alpha stable channel noise and for generalized gaussian channel noise noise enhanced correlation detection leads to noise enhanced watermark extraction based on such nonlinear detection at the pixel or bit level this yields a noise based algorithm for digital watermark decoding using two new noise benefit theorems the first theorem gives a necessary and sufficient condition for quantizer noise to increase the detection probability of a constant signal for a fixed false alarm probability if the channel noise is symmetric and if the sample size is large the second theorem shows that the array must contain more than one quantizer for such a stochastic resonance noise benefit if the symmetric channel noise is unimodal it also shows that the noise benefit rate improves in the small quantizer noise limit as the number of array quantizers increases the second theorem further shows that symmetric uniform quantizer noise gives the optimal rate for an initial noise benefit among all finite variance symmetric scale family noise two corollaries give similar results for stochastic resonance noise benefits in ml detection of a signal sequence with known shape but unknown amplitude

stochastic resonance in threshold systems we consider signal processing in simple threshold systems with nonstationary additive and or multiplicative noise a discrete time process with a small periodical signal masked by noise represents an input the systems convert sampled input data to a nonstationary random point event flow carrying some information on an input signal as it is shown in our previous study m m alibegov astron lett 22 564 1996 the rayleigh spectral function of a random point event train estimates a signal to noise ratio snr at selected frequencies based on these results we compute a system response at signal frequencies as a function of threshold and input noise intensity the threshold systems are shown to reveal stochastic resonance sr i e output snr exhibits a maximum at resonant noise intensity intensities and threshold s at rather common conditions we show that sr and rayleigh spectral technique allow us to carry out numerical signal detection in data sets with noise

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

noise benefits in combined nonlinear bayesian estimators this paper investigates the benefits of intentionally adding noise to a bayesian estimator which comprises a linear combination of a number of individual bayesian estimators that are perturbed by mutually independent noise sources and multiplied by a set of adjustable weighting coefficients we prove that the bayes risk for the mean square error mse criterion is minimized when the same optimum weighting coefficients are assigned to the identical estimators in the combiner this property leads to a simplified analysis of the noise benefit to the mse of the combined bayesian estimator even when the number of individual estimators tends to infinity it is shown that for a sufficiently large number of individual estimators the mse of the designed bayesian estimator approaches a plateau for a wide range of added noise levels this robust feature facilitates the incorporation of the added noise into the design of bayesian estimators without tuning the noise level for an easily implementable bayesian estimator composed of quantizers the benefit of the symmetric scale family noise is demonstrated and the optimal noise probability density function is approximated by solving a constrained nonlinear optimization problem we further extend this potential bayesian estimator to the nonlinear filter design finally examples of the noise benefits in random parameter estimation and nonlinear filtering support the theoretical analyses

effects of sampling and quantization on single tone frequency estimation the effects of sampling and quantization on frequency estimation for a single sinusoid are investigated the cramer rao bound for 1 bit quantization is derived and compared with the limit of infinite quantization it is found that 1 bit quantization gives a slightly worse performance however with a dramatic increase of variance at certain frequencies this can be avoided by using four times oversampling the effect of sampling when using nonideal antialiasing lowpass filters is therefore investigated through derivation of the cramer rao lower bounds finally fast estimators for 1 bit quantization in particular correlation based estimators are derived and their performance is investigated the paper is concluded with simulation results for four times oversampled 1 bit quantization

theory of stochastic resonance in signal transmission by static nonlinear systems a deterministic periodic signal plus a stationary random noise is applied to a static nonlinearity taking the form of a monovariable arbitrary function on real numbers the property of noise enhanced signal transmission through stochastic resonance is studied for this class of static nonlinear systems a theory is developed that provides expressions for the output autocorrelation function power spectral density signal to noise ratio and input output phase shift in the presence of a periodic input a noise distribution and a static nonlinearity all three being arbitrary both white and colored input noises are successively considered for white input noise exact expressions are derived in a discrete time framework directly confrontable to simulations or experiments the theory is applied to describe stochastic resonance in various examples of static nonlinear systems for instance a diode nonlinearity in addition confrontations with experiments and simulations are given that support the theory in particular interesting effects are reported such as a signal to noise ratio larger at the output than at the input or stochastic resonance at zero frequency finally the validity of the theory is extended to dynamic nonlinear systems that can be decomposed into a static nonlinearity followed by an arbitrary dynamic linear system s1063 651x 97 12002 5

noise aided processing revisiting ditheringin a spl sigma spl delta quantizer in this paper we show that a particular spl sigma spl delta quantizer which is a strongly nonlinear dynamical system can provide noise enhanced processing effects in some sense in particular we will show that quantizing a sine which means adding a small amount of noise in the input can improve the quantization process in particular the output local signal to noise ratio snr exhibits a maximum when plotted against the noise amplitude

dithering and its effects on sigma delta and multistage sigma delta modulation the spectrum of the quantization error in a dithered sigma delta modulator is derived under the constraint that the dithering signal does not cause overload the results apply to dc sinusoidal and more general quasi stationary signals it is shown in the case of a simple sigma delta modulation that no overload dithering can smooth the error spectrum and can make the quantization error asymptotically uncorrelated with the input it does not however make the quantization error white in the case of multistage sigma delta modulation with the appropriate dithering the quantization error becomes white even for a system with only two stages the signal to quantization noise ratio sqnr is derived for sigma delta and multistage sigma delta oversampled analog to digital conversion with additive dithering simulation results are presented to support the theoretical analysis

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

noise enhanced hypothesis testing in the restricted bayesian framework performance of some suboptimal detectors can be enhanced by adding independent noise to their observations in this paper the effects of additive noise are investigated according to the restricted bayes criterion which provides a generalization of the bayes and minimax criteria based on a generic m ary composite hypothesis testing formulation the optimal probability distribution of additive noise is investigated also sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived in addition simple hypothesis testing problems are studied in more detail and additional improvability conditions that are specific to simple hypotheses are obtained furthermore the optimal probability distribution of the additive noise is shown to include at most m mass points in a simple m ary hypothesis testing problem under certain conditions then global optimization analytical and convex relaxation approaches are considered to obtain the optimal noise distribution finally detection examples are presented to investigate the theoretical results

theory of the stochastic resonance effect in signal detection part ii variable detectors in part i of this paper ldquotheory of the stochastic resonance effect in signal detection part i fixed detectors rdquo ieee transactions on signal processing vol 55 no 7 pt 1 pp 3172 3184 the mechanism of the stochastic resonance sr effect for a fixed detector has been examined this paper analyzes the stochastic resonance sr effect under the condition that the detector structure or its parameters can also be changed the detector optimization problem with sr noise under both neyman pearson and bayesian criteria is examined in the bayesian approach when the prior probabilities are unknown the minimax approach is adopted the form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined the developed theory is then applied to a general class of weak signal detection problems under the assumptions that the sample size n is large enough and the test statistics satisfies the conditions of central limit theorem the optimal sr noise is shown to be a constant vector and independent of the signal strength for both neyman pearson and bayesian criteria illustrative examples are presented where performance comparisons are made between the original detector and the optimal sr noise modified detector for different types of sr noise

stochastic resonance as dithering a direct correspondence is demonstrated between the phenomenon of stochastic resonance in static nonlinear systems and the dithering effect well known in the theory of digital waveform coding it is argued that many static systems displaying stochastic resonance are forms of dithered quantizers and that the existence or absence of stochastic resonance in such systems can be predicted from the effects of dither averaging upon their transfer characteristics also results are introduced regarding stochastic resonance in certain nonlinear systems with memory e g hysteretic systems

on doubly structured matrices and pencils that arise in linear response theory abstract we discuss matrix pencils with a double symmetry structure that arise in the hartree fock model in quantum chemistry we derive anti triangular condensed forms from which the eigenvalues can be read off ideally these would be condensed forms under unitary equivalence transformations that can be turned into stable structure preserving numerical methods for the pencils under consideration this is a difficult task and not always possible we present necessary and sufficient conditions when this is possible if this is not possible then we show how we can include other transformations that allow to reduce the pencil to an almost anti triangular form

axisymmetric forced vibrations of an elastic free circular plate on a tensionless two parameter foundation the static and dynamic responses of a circular elastic plate on a two parameter tensionless foundation are investigated by assuming that the external load is rotationally symmetric and the plate experiences axially symmetric displacements in the solution procedure the vertical displacement of the foundation is determined by the corresponding governing equation whereas the vertical displacement of the plate is expressed in series in terms of the mode shapes of the completely free circular plate for the case of complete contact the corresponding governing equation of the plate incorporated with the edge reaction from the foundation is satisfied through the galerkin s approximation technique the contact radius is obtained by requiring that the surface of the foundation satisfies the corresponding continuity equations it is shown that the problem displays a highly nonlinear character due to the lift off of the plate from the foundation and the numerical treatment of the governing equation is accomplished by adopting iterative processes in terms of the contact radius the governing equation of the problem is solved numerically for the static and dynamic cases and the results are presented in figures to demonstrate the nonlinear behavior of the plate for various values of the parameters of the problem comparatively