beyond time frequency analysis energy densities in one and many dimensions given a unitary operator a representing a physical quantity of interest we employ concepts from group representation theory to define two natural signal energy densities for a the first is invariant to a and proves useful when the effect of a is to be ignored the second is covariant to a and measures the a content of signals we also consider joint densities for multiple operators and in the process provide an alternative interpretation of cohen s see englewood cliffs nj prentice hall 1995 general construction for joint distributions of arbitrary variables

strong stability of an unstable wave equation by boundary feedback with only displacement observation the stabilization of a 1 d wave equation that contains instability at its free end and control at the other end is considered the controller is designed through the estimated state that is designed in the case that only displacement is available the method of backstepping is adopted in investigation the c0 semigroup theory and lyapunov method are used to show that the closed loop system is asymptotically stable

speech enhancement using empirical mode decomposition and the teager kaiser energy operator in this paper a speech denoising strategy based on time adaptive thresholding of intrinsic modes functions imfs of the signal extracted by empirical mode decomposition emd is introduced the denoised signal is reconstructed by the superposition of its adaptive thresholded imfs adaptive thresholds are estimated using the teager kaiser energy operator tkeo of signal imfs more precisely tkeo identifies the type of frame by expanding differences between speech and non speech frames in each imf based on the emd the proposed speech denoising scheme is a fully data driven approach the method is tested on speech signals with different noise levels and the results are compared to emd shrinkage and wavelet transform wt coupled with tkeo speech enhancement performance is evaluated using output signal to noise ratio snr and perceptual evaluation of speech quality pesq measure based on the analyzed speech signals the proposed enhancement scheme performs better than wt tkeo and emd shrinkage approaches in terms of output snr and pesq the noise is greatly reduced using time adaptive thresholding than universal thresholding the study is limited to signals corrupted by additive white gaussian noise v c 2014 acoustical society of america http dx doi org 10 1121 1 4837835

multicomponent am fm demodulation via periodicity based algebraic separation and energy based demodulation previously investigated multicomponent am fm demodulation techniques either assume that the individual component signals are spectrally isolated from each other or that the components can be isolated by linear time invariant filtering techniques and consequently break down in the case where the components overlap spectrally or when one of the components is stronger than the other in this paper we present a nonlinear algorithm for the separation and demodulation of discrete time multicomponent am fm signals our approach divides the demodulation problem into two independent tasks algebraic separation of the components based on periodicity assumptions and then monocomponent demodulation of each component by instantaneously tracking and separating its source energy into its amplitude and frequency parts the proposed new algorithm avoids the shortcomings of previous approaches and works well for extremely small spectral separations of the components and for a wide range of relative amplitude power ratios we present its theoretical analysis and experimental results and outline its application to demodulation of cochannel fm voice signals

inferential models a framework for prior free posterior probabilistic inference posterior probabilistic statistical inference without priors is an important but so far elusive goal fisher s fiducial inference dempster shafer theory of belief functions and bayesian inference with default priors are attempts to achieve this goal but to date none has given a completely satisfactory picture this article presents a new framework for probabilistic inference based on inferential models ims which not only provides data dependent probabilistic measures of uncertainty about the unknown parameter but also does so with an automatic long run frequency calibration property the key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter and the prediction of this auxiliary variable with a random set before conditioning on data here we present a three step im construction and prove a frequency calibration property of the im s belief function under mild conditions a corresponding optimality theory is develo

optimal differentiation based on stochastic signal models the problem of estimating the time derivative of a signal from sampled measurements is addressed the measurements may be corrupted by colored noise a key idea is to use stochastic models of the signal to be differentiated and of the measurement noise two approaches are suggested the first is based on a continuous time stochastic process as a model of the signal the second uses a discrete time arma model of the signal and a discrete time approximation of the derivative operator digital differentiators are presented in a shift operator polynomial form they minimize the mean square estimation error and are calculated from a linear polynomial equation and a polynomial spectral factorization the three obstacles to perfect differentiation namely a finite smoothing lag measurement noise and aliasing effects due to sampling are discussed

on solutions for a hyperbolic system with differential inclusion and memory source term on the boundary in this paper we investigate the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi valued term and a nonlinear memory source term on the boundary

marginal inferential models prior free probabilistic inference on interest parameters the inferential models im framework provides prior free frequency calibrated and posterior probabilistic inference the key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters when nuisance parameters are present a marginalization step can reduce the dimension of the auxiliary variable which in turn leads to more efficient inference for regular problems exact marginalization can be achieved and we give conditions for marginal im validity we show that our approach provides exact and efficient marginal inference in several challenging problems including a many normal means problem in nonregular problems we propose a generalized marginalization technique and prove its validity details are given for two benchmark examples namely the behrens fisher and gamma mean problems

fiducial generalized confidence intervals generalized pivotal quantities gpqs and generalized confidence intervals gcis have proven to be useful tools for making inferences in many practical problems although gcis are not guaranteed to have exact frequentist coverage a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so as to be useful in practice in this article we single out a subclass of generalized pivotal quantities which we call fiducial generalized pivotal quantities fgpqs and show that under some mild conditions gcis constructed using fgpqs have correct frequentist coverage at least asymptotically we describe three general approaches for constructing fgpqs a recipe based on invertible pivotal relationships and two extensions of it and demonstrate their usefulness by deriving some previously unknown gpqs and gcis it is fair to say that nearly every published gci can be obtained using one of these recipes as an inte

global exact controllability of a class of quasilinear hyperbolic systems in this paper we consider a distributed parameter boundary control system described by a reducible quasilinear hyperbolic system formula posed on the domain 0 x 1 with the nonlinear boundary conditions formula in the case that the system islinear degenerate we show that it isgloballyexactly boundary controllable

am fm energy detection and separation in noise using multiband energy operators this paper develops a multiband or wavelet approach for capturing the am fm components of modulated signals immersed in noise the technique utilizes the recently popularized nonlinear energy operator psi s s sup 2 ss to isolate the am fm energy and an energy separation algorithm esa to extract the instantaneous amplitudes and frequencies it is demonstrated that the performance of the energy operator esa approach is vastly improved if the signal is first filtered through a bank of bandpass filters and at each instant analyzed via psi and the esa using the dominant local channel response moreover it is found that uniform worst case performance across the frequency spectrum is attained by using a constant q or multiscale wavelet like filter bank the elementary stochastic properties of psi and of the esa are developed first the performance of psi and the esa when applied to bandpass filtered versions of an am fm signal plus noise combination is then analyzed the predicted performance is greatly improved by filtering if the local signal frequencies occur in band these observations motivate the multiband energy operator and esa approach ensuring the in band analysis of local am pm energy in particular the multi bands must have the constant q or wavelet scaling property to ensure uniform performance across bands the theoretical predictions and the simulation results indicate that improved practical strategies are feasible for tracking and identifying am fm components in signals possessing pattern coherencies manifested as local concentrations of frequencies

fiducial theory and optimal inference it is shown that the fiducial distribution in a group model or more generally a quasigroup model determines the optimal equivariant frequentist inference procedures the proof does not rely on existence of invariant measures and generalizes results corresponding to the choice of the right haar measure as a bayesian prior classical and more recent examples show that fiducial arguments can be used to give good candidates for exact or approximate confidence distributions it is here suggested that the fiducial algorithm can be considered as an alternative to the bayesian algorithm for the construction of good frequentist inference procedures more generally

frictional versus viscoelastic damping in a semilinear wave equation in this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping the equation that models this problem is given by begin eqnarray u tt kappa 0 delta u int 0 t mbox div a x g t s nabla u s ds f u b x h u t 0 mbox in omega times bbb r quad end eqnarray where a b are nonnegative functions a in c 1 overline omega b in l infty omega satisfying the assumption begin eqnarray a x b x geq delta 0 quad forall x in omega end eqnarray and f and h are power like functions we observe that the assumption 0 2 gives us a wide assortment of possibilities from which to choose the functions a x and b x and the most interesting case occurs when one has simultaneous and complementary damping mechanisms taking this point of view into account a distinctive feature of our paper is exactly to consider different and localized damping mechanisms acting in the domain but not necessarily strategically localized dissipations as considered in the prior literature

asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star shaped domain we study the asymptotic stability and give the energy decay rates for solutions of the wave equation with boundary dissipation of the memory type

the problem of low counts in a signal plus noise model consider the model x b s where b and s are independent poisson random variables with means and is unknown but is known the model arises in particle physics and some recent articles have suggested conditioning on the observed bound on b that is if x n is observed then the suggestion is to base inference on the conditional distribution of x given b n this conditioning is non standard in that it does not correspond to a partition of the sample space it is examined here from the view point of decision theory and shown to lead to admissible formal bayes procedures 1 introduction in some problems a signal s may be superimposed on a background b leaving an observed count x b s here we suppose that b and s are independent poisson random variables with means and so that x has a poisson distribution with mean is regarded as an unknown parameter but is assumed to be known as might be appropriate if there were historical data on the background what special techniques if any are appropriate if the observed count x is smaller than the expected background a problem of this nature has arisen recently in physics the karmen 2 group has been searching for a neutrino oscillation reported earlier from an experiment at the los alamos neutrino detector as of summer 1998 they had expected to see about 3 1 background events and at least one signal event based on the earlier findings and using rounded values but had observed nothing see zeitnitz et al 1998 what inference about is appropriate here can the hypothesis h0 1 be rejected a naive analysis suggests that it can if 3 is regarded as a known quantity and the hypothesis is rewritten as h0 4 then the p value is p x 0 e 4 for 4 and this is less than the usual levels of significance but this analysis is suspect because if x 0 then both b and s must be zero and p4 s 0 e 1 which is not less than the usual levels of significance the second value is obtained by conditioning on the ancillary variable b 0 and seems right in this context the problem becomes much more interesting when the observed count is non zero but smaller than the expected background since then it is no longer possible to recover the value of b roe and woodroofe 1999 argue that if x n then it is appropriate to base inferences on the conditional distribu

energy decay for nondissipative distributed systems with boundary damping and source term abstract in this paper we consider energy decay for nondissipative distributed systems with boundary damping and source terms first we consider the wave equation u u h u u u second we consider the case h u u in both first and second cases we have the nonlinear boundary condition u 0 t k t s x u s d s a x g u 0 we study energy decay using the multiplier technique and equivalent energy

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term the wave equation with a source term is considered utt u u uin 0 we prove the existence and uniform decay rates of the energy by assuming a nonlinear feedback ut acting on the boundary provided that has necessarily not a polynomial growth near the origin to obtain the existence of global solutions we make use of the potential well method combined with the faedo galerkin procedure and constructing a special basis furthermore we prove that the energy of the system decays uniformly to zero and we obtain an explicit decay rate estimate adapting the ideas of lasiecka and tataru differential integral equations 6 3 1993 507 and patrick martinez esain control optimisation calc var 4 1999 419 the resulting problem generalizes martinez results and complements the works of lasiecka and tataru 1993 and vitillaro glasgow math j 44 2002 375

a note on the boundary stabilization of the wave equation we study the energy decay rates of the wave equation in a domain where boundary damping is present we generalize the geometrical conditions obtained earlier in j math purer appl 58 1979 pp 249 273 by using some more general multipliers of strauss comm pure appl math 28 1975 pp 265 278 the interaction between distributed damping and boundary damping is discussed a regulator problem is also formally discussed by the synthesis method

boundary observability controllability and stabilization of linear elastodynamic systems in 1988 lions obtained observability and exact controllability results for linear homogeneous isotropic elastodynamic systems siam rev 30 1988 pp 1 68 applying some new identities we extend his theorems to nonisotropic systems in 1991 lagnese obtained uniform stabilizability results for two dimensional linear homogeneous isotropic systems by applying a somewhat artificial feedback nonlinear anal 16 1991 pp 35 54 then he asked whether analogous results hold for a natural and physically implementable boundary feedback using some new identities and applying a method introduced in 1987 by zuazua and the second author j math pures appl 69 1990 pp 33 54 we give an affirmative answer to this question in all dimensions and also for nonisotropic systems moreover we obtain good decay estimates finally applying a recent general method of uniform stabilization we construct boundary feedbacks leading to arbitrarily large energy decay rates

generalized fiducial inference a review and new results abstractr a fisher the father of modern statistics proposed the idea of fiducial inference during the first half of the 20th century while his proposal led to interesting methods for quantifying uncertainty other prominent statisticians of the time did not accept fisher s approach as it became apparent that some of fisher s bold claims about the properties of fiducial distribution did not hold up for multi parameter problems beginning around the year 2000 the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that fisher s approach when properly generalized would open doors to solve many important and difficult inference problems they termed their generalization of fisher s idea as generalized fiducial inference gfi the main idea of gfi is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of bayes theorem the resulting generalized fiducial distribution gfd can

decay of solutions of wave equations in a bounded region with boundary dissipation abstract an energy decay rate is obtained for solutions of wave type equations in a bounded region in rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface

a comparison of the squared energy and teager kaiser operators for short term energy estimation in additive noise time frequency distributions that evaluate the signal s energy content both in the time and frequency domains are indispensable signal processing tools especially for nonstationary signals various short time energy computation schemes are used in practice including the mean squared amplitude and teager kaiser energy approaches herein we focus primarily on the short and medium term properties of these two energy estimation schemes as well as on their performance in the presence of additive noise to facilitate this analysis and generalize the approach we use a harmonic noise model to approximate the noise component the error analysis is conducted both in the continuous and discrete time domains deriving similar conclusions the estimation errors are measured in terms of normalized deviations from the expected signal energy and are shown to greatly depend on both the signals spectral content and the analysis window length when medium and long term analysis windows are employed the teager kaiser energy operator is proven superior to the common squared energy operator provided that the spectral content of the noise is more lowpass than the corresponding signal content and vice versa however for shorter window lengths the teager kaiser operator always outperforms the squared energy operator the theoretical results are experimentally verified for synthetic signals finally the performance of the proposed energy operators is evaluated for short term analysis of noisy speech signals and the implications for speech processing applications are outlined

on amplitude and frequency demodulation using energy operators it is shown that the nonlinear energy tracking signal operator psi x dx dt sup 2 xd sup 2 x dt sup 2 and its discrete time counterpart can estimate the am and fm modulating signals specifically psi can approximately estimate the amplitude envelope of am signals and the instantaneous frequency of fm signals bounds are derived for the approximation errors which are negligible under general realistic conditions these results coupled with the simplicity of psi establish the usefulness of the energy operator for am and fm signal demodulation these ideas are then extended to a more general class of signals that are sine waves with a time varying amplitude and frequency and thus contain both an am and an fm component for such signals it is shown that psi can approximately track the product of their amplitude envelope and their instantaneous frequency the theoretical analysis is done for both continuous and discrete time signals

energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms abstract in this paper we develop an intrinsic approach to derivation of energy decay rates for the semilinear wave equation with localized interior nonlinear monotone damping g u t and a source term f u the proposed approach allows to consider in an unified way much more general classes of hyperbolic problems than addressed before in the literature these generalizations refer to both geometric and topological aspects of the problem the method leads to optimal decay rates for solutions of semilinear hyperbolic equations driven by a source of critical exponent and subjected to a nonlinear damping localized in a small region adjacent to a portion of the boundary the distinct features of the model include i neumann boundary conditions are assumed and ii no growth conditions are imposed on the damping g s it is well known that neumann boundary does not satisfy lopatinski condition and therefore the analysis of propagation of energy in the absence of the damping on the neumann part of the boundary requires special geometric considerations in addition the sole conditions assumed on g s are monotonicity continuity and g 0 0 in particular no differentiability and no growth conditions are imposed on the damping both at the origin and at the infinity the asymptotic decay rates for the energy function are obtained from an intrinsic algorithm driven by solutions of simple ode several examples illustrate the theory by exhibiting various decay rates exponential algebraic rational logarithmic etc for the energy functional an important corollary of our energy decay theorem is a stability result which shows that under certain conditions when dissipation is sublinear at infinity the solution of the system remains uniformly bounded for all time in the norms above the finite energy level even in the presence of a nonlinear source term

second order systems with acceleration measurements accelerometers are often used to measure the output of second order systems such as structural vibrations conditions under which these systems are well posed are obtained we also establish conditions under which these systems have minimum phase transfer functions

amenability a survey for statistical applications of hunt stein and related conditions on groups a number of conditions on groups have appeared in the literature of invariant statistical models in connection with minimaxity approximation of invariant bayes priors by proper priors the relationship between bayesian and classical inference ergodic theorems and other matters in the last decade rapid development has occurred in the field and many of these conditions are now known to be equivalent we survey the subject make the equivalences explicit and list some groups of statistical interest which do and also some which do not have these properties in particular it is shown that the existence of the asymptotically invariant sequence of probabilities in the hypothesis of the hunt stein theorem is equivalent to amenability a condition that has been much studied by functional analysts

energy decay of solutions to the cauchy problem for a nondissipative wave equation in this paper we consider energy decay for nondissipative wave equation in unbounded domain the usual energy is not decreasing we use an approach introduced by guesmia which leads to decay estimates known in the dissipative case when the integral inequalities method by komornik exact controllability and stabilization the multiplier method masson wiley paris 1994 cannot be applied due to the lack of dissipativity first we study the stability of a wave equation with a weak nonlinear dissipative term based on the equation u xu 2 x u t g u t h xu 0 in irn we consider the general case with a function h satisfying a smallness condition and we obtain decay of solutions under weak growth assumptions on the feedback function and without any control of the sign of the derivative of the energy related to the above equation in the second case we consider the case h u u we prove some precise decay estimates of equivalent energy

quadratic detectors for energy estimation the estimation of signal energy is an important part of physics and signal processing a commonly used energy estimate in signal processing is instantaneous energy that is defined by the square of the signal magnitude at time t i e

uniform decay of the solution to a wave equation with memory conditions on the boundary abstract a wave equation with variable coefficients in principal part and memory conditions on the boundary is considered the riemannian geometry method is applied to prove the exponential decay of the energy provided the relaxation function also decays exponentially

belief functions and parametric models the theory of belief functions assesses evidence by fitting it to a scale of canonical examples in which the meaning of a message depends on chance in order to analyse parametric statistical problems within the framework of this theory we must specify the evidence on which the parametric model is based this article gives several examples to show how the nature of this evidence affects the analysis these examples also illustrate how the theory of belief functions can deal with problems where the evidence is too weak to support a parametric model

nonlinear modeling and processing of speech based on sums of am fm formant models we describe a new statistical approach based on nonlinear filtering ideas for decomposing signals that are modeled as a sum of jointly amplitude and frequency modulated cosines where each cosine has a slowly varying center frequency and the sum of terms is observed in additive noise this is an alternative approach to methods based on deterministic models such as the kaiser teager see proc ieee icassp 93 vol iii p 149 and ieee trans acoust speech signal processing vol 28 no 5 pp 599 1980 energy operator the cramer rao bound for the resulting statistical estimation problem is computed a practical nonlinear filter an extended kalman filter is described we demonstrate the ideas on a variety of speech problems

blow up for semilinear wave equation with boundary damping and source terms abstract in this paper we consider the semilinear wave equation with boundary damping and source terms this work is devoted to prove a finite time blow up result under suitable condition on the initial data and positive initial energy

texture analysis and segmentation using modulation features generative models and weighted curve evolution in this work we approach the analysis and segmentation of natural textured images by combining ideas from image analysis and probabilistic modeling we rely on am fm texture models and specifically on the dominant component analysis dca paradigm for feature extraction this method provides a low dimensional dense and smooth descriptor capturing essential aspects of texture namely scale orientation and contrast our contributions are at three levels of the texture analysis and segmentation problems first at the feature extraction stage we propose a regularized demodulation algorithm that provides more robust texture features and explore the merits of modifying the channel selection criterion of dca second we propose a probabilistic interpretation of dca and gabor filtering in general in terms of local generative models extending this point of view to edge detection facilitates the estimation of posterior probabilities for the edge and texture classes third we propose the weighted curve evolution scheme that enhances the region competition geodesic active regions methods by allowing for the locally adaptive fusion of heterogeneous cues our segmentation results are evaluated on the berkeley segmentation benchmark and compare favorably to current state of the art methods

generalized fiducial inference for wavelet regression we apply fisher s fiducial idea to conduct statistical inference for wavelet regression we first develop a general methodology for handling model selection problems within the fiducial framework with this new methodology we then propose fiduical based methods for performing wavelet curve estimation as well as constructing both pointwise and curvewise confidence intervals it is shown that under some mild regularity conditions both the new fiducial based pointwise and curvewise confidence intervals have asymptotically correct coverage furthermore simulation results show that these new fiducial based methods especially for constructing pointwise confidence intervals also possess promising empirical properties to the best of our knowledge this is the first time that the fiducial idea has been applied to a nonparametric estimation problem

limits on discrete modulated signals we develop theorems of a general nature that apply to the analysis of am fm signals of the form a m exp j spl phi m or a m cos spl phi m and to their behavior both in linear systems and in simple nonlinear systems comprised of products of linear elements such product systems include interesting nonlinear demodulation operators such as the teager kaiser 1990 operator expressions for the approximate system responses to am fm signals are derived by making an analogy to the eigenfunction interpretation of sinusoids in linear systems for the case of sinusoidal signals the approximations are exact these expressions are collectively called quasieigenfunction approximations qeas for nonsinusoidal am fm signals the approximations have errors that are tightly bounded by functionals that express the smoothness of the am and fm information signals and the durations of the involved system impulse responses the bounds are independent of the bandwidths of the am and fm functions two general applications are considered first the approximations are found to be useful for analyzing discrete time nonlinear energy operators including the teager kaiser operator next the approximation theorems lead to the selection of an optimal class of bandpass filters for use in a discrete multiband am fm demodulation system the filter class selected is optimal in the sense of achieving the lower bound of a novel discrete uncertainty principle

mellin transforms and asymptotics finite differences and rice s integrals high order differences of simple number sequences may be analysed asymptotically by means of integral representations residue calculus and contour integration this technique akin to mellin transform asymptotics is put in perspective and illustrated by means of several examples related to combinatorics and the analysis of algorithms like digital tries digital search trees quadtrees and distributed leader election

a new approach of stabilization of nondissipative distributed systems in this paper we propose a new approach to prove the nonlinear internal or boundary stabilization of certain nondissipative distributed systems the usual energy is not decreasing this approach leads to decay estimates known in the dissipative case when the integral inequalities method due to komornik exact controllability and stabilization the multiplier method masson paris john wiley chichester uk 1994 cannot be applied due to the lack of dissipativity first we study the stability of a semilinear wave equation with a nonlinear damping based on the equation u delta u h nabla u f u g u 0 we consider the general case with a function h satisfying a smallness condition and we obtain uniform decay of strong and weak solutions under weak growth assumptions on the feedback function and without any control of the sign of the derivative of the energy related with the above equation in the second part we consider the case h nabla u nabla phi cdot nabla u with phi in w 1 infty omega we prove some precise decay estimates exponential or polynomial of equivalent energy without any restriction on phi the same results will be proved in the case of boundary feedback finally we comment on some applications of our approach to certain nondissipative distributed systems some results of this paper were announced without proof in a guesmia c r acad sci paris ser i math 332 2001 pp 633 636