performance analysis of an adaptive notch filter with constrained poles and zeros a statistical analysis of the sine wave frequency estimate obtained by the adaptive notch filter anf recently proposed by a nehorai ibid vol assp 33 p 983 96 aug 1985 is presented asymptotically valid expressions for the bias and mean square error of the frequency estimate are provided the analysis verifies the performance exhibited by the anf and clarifies the role of some user variables such as the notch bandwidth and the number of data samples processed

on the vectoral ekeland s variational principle and minimal points in product spaces abstract phelps 13 noticed that the scalar ekeland s variational principle evp is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order attouch and riahi 1 showed that evp is equivalent to the existence of maximal points with respect to cones satisfying some additional conditions taking these into account gopfert and tammer 6 7 established a maximal point theorem in a product space the aim of this paper is to obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial evp

a pre order principle and set valued ekeland variational principle abstract we establish a pre order principle from the principle we obtain a very general set valued ekeland variational principle where the objective function is a set valued map taking values in a quasi ordered linear space and the perturbation contains a family of set valued maps satisfying certain property from this general set valued ekeland variational principle we deduce a number of particular versions of set valued ekeland variational principle which include many known ekeland variational principles their improvements and some new results

ekeland s variational principle and its equivalent theorems in vector optimization we present a simple proof of vectorial ekeland s variational principle vectorial caristi s fixed point theorem and vectorial takahashi s nonconvex minimization theorem equivalences between the three theorems are also given

a brezis browder principle on partially ordered spaces and related ordering theorems abstract through a simple extension of brezis browder principle to partially ordered spaces a very general strong minimal point existence theorem on quasi ordered spaces is proved this theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems and three general ekeland variational principles in optimization problems where the objective space is quasi ordered then they are applied to prove strong minimal point existence results generalizations of bishop phelps lemma in linear spaces and ekeland variational principles in set valued optimization problems through a set solution criterion

multiframe temporal estimation of cardiac nonrigid motion a robust flexible system for tracking the point to point nonrigid motion of the left ventricular lv endocardial wall in image sequences has been developed this system is unique in its ability to model motion trajectories across multiple frames the foundation of this system is an adaptive transversal filter based on the recursive least squares algorithm this filter facilitates the integration of models for periodicity and proximal smoothness as appropriate using a contour based description of the object s boundaries a set of correspondences between contours and an associated set of correspondence quality measures comprise the input to the system frame to frame relationships from two different frames of reference are derived and analyzed using synthetic and actual images two multiframe temporal models both based on a sum of sinusoids are derived illustrative examples of the system s output are presented for quantitative analysis validation of the system is performed by comparing computed trajectory estimates with the trajectories of physical markers implanted in the lv wall sample case studies of marker trajectory comparisons are presented ensemble statistics from comparisons with 15 marker trajectories are acquired and analyzed a multiframe temporal model without spatial periodicity constraints was determined to provide excellent performance with the least computational cost a multiframe spatiotemporal model provided the best performance based on statistical standard deviation although at significant computational expense

a minimal parameter adaptive notch filter with constrained poles and zeros a new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow band or sine wave signals in an additive broad band process the algorithm is of recursive prediction error rpe form and uses a special constrained model of infinite impulse response iir with a minimal number of parameters the convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape for sufficiently large data sets the variances of the sine wave frequency estimates are of the same order of magnitude as the cramer rao bound results from simulations illustrate the performance of the algorithm under a wide range of conditions

principal decomposition of time frequency distributions the authors present a novel time frequency analysis technique which uses principal components analysis to map any given time frequency distribution tfd of a signal into a set of three 1 d principal decomposition functions these three functions may then be considered to be separable components of a time frequency function which they refer to as the principal approximation function for the original tfd they show how principal decomposition analysis is useful for the enhancement and frequency tracking of nonstationary harmonic signals

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

a generalized least squares method for frequency estimation the application of the generalized least squares gls method to the estimation of the frequencies of sinusoids in additive colored noise is discussed an iterative algorithm is proposed starting from the assumption that the parameter vector in the model of the sinusoids is symmetric the algorithm utilizes an adaptive strategy for contracting the poles of the estimated signal model expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case possible convergence points and the asymptotic behavior of the algorithm in the case of low snrs signal to noise ratios are analyzed extensive simulation results show that the algorithm represents a simple and reliable tool for practical applications

nonlinear techniques for interference suppression in spread spectrum systems the binary nature of direct sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose the case of a gaussian interferer with known autoregressive parameters is considered using simulations it is shown that an approximate conditional mean acm filter of the masreliez type performs significantly better than the optimum linear kalman bucy filter for the case of interferers with unknown parameters the nature of the nonlinearity in the acm filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction two versions of this filter are considered one in which the filter coefficients are updated using the widrow lms algorithm and another in which the coefficients are updated using an approximate gradient algorithm simulations indicate that the nonlinear filter with lms updates performs substantially better than the linear filter for both narrowband gaussian and single tone interferers whereas the gradient algorithm gives slightly better performance for gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer

conditional mean and maximum likelihood approaches to multiharmonic frequency estimation the performance of an extended kalman filter ekf applied to the problem of estimating the assumed constant parameters fundamental frequency harmonic phases and amplitudes of a complex multiharmonic signal measured in noise is shown to be asymptotically i e as the number of measurements tends to infinity efficient the cramer rao cr bounds associated with the estimation problem are derived for the case where the measurements commence at an arbitrary time distinct from zero

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

estimating the parameters of general frequency modulated signals a general frequency modulated gfm signal characterizes the vibrations produced by compressors turbines propellers gears and other rotating machines in a dynamic environment a gfm signal is defined as the composition of a real or complex periodic or almost periodic carrier function with a real differentiable modulation function a gfm signal therefore contains sinusoids whose frequencies are possibly nonintegral multiples of a fundamental to distinguish a gfm signal from a set of unrelated sinusoids it is necessary to track them as a group this paper develops the general frequency modulation tracker gfmt for one or more gfm signals in noise using the expectation conditional maximization ecm algorithm that is an extension of the expectation maximization em algorithm three advantages of this approach are that the ratios harmonic numbers of the carrier functions do not need to be known a priori that the parameters of multiple signals are estimated simultaneously and that the gfmt algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required several simulated examples are presented to illustrate the algorithm s performance

technical communique convergence analysis of recursive identification algorithms with forgetting factor a convergence analysis of a modified version of the least squares recursive identification algorithm with forgetting factor is given it is shown that the parametric distance converges to a zero mean random variable it is also shown that under persistent excitation condition on both system input and output the condition number of the adaptation gain matrix is bounded the variance of the parametric distance is bounded by the product of the noise variance times the upper bound of the condition number of the gain matrix this is done by normalizing the measurement vector entering in the identification algorithm and by using a forgetting factor verifying l t 0

new speech harmonic structure measure and its applications to speech processing the harmonic structure can be easily recognized in time frequency representation of speech signals in adverse environment the harmonicity is a measure of the completeness of a harmonic structure this paper presents a new harmonic structure measure that extends the conventional harmonicity to a set of harmonicities they are expressed in terms of the grid harmonicity the temporal harmonicity the segment spectral harmonicity and the segmental harmonicity the grid harmonicity measures the completeness of individual harmonics in each frame the grid harmonicities in a frame are summed up to form a temporal harmonicity for representing the strength of harmonicity the segment spectral harmonicity computed by summing specific grid harmonicity over a segment evaluates the integrity of individual harmonics across a segment the segmental harmonicity evaluates the total strength of harmonic structure within a segment this set of harmonicities is available for a systematic analysis of the harmonic structure and effective to several speech processing tasks the applications to speech distortion analysis robust fundamental frequency estimation robust voicing detection and speech enhancement are demonstrated

arma spectral estimation for noisy signals observed through a linear system spectral estimation for autoregressive moving average arma processes observed through a known linear system is considered an algorithm based on a system identification parameter estimation technique known as the recursive prediction error method is used for spectral estimation the algorithm is formulated in the state space to incorporate the constraints imposed by the linear system the linear system may represent the distortion introduced by the sensor or the channel several simulation examples are presented to illustrate the performance of the estimator

a recursive maximum likelihood algorithm for arma line enhancement optimal filtering of narrow band signals corrupted by noise requires an infinite impulse response iir filter a recursive maximum likelihood algorithm is proposed for adaptively adjusting the coefficients of an iir line enhancer the performance of this adaptive iir filter is analyzed and compared to that of a finite impulse response filter preliminary simulation results are presented to illustrate the behavior of the proposed algorithm under various signal to noise conditions

stochastic approximation method with gradient averaging for unconstrained problems a stochastic approximation algorithm is studied in which random gradient estimates are averaged by an auxiliary filter convergence of the algorithm is proved under a rather general noise condition a practical version of the method is described and numerical results are given

a fast recursive algorithm for the maximum likelihood estimation of the parameters of a periodic signal describes a new recursive algorithm for the estimation of the parameters of a periodic signal in additive gaussian white noise these parameters are the period and the complex amplitudes of the harmonics present the proposed algorithm is based on recursive maximum likelihood ml algorithms for incomplete data as described by titterington 1985 and others these algorithms are of complexity o nm where n is the number of harmonics and m is the signal length the performance of the method is compared to that of the extended kalman filter with the aid of simulations

the vector valued variational principle in banach spaces ordered by cones with nonempty interiors we prove sharpness of efficient solutions x k to vector optimization problems resulting from ekeland vector variational principles we achieve this by sharpening some of the existing vector variational principles and showing that x k remains efficient not only for perturbations in the direction k but also for other directions of perturbations

relative pareto minimizers for multiobjective problems existence and optimality conditions in this paper we introduce and study enhanced notions of relative pareto minimizers for constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of pareto and weak pareto efficiency minimality using advanced tools of variational analysis and generalized differentiation we establish the existence of relative pareto minimizers for general multiobjective problems under a refined version of the subdifferential palais smale condition for set valued mappings with values in partially ordered spaces and then derive necessary optimality conditions for these minimizers as well as for conventional efficient and weak efficient counterparts that are new in both finite dimensional and infinite dimensional settings our proofs are based on variational and extremal principles of variational analysis in particular on new versions of the ekeland variational principle and the subdifferential variational principle for set valued and single valued mappings in infinite dimensional spaces

tracking characteristics of the constrained iir adaptive notch filter the tracking behavior of a constrained iir notch filter the coefficients of which are estimated using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that the mean behavior of the adaptive filter coefficients can be studied by using an ordinary differential equation ode approximate and simple closed form results are derived for the tracking behavior of a second order notch filter computer simulations are presented to substantiate the analysis

analysis and performance evaluation of an adaptive notch filter an adaptive notch filter is derived by using a general prediction error framework the proposed infinite impulse response filler has a special structure that guarantees the desired transfer characteristics the filter coefficients are updated by a version of the recursive maximum likelihood algorithm the convergence properties of the algorithm and its asymptotic behavior are discussed and its performance is evaluated by simulation results

minimal element theorems revisited abstract starting with the brezis browder principle we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature relationships among the elements of different sets of assumptions are discussed and clarified i e assumptions to the metric structure of the underlying space and boundedness assumptions new results involving set valued maps and the increasingly popular set relations are obtained along the way

gradient based adaptive iir notch filtering for frequency estimation the use of gradient based algorithms with infinite impulse response iir notch filtering for estimating sinusoids imbedded in noise is investigated two notch filter model structures are presented the first is for applications where two signal sources with correlated noise components can be assessed the second can be used in situations where only one composite signal source is available error surface analysis indicates that second order modules are unimodal and result in guaranteed convergence higher order modules are multimodal and require judicious choice of initial parameter estimates simulation results are included to demonstrate the performance characteristics of both filter structures

adaptive polynomial factorization by coefficient matching a polynomial factorization algorithm is presented which updates all roots simultaneously and efficiently in response to coefficient perturbations the algorithm requires approximately 2n sup 2 complex floating point operations to update all roots of nth order polynomial close to the true root vector the algorithm s convergence rate is quadratic the root update requires only the solution of two sets of structured linear equations and a convolution the algorithm can be used to track the roots of time varying polynomials which is useful for application in adaptive signal processing

equivalents to ekeland s variational principle in uniform spaces abstract a minimal element theorem on sequentially complete uniform spaces is presented that generalizes earlier results of pacific j math 55 2 1974 335 341 proc amer math soc 108 3 1990 707 714 two more equivalent formulations of the minimal element theorem are given it is applied to derive new versions of ekeland type theorems which improve results of j math anal appl 202 1996 398 412 finally the minimal element theorem is used to obtain an ekeland type theorem for functions with values in a linear space without topological structure

adaptive stochastic filters with no strict positive real condition a new adaptive stochastic filter structure is introduced which avoids the strict passivity test used as a sufficient condition for convergence required by existing adaptive schemes the proposed algorithm consists of three stages in the first stage an autoregressive model is fitted and the residue obtained is used as an estimate of the noise in the second stage an autoregressive recursive moving average model is fitted using the residual of the first stage a modified residual is then filtered using a parameter and the model obtained from the second stage to generate an improved estimate of the noise in the third stage this improved estimate of the noise is used to obtain a better autoregressive moving average model it is shown that the proposed algorithm will also reduce the bias in the estimated parameters the simulation results given show that the proposed filter compares favorably to the algorithm introduced by mayne and clark and also landau this filter is then applied to the adaptive line enhancement sinusoidal detection and adaptive spectral estimation problems to illustrate its usefulness

new nonlinear algorithms for estimating and suppressing narrowband interference in ds spread spectrum systems it has been shown that the narrowband nb interference suppression capability of a direct sequence ds spread spectrum system can be enhanced considerably by processing the received signal via a prediction error filter the conventional approach to this problem makes use of a linear filter however the binary ds signal that acts as noise in the prediction process is highly non gaussian thus linear filtering is not optimal vijayan and poor 1990 first proposed using a nonlinear approximate conditional mean acm filter of the masreliez 1975 type and obtained significant results this paper proposes a number of new nonlinear algorithms our work consists of three parts 1 we develop a decision directed kalman ddk filter that has the same performance as the acm filter but a simpler structure 2 using the nonlinear function in the acm and the ddk filters we develop other nonlinear least mean square lms filters with improved performance 3 we further use the nonlinear functions to develop nonlinear recursive least squares rls filters that can be used independently as predictors or as interference identifiers so that the acm or the ddk filter can be applied simulations show that our nonlinear algorithms outperform conventional ones

adaptive algorithms for constrained arma signals in the presence of noise a family of algorithms is developed for adaptive parameter estimation of constrained autoregressive moving average arma signals in the presence of noise these algorithms utilize a priori information about the signal s properties such as its spectral type for example low pass bandpass etc or a spatial domain characteristic special applications include modeling of autoregressions ar and signals of known spectral type in the presence of noise signal deconvolution image deblurring and multipath parameter estimation selected results of simulations are included to demonstrate the performance of the algorithms

a recursive maximum likelihood algorithm for arma spectral estimation a spectral estimation technique is presented for autoregressive moving average arma processes the technique is based on a parameter estimation technique known as the rec ursive maximum likelihood rml method the recursive spectral estimation algorithm is presented and its asymptotic properties are discussed simulation results are presented to illustrate the performance of the estimator for various types of data

on nonparametric identification of wiener systems in this paper a new method for the identification of the wiener nonlinear system is proposed the system being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element is identified by a two step semiparametric approach the impulse response function of the linear part is identified via the nonlinear least squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate the obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the wiener system the proposed method permits recovery of a wide class of nonlinearities which need not be invertible as a result the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate furthermore our approach allows non gaussian input signals and the presence of additive measurement noise however only linear systems with a finite memory are admissible the conditions for the convergence of the proposed estimates are given computer simulations are included to verify the basic theory

adaptive parameter estimation for a constrained low pass system a novel algorithm is presented for adaptive parameter estimation for a constrained low pass butterworth system model the algorithm will estimate the system cutoff frequency and gain online when it is known that the true system has a low pass butterworth structure or some transfer function similar to it and its true order is used the algorithm will lead to a substantial savings in computation and more accurate results than unconstrained algorithms potential applications include filter design and adaptive decision on nyquist rate for systems

a generalized ekeland vector variational principle and its applications in optimization abstract in this paper we give a generalized ekeland vector variational principle by using the principle we extend and improve the related results in sharp efficiency in the framework of locally convex spaces we introduce two kinds of generalized sharp efficiencies and prove that they are equivalent in particular we show that a sharp efficient solution with respect to an interior point of the ordering cone is also one with respect to every interior point moreover we introduce the generalized takahashi s condition and the generalized hamel s condition for vector valued functions from the generalized ekeland principle we deduce that the two conditions are equivalent from this we discuss the relationship between the distance of f x from e f x and the distance of x from e f where e f x denotes the efficient point set of f x and e f denotes the efficient solution set

geometry of domains with the uniform squeezing property abstract we introduce the notion of domains with uniform squeezing property study various analytic and geometric properties of such domains and show that they cover many interesting examples including teichmuller spaces and hermitian symmetric spaces of non compact type the properties supported by such manifolds include pseudoconvexity hyperconvexity kahler hyperbolicity vanishing of cohomology groups and quasi isometry of various invariant metrics it also leads to nice geometric properties for manifolds covered by bounded domains and a simple criterion to provide positive examples to a problem of serre about stein properties of holomorphic fiber bundles

periodic signal analysis by maximum likelihood modeling of orbits of nonlinear odes this paper treats a new approach to the problem of periodic signal estimation the idea is to model the periodic signal as a function of the state of a second order nonlinear ordinary differential equation ode this is motivated by poincare theory which is useful for proving the existence of periodic orbits for second order odes the functions of the right hand side of the nonlinear ode are then parameterized by a multivariate polynomial in the states where each term is multiplied by an unknown parameter a maximum likelihood algorithm is developed for estimation of the unknown parameters from the measured periodic signal the approach is analyzed by derivation and solution of a system of odes that describes the evolution of the cramer rao bound over time this allows the theoretically achievable accuracy of the proposed method to be assessed in the ideal case where the signals can be exactly described by the imposed model the proposed methodology reduces the number of estimated unknowns at least in cases where the actual signal generation resembles that of the imposed model this in turn is expected to result in an improved accuracy of the estimated parameters

adaptive pole estimation an adaptive algorithm is developed for online estimation of the poles of autoregressive ar processes the method estimates the poles directly from the data without intermediate estimation of the ar coefficients or polynomial factorization it converges rapidly is computationally efficient and attains the cramer rao bound crb asymptotically a closed form expression for the asymptotic crb is provided convergence to the true solution is proved and methods are discussed for extending the algorithm for use with more general e g autoregressive moving average models numerical examples are presented to demonstrate the performance of the algorithm

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

a stable and efficient adaptive notch filter for direct frequency estimation we investigate the problem of direct frequency estimation a new adaptive algorithm is developed for constrained pole zero notch filters the basic characteristic of this algorithm is that the notch filter is cascaded and hence purely parametrized by the notching frequencies this makes the algorithm much simpler and hence more efficient and more robust such that the poles and zeros are automatically located on the respective constrained circle no matter if the algorithm is implemented with infinite or finite precision the algorithm is analyzed and compared with some existing algorithms several numerical examples are given as well as the corresponding simulations

asymptotic cramer rao bounds for estimation of the parameters of damped sine waves in noise the problem of estimating the parameters of a signal composed of several damped sine waves in noise has applications for example in transient signal analysis explicit closed form expressions are derived for the cramer rao bound of this problem in the case of low damping low spectral interference between the signal components and a sufficiently large number of samples among several conclusions which are drawn from the expressions it is found that the estimation problem is much more sensitive to errors in the damping factor and frequency than to errors in amplitude and phase

stationary points of the recursive generalized least squares algorithm for adaptive notch filtering possible convergence points of the generalized least squares adaptive notch filtering algorithm are analytically derived for the multiple sinusoid case showing explicitly the dependence of the asymptotic bias on the pole contraction factor signal to noise ratio and the true model parameters the results for symmetric and nonsymmetric parameterization are compared

generalized adaptive comb filters smoothers and their application to the identification of quasi periodically varying systems and signals the problem of both causal and noncausal identification of linear stochastic systems with quasi harmonically varying parameters is considered the quasi harmonic description allows one to model nonsinusoidal quasi periodic parameter changes the proposed identification algorithms are called generalized adaptive comb filters smoothers because in the special signal case they reduce down to adaptive comb algorithms used to enhance or suppress nonstationary harmonic signals embedded in noise the paper presents a thorough statistical analysis of generalized adaptive comb algorithms and demonstrates their statistical efficiency in the case where the fundamental frequency of parameter changes varies slowly with time according to the integrated random walk model

vector valued variational principles in the context of vector valued extensions of variational principles we are dealing with functions taking values in a banach space partially ordered by a closed convex pointed cone we introduce and study a new notion of semi continuity connected with the order and we improve the vector valued extensions of deville godefroy zizler perturbed minimization principle

canonical metrics on the moduli space of riemann surfaces i in this paper we continue our study of the canonical metrics on the moduli space of curves we first prove the bounded geometry of the ricci and perturbed ricci metrics by carefully choosing the pertubation constant and by studying the asymptotics we show that the ricci and holomorphic sectional curvatures of the perturbed ricci metric are bounded from above and below by negative constants based on our understanding of the kahler einstein metric we show that the logarithmic cotangent bundle over the deligne mumford moduli space is stable with respect to the canonical polarization finally in the last section we prove the strongly bounded geometry of the kahler einstein metric by using the kahler ricci flow and a priori estimates of the complex monge ampere equation

metrics for vector quantization based parametric speech enhancement and separation speech enhancement and separation algorithms sometimes employ a two stage processing scheme wherein the signal is first mapped to an intermediate low dimensional parametric description after which the parameters are mapped to vectors in codebooks trained on for example individual noise free sources using a vector quantizer to obtain accurate parameters one must employ a good estimator in finding the parameters of the intermediate representation like a maximum likelihood estimator this leaves some unanswered questions however like what metrics to use in the subsequent vector quantization process and how to systematically derive them this paper aims at answering these questions metrics for this are presented and derived and their use is exemplified on a number of different signal models by deriving closed form expressions the metrics essentially take into account in the vector quantization process that some parameters may have been estimated more accurately than others and that there may be dependencies between the estimation errors

permutation filter lattices a general order statistic filtering framework a general nonlinear filtering framework permutation order statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination permutation filters much like polynomial filters are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions at the simplest level in the filter lattice permutation filters reduce to either a simple linear fir or to an order statistic os filter but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties in order to enhance the robustness of permutation fitters we develop spl alpha trimmed permutation indicators and their associated filter lattices we conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system this paper thus extends the potential of order statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

estimate of the squeezing function for a class of bounded domains we construct a class of bounded domains on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point

adaptive notch filtering for the retrieval of sinusoids in noise in this paper an adaptive notch filter is developed employing a frequency domain and time domain analysis for the enhancement and tracking of sinusoids in additive noise colored or white the notch filter is implemented as a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter the resulting notch filter requires few parameters facilitates the formation of the desired band rejection filter response and also leads to various useful implementations cascade parallel for the adaptation of the filter coefficients the stochastic gauss newton algorithm is used the convergence of this updating procedure is established by studying the associated differential equation also it is shown that the structure present in the problem enables truncation of the gradient thereby reducing the complexity of adapting the filter coefficients simulation results are presented to substantiate the analysis and to demonstrate the potential of the notch filtering technique

properties of squeezing functions and global transformations of bounded domains the central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains we prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary in fact such an estimate is proved for the squeezing function on any domain near its globally strongly convex boundary points we also study the stability of squeezing functions on a sequence of bounded domains and give comparisons of intrinsic measures and metrics on bounded domains in terms of squeezing functions as applications we give new and simple proofs of several well known results about geometry of strongly pseudoconvex do mains and prove that all cartan hartogs domains are homogenous regular finally some related problems that ask for further study are proposed

a robust spectral estimation by modeling an estimated autocovariance with an arma model the development analysis simulation results and comparison of techniques for estimating spectral peaks of stationary signals in environments with low signal to noise ratio are discussed unlike traditional parametric methods the proposed method estimates parameters of a model which best approximates the estimated autocovariance lag rather than the received signal this technique is studied and evaluated in three different respects using a performance index in the spectral domain suppression of the moving average ma portion and in terms of effective signal to noise ratio this estimation technique demonstrates outstanding robustness and resolution for estimating both spectral peaks and amplitudes of multiple sinusoids embedded in white gaussian noise compared to traditional methods when used in conjunction with cadzow s autoregressive moving average arma method using singular value decomposition svd the technique extracts frequencies and amplitudes of existing sinusoids down to 17 db while the arma method alone achieves only 10 db on average

the domination property for efficiency and bishop phelps theorem in locally convex spaces abstract we introduce the notion of closedness for any bounded convex set and investigate the relationship between closedness and local closedness moreover we study some properties of convex sets by using closedness local closedness and convexity we give two main theorems on the domination property and the existence of efficient points in locally convex spaces from these two main theorems we deduce a number of corollaries which improve the related known results as an application of the main results we obtain several support point theorems in locally convex spaces which generalize the famous bishop phelps theorem

the squeezing function on doubly connected domains via the loewner differential equation for any bounded domains varomega in mathbb c n deng guan and zhang introduced the squeezing function s varomega z which is a biholomorphic invariant of bounded domains we show that for n 1 the squeezing function on an annulus a r lbrace z in mathbb c r z 1 rbrace is given by s a r z max left z frac r z right for all 0 r 1 this disproves the conjectured formula for the squeezing function proposed by deng guan and zhang and establishes up to biholomorphisms the squeezing function for all doubly connected domains in mathbb c other than the punctured plane it provides the first non trivial formula for the squeezing function for a wide class of plane domains and answers a question of wold our main tools used to prove this result are the schottky klein prime function following the work of crowdy and a version of the loewner differential equation on annuli due to komatu we also show that these results can be used to obtain lower bounds on the squeezing function for certain product domains in mathbb c n

the extended kalman filter as a pulmonary blood flow estimator pulmonary blood flow is represented as a time varying parameter in a simple model of the bodily uptake of gases that are soluble in blood the pulmonary blood flow is estimated on line using ljung s modification of the extended kalman filter the experimental technique for estimation of pulmonary blood flow is based on zwart s soluble gas method modified to permit time varying ventilation and pulmonary perfusion and also to permit binary dynamic forcing of the inhaled soluble gas computer simulations were performed to determine the convergence time and to choose values of algorithmic parameters experiments done in humans gave agreement to within the accuracy of that measured invasively by a thermal dilution technique the method shows promise for use in many biomedical applications including patient monitoring physiological experimentation and clinical heart function tests

ekeland s variational principle for set valued functions we establish several set valued function versions of ekeland s variational principle and hence provide some sufficient conditions ensuring the existence of error bounds for inequality systems defined by finitely many lower semicontinuous functions

recursive identification algorithms for right matrix fraction description models multivariable identification algorithms are usually designed only for left matrix fraction description lmfd models in this paper we consider recursive identification algorithms for right matrix fraction description rmfd models with diagonal denominator matrices the algorithms are of prediction error pe and model reference mr type results from simulations illustrate the performance of the algorithms

ramanujan sums in the context of signal processing part ii fir representations and applications the mathematician ramanujan introduced a summation in 1918 now known as the ramanujan sum c q n in a companion paper part i properties of ramanujan sums were reviewed and ramanujan subspaces s q introduced of which the ramanujan sum is a member in this paper the problem of representing finite duration fir signals based on ramanujan sums and spaces is considered first it is shown that the traditional way to solve for the expansion coefficients in the ramanujan sum expansion does not work in the fir case two solutions are then developed the first one is based on a linear combination of the first n ramanujan sums with n being the length of the signal the second solution is based on ramanujan subspaces with q 1 q 2 q k denoting the divisors of n it is shown that x n can be written as a sum of k signals x qi n s qi furthermore the i th signal x qi n has period q i and any pair of these periodic components is orthogonal the components x qi n can be calculated as orthogonal projections of x n onto ramanujan spaces s qi then the ramanujan periodic transform rpt is defined based on this and is useful to identify hidden periodicities it is shown that the projection matrices which compute x qi n from x n are integer matrices except for an overall scale factor the calculation of projections is therefore rendered easy to estimate internal periods n n of x n one only needs to know which projection energies are nonzero

an iterative method for exact maximum likelihood estimation of the parameters of a harmonic series a procedure is described for determining the exact maximum likelihood ml estimates of the parameters of a harmonic series i e the fundamental frequency and the amplitude and phase of each harmonic existing ml methods are only approximate in the sense that terms present due to mixing between the harmonics are ignored these terms asymptotically reduce to zero as the sample size increases to infinity it is argued that these terms can be significant for short signal lengths the application of the expectation maximization algorithm results in an iterative procedure that converges to a stationary point on the true parameter likelihood surface if global convergence results this point yields the exact ml estimates simulation studies illustrate the advantages of the method when short data lengths are used

adaptive algorithms for joint time delay estimation and iir filtering a new class of gradient based algorithms for joint adaptive time delay estimation and iir filtering for the recursive identification of systems with long pure delays is introduced the algorithms update an adaptive delay estimate and the coefficients of an iir filter using familiar gradient descent methods in addition interpolation of the input sequence is used to obtain delays that are not constrained to integer numbers of samples three algorithms using a direct form filter parametrization and one using a normalized lattice filter are derived and computer simulations are used to demonstrate their convergence and tracking properties

paper adaptive control based on explicit criterion minimization a common approach to regulator design is to define an objective function which is minimized with respect to adjustable regulator parameters here we discuss how such objective functions can be minimized on line thus providing adaptive control such an approach to adaptive control has its roots in early contributions to learning systems and it is here further developed and discussed in the light of the recent development of the field a general algorithm is given and special attention is paid to minimization of quadratic criteria a key problem is to obtain information about the system dynamics in order to compute the derivatives of the criterion with respect to the regulator parameters it is shown that the self tuning regulator is obtained as a special case corresponding to a particular quadratic criterion and a particular way of estimating the system dynamics explicit ways using instrumental variables techniques based on extra injected noise are also discussed a specific feature of the algorithm is that it does not utilize specific knowledge about how to calculate the optimal regulator the algorithm is the same for minimum phase as well as for non minimum phase systems

set valued quasi metrics and a general ekeland s variational principle in vector optimization we introduce the notion of compatibility between a set valued quasi metric and the original metric by using this notion we prove a general set valued ekeland s variational principle evp where the perturbation contains a set valued quasi metric which is compatible with the original metric here we need not assume that the order cone is w normal by using the unified approach for approximate solutions introduced by gutierrez jimenez and novo we deduce a general version of set valued evp based on c epsilon efficient solutions where c is a coradiant set contained in the order cone by choosing two specific versions of the coradiant set c in the general version of evp we obtain several particular set valued evps for epsilon efficient solutions in the sense of nemeth and of dentcheva and helbig respectively these set valued evps improve and generalize the related interesting results in c gutierrez b jimenez and v novo siam j control optim 47 2008 pp 883 903

periodic signal modeling based on lie spl acute nard s equation the problem of modeling periodic signals is considered the approach taken here is motivated by the well known theoretical results on the existence of periodic orbits for lie spl acute nard systems and previous results on modeling periodic signals by means of second order nonlinear ordinary differential equations the approach makes use of the appropriate conditions imposed on the polynomials of the lie spl acute nard s system to guarantee the existence of a unique and stable limit cycle these conditions reduce the number of parameters required to generate accurate models

a set valued ekeland s variational principle in vector optimization this paper deals with ekeland s variational principle for vector optimization problems by using a set valued metric a set valued perturbed map and a cone boundedness concept based on scalarization we introduce an original approach to extending the well known scalar ekeland s principle to vector valued maps as a consequence of this approach we obtain an ekeland s variational principle that does not depend on any approximate efficiency notion this result is related to other ekeland s principles proved in the literature and the finite dimensional case is developed via an varepsilon efficiency notion that we introduced in math methods oper res 64 2006 pp 165 185 siam j optim 17 2006 pp 688 710

recursive parameter estimation for noisy autoregressive signals corresp the problem of recursively estimating the unknown parameters of a scalar autoregressive ar signal observed in additive white noise including signal power and noise variance is considered a state space model in a canonical but noninnovations form is used to represent the noisy ar signal an algorithm based on a system identification parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation two simulation examples illustrate the effectiveness of the proposed algorithm

adaptive comb filtering for harmonic signal enhancement a new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise the algorithm is composed of two cascaded parts the first estimates the fundamental frequency and enhances the harmonic component in the input and the second estimates the harmonic amplitudes and phases performance analysis provides new results for the asymptotic cramer rao bound crb on the parameters of harmonic signals with additive white noise results of simulations indicate that the variances of the estimates are of the same order of magnitude as the crb for sufficiently large data sets and illustrate the performance in enhancing noisy artificial periodic signals

on the accuracy of the kumaresan tufts method for estimating complex damped exponentials recently kumaresan and tufts kt presented a method for estimating the parameters of damped exponential waveforms in additive white noise the kt method uses singular value decomposition svd of the data matrix with truncation and backward prediction to improve the accuracy of the estimates the kt method was demonstrated to have a very good performance in comparison to traditional methods used for the same problem e g prony s method kumaresan and tufts also showed by numerical simulations that the variances of the estimates obtained by their method approaches the cramer rao lower bounds for selected test cases in this correspondence we provide a quantitative accuracy analysis of the kt method the analysis is based on first order taylor series approximations of the estimated parameters around their true values no assumptions are made on the number of data points used but it is assumed that the noise level is small enough for the first order approximations to be valid results of the analysis are illustrated by some numerical examples these results confirm the good performance of the kt method and show the effect of the user chosen parameters on the accuracy of the estimates

generalized adaptive notch and comb filters for identification of quasi periodically varying systems the problem of identification tracking of quasi periodically varying real valued systems is considered this problem is a generalization to the system case of a classical signal processing task of either elimination or extraction of nonstationary sinusoidal signals buried in noise the solution is based on the exponentially weighted basis function ewbf approach the proposed algorithms are capable of tracking slow changes in system frequencies which means that not only the expansion coefficients in the basis function description of the analyzed system but also the basis functions themselves are adjusted in an adaptive manner first assuming that the system frequencies are known and constant the running basis and fixed basis variants of the ewbf algorithm are derived and their relationship to the classical notch filter with constrained poles and zeros is established next the frequency adaptive versions of both algorithms are obtained using the gradient search and recursive prediction error principles respectively finally the interrelated frequencies case is analyzed and two additional parameter tracking algorithms generalized adaptive comb filters are derived

tracking analysis of an adaptive notch filter with constrained poles and zeros this paper analyzes the asymptotic tracking properties of an adaptive notch filter anf with pole zero constraints for the cancellation or retrieval of multiple time varying sine waves in additive noise the asymptotic mean square error mse is analyzed using the methods of ljung and gunnarsson 1990 when the variations in the underlying frequencies are assumed to be sufficiently small closed form expressions for the mse are derived as functions of the tuning variables of the algorithm the results give insight into the operational properties of the algorithm and are used in order to minimize the mse with respect to the tuning variables computer simulations confirm the validity of the derived results