robust shrinkage affine projection sign adaptive filtering algorithms for impulsive noise environments two robust affine projection sign raps algorithms both of which minimize the mixed norm of l 1 and l 2 of the error signal are proposed the direction vector of the raps algorithms is obtained from the gradient of an l 1 norm based objective function while two related l 2 norm based minimization problems are solved to obtain the line search of the two raps algorithms the l 1 norm based direction vector reduces the impact of impulsive noise whereas the l 2 norm based line search produces an unbiased solution in the proposed algorithms in addition one of the two raps algorithms shares the data selective adaptation used in the set membership sm affine projection smap algorithm the proposed algorithms are shown to offer a significant improvement in the convergence speed as well as a significant reduction in the steady state misalignment relative to the pseudo affine projection sign paps algorithm in addition the proposed algorithms offer robust performance with respect to impulsive noise and improved tracking of the unknown system in comparison to that provided by the paps and affine projection sign aps algorithms these features of the proposed algorithms are demonstrated using simulation results in system identification and echo cancellation applications

optimal design of constrained fir filters without phase response specifications finite impulse response fir filters without phase response specifications have found many applications in signal processing and communications it is shown in this paper that the constrained lp magnitude error design of such an fir filter is equivalent to a constrained lp approximation of a given response with a phase equal to that of the optimal filter of the original problem an iterative method is then proposed to compute that phase by converting the nonconvex constrained lp magnitude error problem into a series of convex constrained lp elliptic frequency response error subproblems it is also shown that the solutions of these convex subproblems converge to a karush kuhn tucker point of the original problem the convergence and its model parameter and initial condition dependence are shown through the designs of fir filters without time domain constraints the iterative method is then applied to the minimax design of evidence filters nyquist filters and step response constrained filters and to the lp design of pulse shaping filters for ultra wideband systems design examples demonstrate that the proposed method obtains better filters in terms of magnitude error group delay and spectrum utilization efficiency than existing methods

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

iterative reweighted least squares design of fir filters develops a new iterative reweighted least squares algorithm for the design of optimal l sub p approximation fir filters the algorithm combines a variable p technique with a newton s method to give excellent robust initial convergence and quadratic final convergence details of the convergence properties when applied to the l sub p optimization problem are given the primary purpose of l sub p approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained l sub 2 approximation filters the new method can also be applied to the complex chebyshev approximation problem and to the design of 2d fir filters

simulation of environmental flow problems in geometrically complex domains part i a general coordinate transformation abstract a two part presentation is given in which a combination of domain splitting coordinate transformation and an implicit algorithm is suggested as a versatile three dimensional program for accurate simulation of geometrically complex environmental flow problems in part 1 a numerical method for solving the time dependent laminar navier stokes equations posed in general curvilinear coordinates is presented the issues of equation form consistency and accuracy are considered as they relate to numerical simulation of incompressible flows on curvilinear grid systems the method is applied to flows in square and polar cavities and evaluated in terms of corresponding benchmark physical and numerical experiments

complex chebyshev approximation for fir digital filters an adaptive approach to fir finite impulse response filter design is applied to a fully general complex specification showing it to be capable of giving an optimum chebyshev solution it is thought to be one of the first practical approaches to achieve this in the case of a complex function design examples include a bandpass filter with nearly linear phase and all pass filters with general shaping phase comparisons are drawn with equivalent results from other algorithms

reduction of symmetric complex filters due to their linear phase property symmetric filters are an interesting class of finite impulse response fir filters moreover symmetric fir filters allow an efficient implementation in this paper we extend the classical definition of hermitian symmetry to a more general symmetry that is also applicable to complex filters this symmetry is called generalized hermitian symmetry we show the usefulness of this definition as it allows for a unified treatment of even and odd length filters central in this paper is a theorem on the reduction of generalized hermitian symmetric filters to hermitian symmetric filters both with finite precision coefficients a constructive proof of this theorem is presented and an associated procedure for reducing generalized hermitian symmetric filters is derived two of the examples show the application of the reduction procedure and the achieved savings on arithmetic costs finally all three examples show that a special instance of the generalized hermitian symmetric filters with finite precision coefficients may have lower arithmetic costs than the hermitian symmetric filter from which it is derived

l sub 1 and l sub infinity minimization via a variant of karmarkar s algorithm simple iterative algorithms are presented for l sub 1 and l sub infinity minimization regression based on a variant of karmarkar s linear programming algorithm although these algorithms are based on entirely different theoretical principles to the popular irls iteratively reweighted least squares algorithm they have almost identical matrix operations also presented are the results of a monte carlo study comparing the numerical convergence properties of the karmarkar algorithm for l sub 1 minimization to those of an irls and a simplex algorithm the test problem involves l sub 1 estimation of ar autoregressive model parameters the karmarkar algorithm outperformed irls by achieving higher numerical accuracy in fewer iterations techniques for reducing the computational cost per iteration of the karmarkar l sub 1 algorithm are discussed

driven cavity flows by efficient numerical techniques abstract efficient and reliable numerical techniques of high order accuracy are presented for solving problems of steady viscous incompressible flow in the plane and are used to obtain accurate solutions for the driven cavity a solution is obtained at reynolds number 10 000 on a 180 180 grid the numerical methods combine an efficient linear system solver an adaptive newton like method for nonlinear systems and a continuation procedure for following a branch of solutions over a range of reynolds numbers

a weighted least squares algorithm for quasi equiripple fir and iir digital filter design it has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of a finite impulse response fir filter the weighted least squares solution is equiripple the crux of the problem lies in the determination of the necessary least squares frequency response weighting function a novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi equiripple design is presented the algorithm converges very rapidly it typically produces a design which is only about 1 db away from the minimax optimum solution in two iterations and converges to within 0 1 db in six iterations convergence speed is independent of the order of the filter it can be used to design filters with arbitrarily prescribed phase and amplitude response

design of fir filters in the complex domain the design of fir digital filters with a complex valued desired frequency response using the chebyshev error is investigated the complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem a standard linear programming algorithm for the chebyshev solution of overdetermined equations is used to solve the real approximation problem additional constraints are introduced which allow weighting of the phase and or group delay of the approximation digital filters are designed which have nearly constant group delay in the passbands the desired constant group delay which gives the minimum chebyshev error is found to be smaller than that of a linear phase filter of the same length these filters in addition to having a smaller approximately constant group delay have better magnitude characteristics than exactly linear phase filters with the same length the filters have nearly equiripple magnitude and group delay

an l_1 method for the design of linear phase fir digital filters this paper considers the design of linear phase finite impulse response digital filters using an l1 optimality criterion the motivation for using such filters as well as a mathematical framework for their design is introduced it is shown that l1 filters possess flat passbands and stopbands while keeping the transition band comparable to that of least squares filters the uniqueness of l1 based filters is explored and an alternation type theorem for the optimal frequency response is derived an efficient algorithm for calculating the optimal filter coefficients is proposed which may be viewed as the analogue of the celebrated remez exchange method a comparison with other design techniques is made demonstrating that the l1 approach may be a good alternative in several applications

random matrix model for dissipative two level systems assuming a random matrix model for the system bath interaction and using a series expansion for the evolution operator we studied the relaxation of a nondegenerate two level system for times larger than the duration of a collision and smaller than the poincare recurrence time we calculate the survival probability of still finding the system at timet in the same state in which it was prepared att 0 for a fixed initial state of the bath we obtain an exponential transition rate but when we average over initial states we may get a mixture of decay constants that could distroy the exponential behavior of the transition rate

fast and stable least squares approach for the design of linear phase fir filters we present a new numerical algorithm for solving the normal equations associated with the least squares design of linear phase fir filters the usual solution methods have a computational complexity of o n sup 3 moreover solving the normal equations with gaussian elimination commonly yields numerical errors especially when the filter is long here we convert a least squares method into the problem of constructing a system of orthonormal functions the proposed design algorithm needs only o n sup 2 computations and numerical errors can be reduced some examples are given to show the performance of the algorithm

on the design of fir filters by complex chebyshev approximation the long standing problem of approximating a complex valued desired function with a finite impulse response fir filter is considered it is formulated as an equalization to be solved using complex valued filters the proposed algorithm deals directly with the complex error function which depends linearly on the coefficients of the filter to be designed the magnitude of this error function is minimized in the chebshev sense using a generalization of the remez exchange algorithm the method can be used to design complex or real valued selective systems as well the well known design of optimal fir filters with linear phase is included here as a special case

least squared error fir filter design with transition bands the authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least squared error fir digital filters with an explicit control of the transition band edges design formulas are derived for approximations to ideal frequency responses which use pth order spline transition functions a mixed analytical and numerical method for zero error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived a variable order spline transition function is developed and a method for choosing the optimal order to minimize the integral squared approximation error is given

a random matrix model of relaxation we consider a two level system coupled to a general n level system via a random matrix we derive an integral representation for the mean reduced density matrix t of in the limit n and we identify a model of which possesses some of the properties expected for macroscopic thermal reservoirs in particular it yields the gibbs form for we also consider an analog of the van hove limit and obtain a master equation markov dynamics for the evolution of t on an appropriate time scale

generalized coordinate forms of governing fluid equations and associated geometrically induced errors the governing equations of fluid flow may be cast into various forms upon application of a generalized coordinate mapping these forms are the nonconservation law form nclf and strong weak and chain rule conservation law forms sclf wclf crclf respectively this paper describes the geometrically induced errors resulting from the failure to satisfy a certain consistency condition for each of these four forms and also demonstrates the ability of the crclf to produce exactly the same numerical solution as the wclf provided a condition is met on where to evaluate the transformation metrics it is also demonstrated that considerably fewer arithmetic operations are required to advance the solution from n to n 1 when the crclf is used in com parison to both the sclf and wclf he effort devoted to the field of computational fluid dynamics is progressing at an ever increasing rate at certain points in time during this natural evolution of numerical methods schemes and ideas it is sometimes in structive to pause to reflect upon past work in an attempt to gain the proper perspective it is important that this reflection reaches all of the way to the fundamental rules and practices used to develop numerical techniques some of these practices are often taken for granted much too soon after their in troduction into the literature only through a global view of this past effort can subtle mutually experienced problem areas and possible causes be identified the present work deals with the numerical solution to the transformed fluid flow equations i e euler equations etc using the finite difference approach the transformed equations are obtained through application of a generalized mapping from physical coordinates to computational coordinates at the time of application of the mapping to the original equations and prior to choosing the numerical in tegration scheme the analyst must decide in which form the equations should be written the choices are the non conservation law form nclf strong conservation law form sclf weak conservation law form wclf and chain rule conservation law form crclf this decision is one of the fundamental practices alluded to in the previous paragraph the present work illustrates how such a fundamental decision can strongly influence both the amount of analysis required to develop a consistent algorithm and the number of arithmetic operations required to execute the algorithm in addition it is shown that large solution errors and in some cases instabilities can result from failure to implement the results of such an analysis

a relationship between the recursive least squares update and homotopy continuation methods the authors present an alternative derivation of the general recursive least squares rls algorithm using homotopy approaches homotopy continuation methods are briefly described and a simple iterative update for path following is derived a homotopy function is then constructed using the rls filtering criteria the equivalence between the iterative update for following the path defined by this homotopy function and the general rls update is derived finally an intuitive explanation of this result is presented

universality of quantum brownian motion abstract are markovian master equations for quantum brownian motion independent of model assumptions used in the derivation and thus universal with the aim of answering this question we use a random band matrix model for the system bath interaction to derive markovian master equations for the time evolution of one dimensional quantum systems weakly coupled to a heat bath we study in detail two simple systems the harmonic oscillator and the two level system our results are in complete agreement with those of earlier models like the caldeira leggett model and in the large band limit with the agarwal equations both with and without rotating wave approximation this proves the universality of these master equations

asymptotic properties of large random matrices with independent entries we study the normalized trace gn z n 1 tr h zi 1 of the resolvent of n n real symmetric matrices h 1 jk wjk n j k 1n assuming that their entries are independent but not necessarily identically distributed random variables we develop a rigorous method of asymptotic analysis of moments of gn z for iz 0 where 0 is determined by the second moment of wjk by using this method we find the asymptotic form of the expectation e gn z and of the connected correlator e gn z1 gn z2 e gn z1 e gn z2 we also prove that the centralized trace ngn z e ngn z has the gaussian distribution in the limit n based on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles

dynamics of a simple quantum system in a complex environment we present a theory for the dynamical evolution of a quantum system coupled to a complex many body intrinsic system environment by modelling the intrinsic many body system with parametric random matrices we study the types of effective stochastic models which emerge from random matrix theory using the feynman vernon path integral formalism we derive the influence functional and obtain either analytical or numerical solutions for the time evolution of the entire quantum system we discuss thoroughly the structure of the solutions for some representative cases and make connections to well known limiting results particularly to brownian motion kramers classical limit and the caldeira leggett approach