direct frequency domain deconvolution when the signals have no spectral inverse a method for frequency domain deconvolution when the kernel has no spectral inverse is presented discrete frequency interpolation is used to avoid zero valued frequency samples the algorithm does not suffer from the spectral singularities of the original kernal and its complexity is proportional to that of the fast fourier transform a comparative noise study showed improved performance relative to the direct frequency domain method

a relaxed condition for perfect cancellation of broadband noise in 3d enclosures this paper presents a relaxed condition for perfect cancellation of broadband noise in 3d enclosures on the basis of a truncated modal model it can be shown that the primary and secondary paths belong to a same subspace if a certain condition is satisfied there exists a finite impulse response fir filter transfer function vector for perfect cancellation of the primary paths the analytical result is verified numerically with an active noise control anc system in a 3d rectangular enclosure the proposed anc scheme is shown to fit well into the framework of an existing multichannel least mean squares lms algorithm for adaptive implementation

least squares methods for stokes equations based on a discrete minus one inner product abstract the purpose of this paper is to develop and analyze least squares approximations for stokes and elasticity problems the major advantage of the least squares formulation is that it does not require that the classical ladyzhenskaya bab ska brezzi lbb condition be satisfied we provide two methods the first is posed in terms of the velocity pressure pair without the introduction of additional variables the second adds a vorticity variable in both cases we employ least squares functionals which involve a discrete inner product which is related to the inner product in h 1 the sobolev space of order minus one on the use of such inner products applied to second order problems was proposed in an earlier paper by bramble lazarov and pasciak 1994

optimal regularization parameter of the multichannel filtered x affine projection algorithm we discuss the optimal regularization parameter of the filtered affine projection fx ap algorithm suitable for feedforward active noise control while the original fx ap algorithm always provides a biased estimate of the minimum mean square solution we show that the optimal regularized fx ap algorithm is capable to eliminate the bias of the asymptotic solution and thus that the regularization parameter can optimize both the convergence speed and the residual mse of the algorithm we derive some expressions for the optimal regularization parameter and we discuss some heuristic estimations of the optimal regularization parameter in practical conditions

a posteriori error estimation for a pde constrained optimization problem involving the generalized oseen equations we derive globally reliable a posteriori error estimators for a linear quadratic optimal control problem involving the generalized oseen equations as state equations control constraints are also considered the corresponding local error indicators are locally efficient the assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods when stabilized methods are considered no a priori relation between the stabilization terms for the state and adjoint equations is required if a lower bound for the inf sup constant is available a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained we illustrate the theory with numerical examples

abundance of strange attractors in 1976 he h non performed a numerical study of the family of diffeomorphisms of the plane ha b x y 1 ax2 y bx and detected for parameter values a l 4 b 0 3 what seemed to be a non trivial attractor with a highly intricate geometric structure this family has since then been the subject of intense research both numerical and theoretical but its dynamics is still far from being completely understood in particular one could not exclude the possibility that the attractor observed by h6non were just a periodic orbit with a very high period recently in a remarkable paper bc2 benedicks and carleson were able to show that this is not the case at least for a positive lebesgue measure set of parameter values near a 2 b o more precisely they showed that if b 0 is small enough then for a positive measure set of a values near a 2 the corresponding diffeomorphism ha b exhibits a strange attractor their argument is a very creative extension of the techniques they had previously developed in bull for the study of the quadratic family on the real line and no doubt it will be important for the understanding of several other situations of complicated nonhyperbolic dynamics when acquainted in 1985 with the work by benedicks and carleson then in progress palls suggested that one should in this context think of the h6non family as a particular although important model for the creation of a horseshoe and that the emphasis should be put on the occurrence of unfoldings of homoclinic tangencies he proposed that the correct setting for benedicks carleson s results is within this more general framework of homoclinic bifurcations and stated the following

least squares finite element methods for optimization and control problems for the stokes equations the approximate solution of optimization and control problems for systems governedby the stokes equations is considered modern computational techniques for such problems are predominantly based on the application of the lagrange multiplier rule while penalty formulations even though widely used in other settings have not enjoyed the same level of popularity for this class of problems a discussion is provided that explains why naively defined penalty methods may not be practical then practical penalty methods are defined using methodologies associated with modern least squares finite element methods the advantages with respect to efficiency of penalty leasts squares methods for optimal control problems compared to methods based on lagrange multipliers are highlighted a tracking problem for the stokes system is used for illustrative purposes

estimating the order of a fir filter for noise cancellation the problem of designing a finite impulse response filter devoted to the joint process problem and in particular to noise cancellation is investigated the goal is restricted to how to choose an optimal order of the fir filter the analysis is based on the maximization of a noise reduction criterion which is in fact perfectly matched to the desired performance namely the minimization of residuals the criterion includes estimation errors introduced by the substitution of the true covariance matrices for estimates since true covariance matrices again enter the noise reduction criterion they must be replaced by estimates the criterion is then modified in order to take this fact into account but the scheme is not iterated any further simulations are presented for various simple cases

numerical simulation of optimal deconvolution in a shallow water environment a fast technique for deconvolving signals in a dispersive multipath shallow water environment using inverse filters is compared with the more commonly used deconvolution technique of time reversal also known as phase conjugation the objective of such techniques is to improve the accuracy of sound transmission from a source array to some receiving space time reversal provides benefits in this regard but here the additional performance that can be gained from inverse filters is examined several strategies for obtaining a set of inverse filters are discussed each aimed at improving the accuracy of the reconstruction of the desired time signals through inverse techniques it will be shown that an optimal inversion in the sense of achieving a flat system response in the frequency domain does not necessarily achieve a realizable time domain filter a fast field model using oases of the giglio basin shallow water test facility is used as the basis for evaluating the various focusing strategies for single receiver locations it will be seen that inverse filter arrays provide enhanced temporal and spatial focusing when compared to time reversal arrays in addition inverse filtering allows multiple receivers to be used thereby increasing bandwidth or improving redundancy

transient and steady state analysis of filtered x affine projection algorithms this paper provides an analysis of transient and steady state behavior of different filtered x affine projection algorithms algorithms suitable for single channel and for multichannel active noise controllers are treated within a unified framework very mild assumptions are posed on the active noise control system model which is only required to have a linear dependence of the output from the filter coefficients therefore the analysis applies not only to the linear finite impulse response models but also to nonlinear volterra filters i e polynomial filters and other nonlinear filter structures the convergence analysis presented in this paper relies on energy conservation arguments and does not apply the independence theory nor does it impose any restriction to the signal distributions it is shown in the paper that filtered x affine projection algorithms always provide a biased estimate of the minimum mean square solution nevertheless in many cases the bias is small and therefore these algorithms can be profitably applied to active noise control

fast design of multichannel fir least squares filters with optimum lag this paper is mainly concerned with the efficient design of optimum lag fir least squares filters these filters result when the minimization of the total mean square error encompasses a time shift between the input signal and the desired response the solution of this problem leads to a family of normal systems of equations whose associated matrix is the same while the right hand side members are parametrized by the lag ranging within a specified interval the fast algorithm derived here for the determination of the optimum lag filter provides the solutions of the above family of systems by step up step down levinson like order recursions coupled with time updating kalman like relations and offers a recursive error capability as well this is achieved by exploiting the near to toeplitz structure of the matrix and a certain shift invariance property the right hand side members possess finally motivated by the optimum lag problem systems of equations with near to toeplitz parameters are considered and a fast algorithm is developed the proposed schemes find important applications in seismic signal processing system identification economic forecasting etc

an error bound for a noise canceller the degradation in performance of the least mean square estimation lmse is evaluated after replacing the covariance matrices with estimates taking advantage of the statistical properties of the complex wishart matrix and its inverse the decrease in performance stemming from this substitution is investigated the performance criterion is based on the computation of the final output error which includes covariance deviations this is carried out for a certain class of linear observation models involving an underlying problem of noise cancelling using noise alone references nars namely array processing techniques using a known array manifold performance limits of the adaptive noise canceller are investigated for the case of a spectral filter to illustrate the ideas it is shown that its performance depends on the quadratic coherency between the corrupted signal and the nar it is preferable to run no processing when this coherency is not strong enough a rule is proposed in order to decide when to switch to the no processing scheme contrary to some previous results the results given are available without any approximations provided the statistical properties are satisfied in the case of a special noise canceller these properties are asymptotically satisfied in the case of a transversal noise canceller acting in the time domain these results are valid for white signals and noises

finite element methods of least squares type we consider the application of least squares variational principles to the numerical solution of partial differential equations our main focus is on the development of least squares finite element methods for elliptic boundary value problems arising in fields such as fluid flows linear elasticity and convection diffusion for many of these problems least squares principles offer numerous theoretical and computational advantages in the algorithmic design and implementation of corresponding finite element methods that are not present in standard galerkin discretizations most notably the use of least squares principles leads to symmetric and positive definite algebraic problems and allows us to circumvent stability conditions such as the inf sup condition arising in mixed methods for the stokes and navier stokes equations as a result application of least squares principles has led to the development of robust and efficient finite element methods for a large class of problems of practical importance

noise reduction for an estimated wiener filter using noise references corresp a simple approach to the adaptation of a linear filter to cope with spectral uncertainties is presented based on the calculation of the total output error power including the errors of spectral estimation a criterion is proposed for deciding whether the estimated filter is effective at any given frequency by forcing the filter response to unity at all ineffective frequencies an improvement in performance is obtained

least squares methods for optimal control optimal control and optimal shape design problems for the navier stokes equations arise in many important practical applications such as design of optimal profiles 7 drag minimization 9 11 and heating and cooling 12 among others typically optimal control problems for the navierstokes equations combine lagrange multiplier techniques to enforce the constraints and to derive an optimality system see e g 11 12 with mixed galerkin discretization for the state equations resulting methods are well studied theoretically for example an abstract framework that can be used for the analyses of such optimal control methods has been suggested in 13 however the use of lagrange multipliers and mixed galerkin discretizations is associated with some complications in the numerical computations which can reduce the overall efficiency and robustness of corresponding algorithms for example resulting discrete problems are in general indefinite similarly it is now well understood that stability of mixed discretizations does not allow one to choose independently the approximation spaces for the velocity and the pressure and that these spaces are subject to a restrictive stability condition known as the inf sup or lbb condition see 8 one possibility to remedy these difficulties is to consider optimal control methods in which the navier stokes constraint is treated by augmented lagrangian techniques see 6 nevertheless the use of mixed galerkin discretization in the method of 6 still requires approximation by finite element spaces that are subject to the inf sup condition

a least squares approach based on a discrete minus one inner product for first order systems the purpose of this paper is to develop and analyze a least squares approximation to a first order system the first order system represents a reformulation of a second order elliptic boundary value problem which may be indefinite and or nonsymmetric the approach taken here is novel in that the least squares functional employed involves a discrete inner product which is related to the inner product in h 1 the sobolev space of order minus one on the use of this inner product results in a method of approximation which is optimal with respect to the required regularity as well as the order of approximation even when applied to problems with low regularity solutions in addition the discrete system of equations which needs to be solved in order to compute the resulting approximation is easily preconditioned thus providing an efficient method for solving the algebraic equations the preconditioner for this discrete system only requires the construction of preconditioners for standard second order problems a task which is well understood

fast algorithms for discrete time wiener filters with optimum lag in many applications including geophysical signal processing and system identification the computation of a fir wiener filter corresponding to the optimum lag between the input signal and the desired response or of an optimum prediction distance predictor are often required these problems lead to the solution of a family of toeplitz systems of equations having the same associated matrix but right hand side vectors which are shifted versions of each other a very efficient method for the solution of the optimum lag problem is the well known simpson s sideways recursions the purpose of this paper is to introduce two new algorithms for the efficient computation of the optimum lag wiener filter as well as the optimum prediction distance predictor their main characteristic is a coupled step down step up recursion which takes full advantage of both the toeplitz nature of the matrix and the shifted structure of the right hand side vectors the proposed algorithms are featured by increased speed they are about twice as fast as simpson s scheme and computational simplicity in addition they provide recursive error computation capability and give further insight into the problem

a new method for d dimensional exact deconvolution deconvolution is an important problem of signal processing and conventional approaches including fourier methods have stability problems due to the zeros of the convolution kernel we present a new method of multidimensional exact deconvolution this method is always stable even when the convolution kernel h n has zeros on the unit circle and there exist closed form solutions for the one dimensional 1 d case d 1 for the multidimensional case d 1 the proposed method yields stable solutions when det h d this solution set covers a portion of all possible convolution kernels including the ones that have zeros on the multidimensional unit circle this novel time domain method is based on the fact that the convolution inverse of a first order kernel can be found exactly in multidimensional space convolution inverses for higher order kernels are obtained using this fact and the zeros of the convolution kernel the presented method is exact stable and computationally efficient several examples are given in order to show the performance of this method in 1 d and multidimensional cases

first order system least squares methods for an optimal control problem by the stokes flow the least squares approximations of an optimal control problem governed by the stokes equations are considered which leads to an unconstrained coupled optimization problem by the lagrange multiplier method the least squares functionals for the two and three dimensional first order coupled optimality systems are employed by modifying those functionals in z cai t a manteuffel and s f mccormick siam j numer anal 34 1997 pp 1727 1741 the established ellipticity and continuity in a product h 1 norm yield the optimal discretization error estimates in the finite element spaces for numerical tests we apply v cycle multigrid methods to the whole discrete algebraic system

analysis and approximation of optimal control problems for first order elliptic systems in three dimensions we examine analytical and numerical aspects of optimal control problems for first order elliptic systems in three dimensions the particular setting we use is that of divcurl systems after formulating some optimization problems we prove the existence and uniqueness of the optimal solution we then demonstrate the existence of lagrange multipliers and derive an optimality system of partial differential equations from which optimal controls and states may be deduced we then define least squares finite element approximations of the solution of the optimality system and derive optimal estimates for the error in these approximations

on stabilized mixed methods for generalized stokes problem based on the velocity pseudostress formulation a priori error estimates abstract in this paper we present an augmented mixed formulation applied to generalized stokes problem and uses it as state equation in an optimal control problem the augmented scheme is obtained adding suitable least squares terms to the corresponding velocity pseudostress formulation of the generalized stokes problem to ensure the existence and uniqueness of solution at continuous and discrete levels we prove coerciveness of the corresponding augmented bilinear form and using approximation properties of the respective discrete subspaces we deduce the optimal rate of convergence as by product and considering the associated optimal control problem we derive error estimates for the approximated control unknown finally we present several numerical examples confirming the theoretical properties of this approach

efficient recursive in order least squares fir filtering and prediction this paper is concerned with the efficient determination of the optimum in the least squares sense fir filter on the basis of data samples of the input and desired response signals by procedures recursive in the filter order this situation typically arises when no a priori statistics are available and the system order is not known the general multiinput multioutput multichannel case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2s 15m multiplications mps per order m s being the number of samples in the special case of linear prediction it calls for about s 12m mps hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of marple 1 and morf et al 2 respectively additionally the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter

levinson type extensions for non toeplitz systems it is shown levinson s basic principle for the solution of normal equations which are of toeplitz form may be extended to the case where these equations do not possess this specific symmetry the method is illustrated by application to various examples which are chosen so that the coefficient matrix possesses various symmetries specifically the solution of the normal equations when the associated matrix is the doubly symmetric non toeplitz covariance matrix is considered next the solution of extended yule walker equations where the coefficient matrix is toeplitz but nonsymmetric is obtained finally the approach is illustrated by considering the determination of the prediction error operator when the normal equations are of symmetric toeplitz form

least squares finite element methods for optimality systems arising in optimization and control problems the approximate solution of optimization and optimal control problems for systems governed by linear elliptic partial differential equations is considered such problems are most often solved using methods based on applying the lagrange multiplier rule to obtain an optimality system consisting of the state system an adjoint state system and optimality conditions galerkin methods applied to this system result in indefinite matrix problems here we consider using modern least squares finite element methods for the solution of the optimality systems the matrix equations resulting from this approach are symmetric and positive definite and are readily amenable to uncoupling strategies this is an important advantage of least squares principles as they allow for a more efficient computational solution of the optimization problem we develop an abstract theory that includes optimal error estimates for least squares finite element methods applied to optimality systems we then provide an application of the theory to optimization problems for the stokes equations

least squares methods for optimal shape design problems abstract a least squares method for solving an optimal shape design problem which appears in semiconductor device physics is described discretization by finite element methods is used for numerical solving an example and experimental results are presented

a least squares penalty method for distributed optimal control problems for stokes equations the purpose of this paper is to construct an unconstrained optimal control problem by using a least squares approach for the constrained distributed optimal control problem associated with incompressible stokes equations the constrained equations are reformulated to the equivalent first order system by introducing vorticity and then the least squares functional corresponding to the system is enforced via a penalty term to the objective functional the existence of a solution of the unconstrained optimal control problem is proved and the convergence of this solution to that of unpenalized one is demonstrated as the penalty parameter tends to zero finite element approximations with error estimates are studied and the relevant computational experiments are presented

inverse filtering of room acoustics a novel method is proposed for realizing exact inverse filtering of acoustic impulse responses in room this method is based on the principle called the multiple input output inverse theorem mint the inverse is constructed from multiple finite impulse response fir filters transversal filters by adding some extra acoustic signal transmission channels produced by multiple loudspeakers or microphones the coefficients of these fir filters can be computed by the well known rules of matrix algebra inverse filtering in a sound field is investigated experimentally it is shown that the proposed method is greatly superior to previous methods that use only one acoustic signal transmission channel the results prove the possibility of sound reproduction and sound reception without any distortion caused by reflected sounds

spectral hp penalty least squares finite element formulation for the steady incompressible navier stokes equations in this paper we present spectral hp penalty least squares finite element formulation for the numerical solution of steady incompressible navier stokes equations the continuity equation is treated as a constraint on velocity field and the constraint is enforced using the penalty method which is equivalent to replacing the pressure variable p with p n p n email protected u where u is the velocity field c is the penalty parameter and superscript n is non linear iteration number the modified navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity dilatation or stresses as additional independent variables and the least squares method is used to develop the finite element model high order basis functions are used to construct the discrete model unlike other penalty finite element formulations equal order integration is used for all terms of the coefficient matrix schur complement method is used and all interior element degrees of freedom are condensed out and interface degrees of freedom are solved either by direct solver banded cholesky factorization or iterative solver preconditioned conjugate gradient present formulation produces very accurate results for even very low penalty parameters 10 40 in this way present formulation and implementation fixes perennial problem of bad conditioning of coefficient matrix associated with penalty formulations proposed formulation is verified using the exact solution of kovasznay flow numerical results are also presented for a number of two dimensional benchmark problems e g 2d lid driven cavity flow flow over a backward facing step steady flow past a circular cylinder and 2d flow past a large circular cylinder in a channel finally the proposed formulation is extended to coupled velocity temperature problems and buoyant flow inside a square enclosure is solved to test the penalty least squares finite element model developed herein

multilevel and weighted reduced basis method for stochastic optimal control problems constrained by stokes equations in this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by stokes equations we prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data the finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space respectively resulting in many large scale optimality systems to solve in order to reduce the unaffordable computational effort we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse grid techniques a weighted a posteriori error bound highlights the contribution stemming from each method numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient especially for solving high dimensional and large scale optimization problems

an adaptive kalman equalizer structure and performance the development of an adaptive infinite impulse response iir linear equalizer is described using discrete time wiener filtering theory a closed form for the optimum mean square error iir filter is derived a performance comparison using both minimum and non minimum phase channels indicates the complexity performance advantages inherent in the iir system compared to an optimum finite impulse response fir solution the minimum phase spectral factorization which is an integral part of the derivation of the iir equalizer may be circumvented through the use of a kalman equalizer such as that originally proposed by lawrence and kaufman the structure is made adaptive by using a system identification algorithm operating in parallel with a kalman equalizer in common with luvison and pirani a least mean squares lms algorithm was chosen for the system identification because the input to the channel is white and hence the lms algorithm will produce consistent predictable results with little added complexity a new technique is introduced which both estimates the variance of channel noise and compensates the kalman filter for errors in the estimate of the channel impulse response computer simulation results show that the convergence performance of this new adaptive iir filter is roughly equivalent to an fir equalizer which is trained using a recursive least squares algorithm however the order of the new filter is always lower than the fir filter

fast affine projection adaptation algorithms with stable and robust symmetric linear system slovers this paper proposes two noniterative approaches to solve a symmetric linear system associated with the fast affine projection adaptation algorithm the first approach using matrix ldlt factorization can provide an exact solution at a moderate complexity in contrast with the fact that existing stable approaches are all approximate based on a reciprocating recursion scheme the second approach has a very low complexity and gives a good approximate solution steady state and transient properties of the proposed and certain previous fap algorithms are studied in detail being stable and optimal under all step size conditions fast affine projection algorithms incorporating the proposed approaches are promising in telecom and other applications of adaptive filtering

a penalty least squares method for optimal control problems for first order elliptic systems a penalty least squares method for optimal control problems for first order elliptic systems is considered wherein the constraint equations are enforced via penalization the convergence as the penalty parameter tends to zero of the solution to the penalized optimal control problem to that of the unpenalized one is demonstrated as is the convergence of a gradient method for determining solutions of the penalized optimal control problem finally finite element approximations of the penalized optimal control problem are studied and optimal error estimates are obtained

an fir estimation filter based on the sampling theorem the estimation of noise perturbed bandlimited stochastic signal samples by fir filtering is considered the mean square error of the estimate is used as the criterion of performance we contrast three types of filters all pass a sampling theorem based filter and the minimum mean square error wiener filter although the wiener filter is linearly optimal its design requires detailed knowledge of the processes second order statistics the sampling theorem filter does not for large signal to noise ratios and large filter orders the two filters perform nearly identically asymptotically furthermore we demonstrate that for a fixed filter order there exists an optimal sampling rate which decreases with increasing signal to noise ratio

minimax robust deconvolution filters under stochastic parametric and noise uncertainties the author consider the design of robust deconvolution filters for linear discrete time systems with stochastic parameter and noise uncertainties it is assumed that some large but bounded uncertainties exist in the driving and measurement noise covariances as well as the second order statistics of stochastic parameters and initial conditions three kinds of minimax sensitivity criteria are used to develop the techniques to the synthesis of minimax deconvolution filters under uncertain linear stochastic systems their approach is based on saddle point theory and the sensitivity analysis of kalman filters the design algorithms give the recursive realization of the minimax deconvolution filters for the time varying uncertain systems under fairly general conditions for the time invariant uncertain case the existence and solutions of steady state deconvolution filters are further developed finally the utility of the minimax design approaches and the properties of the resulting minimax deconvolution filters are illustrated by a numerical example

wavelet deconvolution this paper studies the issue of optimal deconvolution density estimation using wavelets the approach taken here can be considered as orthogonal series estimation in the more general context of the density estimation we explore the asymptotic properties of estimators based on thresholding of estimated wavelet coefficients minimax rates of convergence under the integrated square loss are studied over besov classes b sub spl sigma pq of functions for both ordinary smooth and supersmooth convolution kernels the minimax rates of convergence depend on the smoothness of functions to be deconvolved and the decay rate of the characteristic function of convolution kernels it is shown that no linear deconvolution estimators can achieve the optimal rates of convergence in the besov spaces with p 2 when the convolution kernel is ordinary smooth and super smooth if the convolution kernel is ordinary smooth then linear estimators can be improved by using thresholding wavelet deconvolution estimators which are asymptotically minimax within logarithmic terms adaptive minimax properties of thresholding wavelet deconvolution estimators are also discussed

lse and mse optimum partition based fir iir deconvolution filters with best delay we considered the least squares error lse and mean square error mse optimum best delay deconvolution filter design we presented the partition based finite impulse response infinite impulse response fir iir filters where the channel zeros are partitioned into two regions the first region is composed of the selected channel zeros inside the unit circle and the second region is composed of the remaining channel zeros outside the first region two methods for obtaining partitions are proposed namely optimum partitioning and ring based partitioning resulting fir iir filters are compared with the fir and fir iir unit circle best delay inverse filters in terms of their lse it is shown that the partition based fir iir filter performances are about 4 5 db better than their fir counterpart for the same complexity then starting with the best delay fir wiener deconvolution filter formulation we extended our results for the design of fir iir mse optimum deconvolution filters we have compared the optimum partitioning and ring based fir iir inverse filters with the fir and iir wiener deconvolution filters it is shown that fir iir best delay inverse filters are less sensitive to the estimation errors compared with the iir wiener filters and they perform better than the fir wiener filters furthermore they are always causal and stable making them suitable for real time implementations

optimal control of the stokes equations a priori error analysis for finite element discretization with postprocessing an optimal control problem for 2d and 3d stokes equations is investigated with pointwise control constraints this paper is concerned with the discretization of the control by piecewise constant functions the state and the adjoint state are discretized by finite element schemes in the paper a postprocessing strategy is suggested which allows for significant improvement of the accuracy

a channel selection criterion for suppressing reverberation in cochlear implants little is known about the extent to which reverberation affects speech intelligibility by cochlear implant ci listeners experiment 1 assessed ci users performance using institute of electrical and electronics engineers ieee sentences corrupted with varying degrees of reverberation reverberation times of 0 30 0 60 0 80 and 1 0 s were used results indicated that for all subjects tested speech intelligibility decreased exponentially with an increase in reverberation time a decaying exponential model provided an excellent fit to the data experiment 2 evaluated offline a speech coding strategy for reverberation suppression using a channel selection criterion based on the signal to reverberant ratio srr of individual frequency channels the srr reflects implicitly the ratio of the energies of the signal originating from the early and direct reflections and the signal originating from the late reflections channels with srr larger than a preset threshold were selected while channels with srr smaller than the threshold were zeroed out results in a highly reverberant scenario indicated that the proposed strategy led to substantial gains over 60 percentage points in speech intelligibility over the subjects daily strategy further analysis indicated that the proposed channel selection criterion reduces the temporal envelope smearing effects introduced by reverberation and also diminishes the self masking effects responsible for flattened formants

symmetry breaking perturbations and strange attractors the asymmetrically forced damped duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with textit symmetry breaking disturbances even a slight fixed asymmetry in the perturbation may cause a substantial change in the asymptotic behavior of the system e g transitions from two sided to one sided strange attractors as the other parameters are varied moreover slight asymmetries may cause substantial asymmetries in the relative size of the basins of attraction of the unforced nearly symmetric attracting regions these changes seems to be associated with homoclinic bifurcations numerical evidence indicates that textit strange attractors appear near curves corresponding to specific secondary homoclinic bifurcations these curves are found using analytical perturbational tools

using lyapunov exponents to predict the onset of chaos in nonlinear oscillators an analytic technique for predicting the emergence of chaotic instability in nonlinear nonautonomous dissipative oscillators is proposed the method is based on the lyapunov type stability analysis of an arbitrary phase trajectory and the standard procedure of calculating the lyapunov characteristic exponents the concept of temporally local lyapunov exponents is then utilized for specifying the area in the phase space where any trajectory is asymptotically stable and therefore the existence of chaotic attractors is impossible the procedure of linear coordinate transform optimizing the linear part of the vector field is developed for the purpose of maximizing the stability area in the vicinity of a stable fixed point by considering the inverse conditions of asymptotic stability this approach allows formulating a necessary condition for chaotic motion in a broad class of nonlinear oscillatory systems including many cases of practical interest the examples of externally excited one and two well duffing oscillators and a planar pendulum demonstrate efficiency of the proposed method as well as a good agreement of the theoretical predictions with the results of numerical experiments the comparison of the proposed method with melnikov s criterion shows a potential advantage of using the former one at high values of dissipation parameter and or multifrequency type of excitation in dynamical systems

a fast quasi newton adaptive filtering algorithm the convergence rate of an adaptive system is closely related to its ability to track a time varying optimum basic adaptive filtering algorithms give poor convergence performance when the input to the adaptive system is colored more sophisticated algorithms which converge very rapidly regardless of the input spectrum algorithms typically require o n sup 2 computation where n is the order of the adaptive filter a significant disadvantage for real time applications also many of these algorithms behave poorly in finite precision implementation an adaptive filtering algorithm is introduced which employs a quasi newton approach to give rapid convergence even with colored inputs the algorithm achieves an overall computational requirement of o n and appears to be quite robust in finite precision implementations

levinson type algorithms for polynomial fitting and for cholesky and q factors of hankel and vandermonde matrices this paper presents levinson 1947 type algorithms for i polynomial fitting ii obtaining a q decomposition of vandermonde matrices and a cholesky factorization of hankel matrices iii obtaining the inverse of hankel matrices the algorithm for the least squares solution of hankel systems of equations requires 3n sup 2 9n 3 multiply and divide operation mdo the algorithm for obtaining an orthogonal representation of an m spl times n vandermonde matrix x and computing the cholesky factors f of hankel matrices requires 5mn n sup 2 2n 3m mdo and the algorithm for generating the inverse of hankel matrices requires 3 n sup 2 n 2 2 mdo our algorithms have been tested by means of fitting of polynomials of various orders and fortran versions of all subroutines are provided in the appendix