multiple subtraction using statistically estimated inverse wavelets surface related multiple elimination srme typically consists of two steps the first step is prediction and the second step is subtraction in subtraction it is important to effectively attenuate multiple events and preserve primary events when multiples cross with or overlap on primaries least square subtraction usually cannot subtract multiples effectively and may also damage the primaries when multiples overlap with primaries least square subtraction cannot always subtract multiples accurately and often damages the primaries to remedy this problem we propose to statistically estimate the inverse source wavelet correct for errors in the estimate of the inverse wavelet and then use the corrected inverse wavelets for multiple subtraction synthetic tests and real data examples show that the proposed method can effectively attenuate multiples while they also preserve the continuity of reflection events and successfully avoid amplitude distortion the proposed method is characterized by low computational costs and ease of implementation

contraction of information in systems far from equilibrium the relationship between a physical model and a time series model or an innovation model is discussed from the viewpoint of contraction of information due to the way of observation in this framework measurable correlation functions are expressed in terms of both models by using the riccati type equation and the singular value decomposition of the hankel matrix a data oriented model is derived from measurable correlation functions there occurs the contraction in a noise source space or random forces from the mechanism of contraction random forces of systems can be identified by using two innovation models in different states

the deconvolution problem fast algorithms including the preconditioned conjugate gradient to compute a map estimator different aspects of the deconvolution problem are discussed and a solution by the map estimator using the a priori knowledge of smoothness and nonnegativity of the unknown signal is proposed several fast algorithms are examined and the conjugate gradient cg method is show to have several advantages it allows computation of a constrained solution and when used with a preconditioning technique it can be faster than other algorithms for general near to toeplitz systems in particular for toeplitz block toeplitz systems

a fast algorithm for solving a toeplitz system of equations a fast algorithm for the solution of a toeplitz system of equations is presented the algorithm requires order n log n 2 computations where n is the number of equations for banded toeplitz matrices the order of computations is reduced to only n log n m log m 2 where 2m is the maximum number of nonzero principal subdiagonals of the toeplitz matrix the algorithm is in essence a fast implementation of the trench algorithm in reverse thus the algorithm involves imbedding of the given matrix in a cyclic matrix and a fast hd half divisor algorithm to compute the first row of the inverse matrix the desired solution is then obtained directly from the first row by applying fast fourier transform techniques in order n log n computations finally the extension of the algorithm to block toeplitz matrices is also presented

transverse nearest neighbor degeneracies on a 2 n lattice an exact 15 term recursion relation and the associated generating function are derived for the number of arrangements of q particles on a 2 n lattice such that s occupied nearest neighbor pairs v of which are transverse and t unoccupied nearest neighbor pairs are formed

fast algorithms for close to toeplitz plus hankel systems and two sided linear prediction the low displacement rank definition of close to toeplitz ct matrices is extended to close to toeplitz plus hankel ctph matrices fast algorithms for solving ctph systems of equations are presented a matrix is defined as ctph if the sum of a ct matrix and a second ct matrix postmultiplied by an exchange matrix an equivalent definition in terms of uv rank is also given this definition is motivated by the application of the algorithms to two sided linear prediction tsp autocorrelation and covariance forms of tsp analogous to those for one sided linear prediction osp are defined the covariance form of tsp is solved using the ctph fast algorithms just as the covariance form of osp is solved using ct fast algorithms numerical examples show that tsp produces smaller residuals than osp and resolves sharp spectral peaks better than osp and that covariance tsp produces smaller residuals than autocorrelation tsp

complements to cost equivalent realizations abstract skelton 1981 and skelton and yousuff 1983 use component cost analysis to obtain a reduced order model that is coat equivalent to a full order stochastic system this paper presents a more direct and numerically efficient method to obtain the same reduced order model which is shown to be a first order autoregressive model

direct multichannel predictive deconvolution the levinson principle generally can be used to compute recursively the solution of linear equations it can also be used to update the error terms directly this is used to do single channel deconvolution directly on seismic data without computing or applying a digital filter multichannel predictive deconvolution is used for seismic multiple attenuation in a standard procedure the prediction error filter matrices are computed with a levinson recursive algorithm using a covariance matrix of the input data the filtered output is the prediction errors or the nonpredictable part of the data starting with the classical levinson recursion wehave derived new algorithms for direct recursive calculationof the prediction errors without computing the data covariance matrix or computing the prediction error filters one algorithm generates recursively the one step forward and backward predic tion errors and the l step forward prediction error computing only the filter matrices with the highest index a numeri

least squares adaptive lattice and transversal filters a unified geometric theory a unified theory is presented to characterize least squares adaptive filters in either lattice or transversal filter form for nonstationary processes the derivations are based upon a geometric formulation of least squares estimation and on the concept of displacement rank a few basic geometric relations are shown to underlie the various algorithms insights into the fundamental concepts that unify lattice and transversal filter approaches to least squares adaptive filters are also given the general results are illustrated by applications to the so called pre windowed and growing memory covariance formulations of the deterministic least squares problem

fast inversion of triangular toeplitz matrices an algorithm requiring 0 n log n operations is proposed for the inversion of triangular toeplitz matrices this algorithm is faster than existing techniques even for relatively small values of n and can easily be written in fortran

the characteristic square of a factor and the cocycle conjugacy of discrete group actions on factors this paper has three main purposes rst to associate to any separable factor m a canonical commuting exact square of groups called the characteristic square ofm secondly to formulate at least in a preliminary way a methodology for approaching non smooth classi cation problems in analysis and thirdly to use this approach in conjunction with the characteristic square to complete the cocycle conjugacy classi cation of actions of discrete amenable groups on injective factors of type iii1 this result and previous works on the cocyle conjugacy classi cation problem combine to produce a cocycle conjugacy classi cation theorem which applies simultaneously to all countable amenable groups and all injective separable factors and in which the characteristic square and our new methodology play a crucial role the cocycle conjugacy classi cation problem has by now a long and distinguished history beginning with connes ground breaking outer conjugacy classi cation of single automorphisms of the approximately nite dimensional or afd factor r0 of type ii1 c3 in the intervening 20 years enormous progress has been made the rst step was taken by v jones j who identi ed the true nature of the cocycle conjugacy invariants and completed the classi cation of actions of nite groups on r0 ocneanu o re ned this work and introduced new analytic techniques enabling him to extend the classi cation to countable amenable groups acting on the semi nite afd factor r0 1 and to some actions on afd factors of type iii also sutherland and takesaki using groupoid and duality techniques originating in jt extended the classi cation results to invent math 132 331 380 1998

on low complexity approximation of matrices the operation multiplication of a vector by a matrix can be represented by a computational scheme or model that acts on the entries of the vector sequentially the number of intermediate quantities states that are needed in the computations is a measure of the complexity of the model if that complexity is low then not only multiplication but also other operations such as inversion can be carried out efficiently using the model rather than the original matrix in the introductory sections we describe an algorithm to derive a computational model of minimal complexity that gives an exact representation of an arbitrary upper triangular matrix the main result of the paper is an algorithm for computing an approximating matrix with a model of much lower complexity than the original as low as possible for a given tolerance on the approximation error as measure for the tolerance we will use a strong norm which we will call the hankel norm it is a generalization of the hankel norm which is used in the classical model approximation theory for complex analytical functions

a look ahead levinson algorithm for general toeplitz systems the authors present an extension of levinson s algorithm that is guaranteed to be weakly stable for a large class of general toeplitz matrices namely those that do not have many consecutive ill conditioned leading principal submatrices the new algorithm adapts itself to the given toeplitz matrix by skipping over all the ill conditioned leading principal submatrices encountered during the solution process this is done by a look ahead strategy that monitors the condition of the leading principal submatrices and if necessary switches to a block step of suitable size the overhead of the look ahead algorithm is typically small compared to the classical levinson algorithm and in addition a reliable condition number estimate is produced

the block processing ftf adaptive algorithm a new block type adaptive filtering algorithm is presented this new block adaptive filter differs from the frequency domain block adaptive filters of ferrara 1980 and of clark mitra and parker 1980 in that the new method applies a deterministic time domain least squares criteria within each of the data blocks information is carried from block to block via a weighted initial condition this new block fast transversal filters bftf algorithm is a numerically stable algorithm and can also be used to perform efficient least squares system identification on any one data block in which case it shows a moderate computational advantage over the previous most efficient single data block algorithms of morf et al 1977 of marple 1981 and of kalouptsidis manolakis and carayannis 1984 1985 mechanisms for tracking and varying block length from block to block are also presented and evaluated finally we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters after computation of the sample correlation lags

pore scale modeling and continuous time random walk analysis of dispersion in porous media 1 we provide a physically based explanation for the complex macroscopic behavior of dispersion in porous media as a function of peclet number pe using a pore scale network model that accurately predicts the experimental dependence of the longitudinal dispersion coefficient dl on pe the asymptotic dispersion coefficient is only reached after the solute has traveled through a large number of pores at high pe this implies that preasymptotic dispersion is the norm even in experiments in statistically homogeneous media interpreting transport as a continuous time random walk we show that 1 the power law dispersion regime is controlled by the variation in average velocity between throats the distribution of local pe giving dl pe with 3 1 2 where is an exponent characterizing the distribution of transit times between pores 2 the crossover to a linear regime dl pe for pe pecrit 400 is due to a transition from a diffusion controlled late time cutoff to transport governed by advective movement and 3 the transverse dispersion coefficient dt pe for all pe 1

maximum entropy and spectral estimation a review the method of maximum entropy is reviewed with emphasis on its relationship to entropy rate wiener filters autoregressive processes extrapolation the levinson algorithm lattice all pole and all pass filters and stability

best stable and invertible approximations for arma systems a method is proposed for finding the best stable and invertible approximations for an autoregressive moving average arma system relative to a general quadratic metric in the coefficient space mathematically the problem is equivalent to projecting the regression and moving average vectors of the system onto the set s of coefficients of monic schur polynomials the geometry of s is too complex to allow the problem to be approached directly in the arma coefficient space a solution is obtained by constrained steepest descent in the hypercube of reflection coefficients which is homomorphic to s

a generalization of the levinson algorithm for hermitian toeplitz matrices with any rank profile the paper describes a recursive algorithm for solving hermitian toeplitz systems of linear equations without any restriction on the ranks of their nested toeplitz subsystems such a general algorithm is needed e g to obtain the eigenfilters for signal processing applications or to compute the inverse of a nondefinite toeplitz matrix the regular portion of the algorithm is made of the classical levinson recursion the singular portion requires solving some well defined systems of linear equations with gradient structure the dimension of each of these sytems equals the amplitude of the corresponding singularity

the classification of rokhlin flows on mathrm c c algebras we study flows on mathrm c algebras with the rokhlin property we show that every kirchberg algebra carries a unique rokhlin flow up to cocycle conjugacy which confirms a long standing conjecture of kishimoto we moreover present a classification theory for rokhlin flows on mathrm c algebras satisfying certain technical properties which hold for many mathrm c algebras covered by the elliott program as a consequence we obtain the following further classification theorems for rokhlin flows firstly we extend the statement of kishimoto s conjecture to the non simple case up to cocycle conjugacy a rokhlin flow on a separable nuclear mathcal o infty absorbing mathrm c algebra is uniquely determined by its induced action on the prime ideal space secondly we give a complete classification of rokhlin flows on simple classifiable kk contractible mathrm c algebras two rokhlin flows on such a mathrm c algebra are cocycle conjugate if and only if their induced actions on the cone of lower semicontinuous traces are affinely conjugate

fixed order stabilising controller design by a mixed randomised deterministic method a novel mixed randomised deterministic method for fixed order controller design is proposed for discrete time single input single output plants it is based on the random generation of schur stable polynomials using reflection coefficients and reflection segments of polynomials stable reflection segments are then projected onto the affine set of closed loop characteristic polynomials and the stable line segments in the controller parameter space are determined a novel approach is proposed for global and local optimisation over reflection segment bunches on the basis of the weighted sum of absolute values of reflection coefficients

error sources and error propagation in the levinson durbin algorithm it is proved that there are two types of numerical error due to finite precision in the levinson durbin algorithms an erratic and a systematic one the erratic one depends on the value the input autocorrelation accidentally takes at an iteration and essentially it affects only the results obtained at this particular recursion on the contrary the systematic numerical error increases with the information the system carries and propagates essentially throughout the algorithm it is shown that for both types of error as well as the overall one there are specific intermediate quantities calculated in the evolution of the algorithm which may serve as precise indicators of the exact number of erroneous digits with which the various quantities are computed including the parcor coefficients and the filter coefficients therefore the generated numerical error can be accurately traced

boundary element solution for periodic acoustic problems abstract this work shows when using the boundary element method to solve 3d acoustic scattering problems from periodic structures the coefficient matrix can be represented as a block toeplitz matrix by exploiting the toeplitz structure the computational time and storage requirements to construct the coefficient matrix are significantly reduced to solve the linear system of equations the original matrix is embedded into a larger and more structured matrix called the block circulant matrix discrete fourier transform is then employed in an iterative algorithm to solve the block toeplitz system to demonstrate the effectiveness of the formulation for periodic acoustic problems two exterior acoustic case studies are considered the first case study examines a continuous structure to predict the noise generated by a sharp edged flat plate under quadrupole excitation directivity plots obtained using the periodic boundary element method technique are compared with numerical results obtained using a conventional boundary element model the second case study examines a discrete periodic structure to predict the acoustic performance of a sonic crystal noise barrier results for the barrier insertion loss are compared with both finite element results and available data in the literature

adaptive tracking of multiple sinusoids whose power levels are widely separated the behavior of the gradient transversal filter lms the gradient lattice gl and the least squares lattice lsl when used to track multiple sinusoidal or narrow band components whose power levels are widely separated is investigated these approaches to the realization of the pth order one step linear predictor of the time series are recursive in time the lags of the instantaneous frequency estimates from their actual underlying values are of particular interest the frequency tracking characteristics of the lms gl and lsl algorithms are illustrated in several situations included are simulations of dual sinusoids undergoing a variety of frequency versus time dynamics and a formant tracking example of real speech

observation noise and zero loci of the time series model the properties of zeros of time series models are examined in a linear stochastic system with white gaussian observation noise each zero has a locus in the complex plane as the variance of observation noise changes from zero to infinity an application of zero loci is presented for understanding the properties of the autoregressive model

olriv a new fast adaptive algorithm for rectangular block toeplitz systems in this paper we propose a new algorithm for solving overdetermined systems when they are rectangular block toeplitz the blocks can have more rows than columns it is based on the expression of the matrix of the system to solve as the intercorrelation between two vectorial processes namely the original and the instrumental processes the instrumental process has generally more components than the original one therefore it takes the overdetermined character of the system into consideration the proposed algorithm known as the overdetermined lattice recursive instrumental variable olriv belongs to the fast rls family and lies on a double lattice structure where one lattice performs the prediction of the original process and the other one the prediction of the instrumental process the geometric complete derivation of the proposed algorithm is given in the paper afterwards we show how olriv can be applied to perform blind adaptive identification of ar channels using high order statistics where the systems to solve are often overdetermined to ensure identifiability both the scalar and the vectorial cases are investigated simulation results are finally given to show the performances of olriv

a fast but unstable orthogonal triangularization technique for toeplitz matrices abstract d sweet s clever qr decomposition algorithm for toeplitz matrices is considered it requires only o n 2 flops to factor an n n matrix we analyze the algorithm to point out its deficiencies and compare it against two other toeplitz solvers

fast inversion of the simplicial bernstein mass matrix we consider the mass matrix arising from bernstein polynomials as finite element shape functions in particular we give an explicit formula for its eigenvalues and exact characterization of the eigenspaces in terms of the bernstein representation of orthogonal polynomials we then derive a fast algorithm for solving linear systems involving the element mass matrix after establishing these results we describe the application of bernstein techniques to the discontinuous galerkin finite element method for hyperbolic conservation laws obtaining optimal complexity algorithms finally we present numerical results investigating the accuracy of the mass inversion algorithms and the scaling of total run time for the function evaluation needed in dg time stepping

szego polynomials applied to frequency analysis abstract this paper is concerned with the problem of determining unknown frequencies 1 i using an observed discrete time signal xn xn m arising from a continuous waveform that is the superposition of a finite number of sinusoidal waves with well defined frequencies j periods p j 2 n j n z j 1 i we investigate the wiener levinson method formulated here in terms of szeg polynomials n n z orthogonal on the unit circle with respect to a distribution function n defined by the n observed values of the signal we prove that if n0 denotes the number of critical points eiwj then for every n n0 and n 1 the zeros z j n n of n n z can be arranged so that limn z j n n eiwj for each of the frequencies wj this result confirms one of the main parts of the conjecture given by jones njastad and saff this journal 1990 on the convergence of zeros of the szeg polynomials a related result on the convergence of corresponding two point pade approximants is also given

fir filters and recursive forms for continuous time invariant state space models an fir finite impulse response filter and an fir smoother are introduced for continuous time invariant state space models it is shown in this note that finite impulse responses of the fir filter and smoother can be easily determined by solving a simple riccati type matrix differential equation on a finite interval especially for systems with stationary processes finite impulse responses of the fir filter and smoother become time invariant and can be computed from simpler equations for fast computational purposes recursive forms of the fir filter and smoother are derived by using adjoint variables in this case all gains for recursive forms are shown to be constant

the weak and strong stability of algorithms in numerical linear algebra the stability of algorithms in numerical linear algebra is discussed the concept of stability is extended to notions of weak stability and strong stability justifications are given for these extensions and the implications of error analyses in terms of these definitions are discussed the concept of weak stability helps to clarify some of the controversy which has arisen concerning the stability of algorithms for toeplitz systems

physical pictures of transport in heterogeneous media advection dispersion random walk and fractional derivative formulations 1 the basic conceptual picture and theoretical basis for development of transport equations in porous media are examined the general form of the governing equations is derived for conservative chemical transport in heterogeneous geological formations for single realizations and for ensemble averages of the domain the application of these transport equations is focused on accounting for the appearance of non fickian anomalous transport behavior the general ensemble averaged transport equation is shown to be equivalent to a continuous time random walk ctrw and reduces to the conventional forms of the advection dispersion equation ade under highly restrictive conditions fractional derivative formulations of the transport equations both temporal and spatial emerge as special cases of the ctrw in particular the use in this context of levy flights is critically examined in order to determine chemical transport in field scale situations the ctrw approach is generalized to nonstationary systems we outline a practical numerical scheme similar to those used with extended geological models to account for the often important effects of unresolved heterogeneities

transport behavior of coupled continuous time random walks the origin of anomalous or non fickian transport in disordered media is the broad spectrum of transition rates intrinsic to these systems a system that contains within it heterogeneities over multiple length scales is geological formations the continuous time random walk ctrw framework which has been demonstrated to be an effective means to model non fickian transport features in these systems and to have predictive capacities has at its core this full spectrum represented as a joint probability density ensuremath psi mathbf s t of random space time displacements mathbf s t transport in a random fracture network rfn has been calculated with a coupled ensuremath psi mathbf s t and has subsequently been shown to be approximated well by a decoupled form ensuremath psi mathbf s t f mathbf s ensuremath psi t the latter form has been used extensively to model non fickian transport in conjunction with a velocity distribution ensuremath phi ensuremath xi ensuremath xi ensuremath equiv 1 v where v is the velocity magnitude the power law behavior of ensuremath psi t ensuremath propto t ensuremath 1 ensuremath ensuremath beta which determines non fickian transport derives from the large ensuremath xi dependence of ensuremath phi ensuremath xi in this study we use numerical ctrw simulations to explore the expanded transport phenomena derived from a coupled ensuremath psi mathbf s t specifically we introduce the features of a power law dependence in the mathbf s distribution with different ensuremath phi ensuremath xi distributions including a constant v coupled by t s ensuremath xi unlike l evy flights in this coupled scenario the spatial moments of the plumes are well defined the shapes of the plumes depend on the entire ensuremath phi ensuremath xi distribution i e both small and large ensuremath xi dependence there is a competition between long displacements which depend on the small ensuremath xi dependence and large time events which depend on a power law for large ensuremath xi these features give rise to an enhanced range of transport behavior with a broader scope of applications e g to correlated migrations in a rfn and in heterogeneous permeability fields the approximation to the decoupled case is investigated as a function of the nature of the mathbf s distribution

causal compensation for erasures in frame representations in a variety of signal processing and communications contexts erasures occur inadvertently or can be intentionally introduced as part of a data reduction strategy this paper discusses causal compensation for erasures in frame representations of signals the approach described assumes linear synthesis of the signal using a prespecified frame but no specific generation mechanism for the coefficients under this assumption it is demonstrated that erasures can be compensated for using low complexity causal systems if the transmitter is aware of the occurrence of the erasure an optimal compensation is to project the erasure error to the remaining coefficients it is demonstrated that the same compensation can be executed using a transmitter receiver combination in which the transmitter is not aware of the erasure occurrence the transmitter precompensates using projections as if assuming erasures will occur the receiver undoes the compensation for the coefficients that have not been erased thus maintaining the compensation only of the erased coefficients the stability of the resulting systems is explored and stability conditions are derived it is shown that stability for any erasure pattern can be enforced by optimizing a constrained quadratic program at the system design stage the paper concludes with examples and simulations that verify the theoretical results and illustrate key issues in the algorithms

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

fast algorithms for generalized displacement structures and lossless systems abstract we derive an efficient recursive procedure for the triangular factorization of strongly regular matrices with generalized displacement structure that includes as special cases a variety of previously studied classes such as toeplitz like and hankel like matrices the derivation is based on combining a simple gaussian elimination procedure with displacement structure and leads to a transmission like interpretation in terms of two cascades of first order sections we further derive state space realizations for each section and for the entire cascades and show that these realizations satisfy a generalized embedding result and a generalized notion of j losslessness the cascades turn out to have intrinsic blocking properties which can be shown to be equivalent to interpolation constrains

equivalence of normal states on von neumann algebras and the flow of weights abstract let m be a von neumann algebra two positive normal functionals on m are called equivalent if is in the norm closure of the orbit of under the action of inner automorphisms our main result is an isometric characterization of the quotient space m we construct a natural isometry a g4 of m into the set of positive normal functionals on the smooth flow of weights of m where the smooth flow of weights is realized as the center z n of the crossed product n m r for some faithful normal semifinite weight on m as an application we obtain that an automorphism on a factor m with separable predual acts trivially on m if and only if acts trivially on the smooth flow of weights i e the connes takesaki modulus mod of vanishes we also obtain a new proof of the diameter formula diam s n m 2 1 1 for the quotient of the state space of a factor of type iii 0 1

generalized chandrasekhar recursions from the generalized schur algorithm presents a new approach to the chandrasekhar recursions and some generalizations thereof the derivation uses the generalized schur recursions which are o n sup 2 recursions for the triangular factorization of n spl times n matrices having a certain toeplitz like displacement structure it is shown that when the extra structure provided by an underlying state space model is properly incorporated into the generalized schur algorithm it reduces to the chandrasekhar recursions which are o nn sup 2 recursions for estimating the n dimensional state of a time invariant or constant parameter system from n measured outputs it is further noted that the generalized schur algorithm factors more general structured matrices and this fact is readily used to extend the chandrasekhar recursions to a class of time variant state space models special cases of which often arise in adaptive filtering

theory of anomalous chemical transport in random fracture networks we show that dominant aspects of chemical particle transport in fracture networks char22 non gaussian propagation char22 result from subtle features of the steady flow field distribution through the network this is an outcome of a theory based on a continuous time random walk formalism structured to retain the key space time correlations of particles as they are advected across each fracture segment the approach is designed to treat the complex geometries of a large variety of fracture networks and multiscale interactions monte carlo simulations of steady flow in these networks are used to determine the distribution of velocities in individual fractures as a function of their orientation the geometry and velocity distributions are used in conjunction with particle mixing rules to map the particle movement between fracture intersections onto a joint probability density ensuremath psi mathbf r t the chemical concentration plume and breakthrough curves can then be calculated analytically particle tracking simulations on these networks exhibit the same non gaussian profiles demonstrating quantitative agreement with the theory the analytic plume shapes display the same basic behavior as extensive field observations at the columbus air force base mississippi the quantitative correlation between the time dependence of the mean and standard deviation of the field plumes and their shape is predicted by the theory

equivalent random force and time series model in systems far from equilibrium under the condition that observed time series data is given a stochastic markovian equation for a physical system can be transformed into an observable non markovian equation used in the time series analysis the physical random force satisfying the fluctuation dissipation theorem is also transformed into a stochastically equivalent random force in the derivation of the time series model of observable variables statistical quantities i e correlation and power spectral density functions for observable variables can be expressed not only by the physical random force but also by the equivalent random force a relation between the variance of physical random force and that of equivalent random force is also found

arma spectral estimation of narrow band processes via model reduction the problem of estimating autoregressive moving average arma models for narrowband processes is considered the following approach is proposed estimate a high order autoregressive ar approximation of the process by model reduction based on a truncated internally balanced realization or optimal hankel norm model reduction reduce the order of this high order ar estimate to find a lower order arma model this algorithm gives arma spectral estimates with excellent resolution properties without using iterative numerical minimization methods as for the maximum likelihood method how to take the narrowband assumption into account in the model reduction step is discussed in detail

on the family of ml spectral estimates for mixed spectrum identification a recently developed point spectrum identification procedure based on a family of ar and ml spectral estimates is exploited to arrive at a mixed spectrum identification procedure to this end a variety of properties of the ar and ml estimates as a function of model order are described these properties relate to amplitude convergence resolution and a characterization of the ar spectral artifact which is used to arrive at improved continuous spectral estimates a variety of examples are presented

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

comparing ls fir filtering and l step ahead linear prediction this comparative study of the l step ahead linear prediction and least squares finite impulse response ls fir filtering problems emphasizes the numerical behavior of the resulting toeplitz systems it is shown that although these systems are similar the restraints on the autocorrelation coefficients fundamentally differentiate them in the process of doing so a new algorithmic scheme for the computation of the lagged lattice coefficients is developed which exhibits fundamentally improved numerical behavior moreover explicit formulas for the supremums of the absolute values of both the lagged lattice and filter coefficients are found theoretically and are experimentally confirmed by using the proposed algorithm finally the bounds of the ls fir filter coefficients are treated in comparison with the supremums of the lagged quantities

linearizing integral transform for the multicomponent lattice kp abstract we present a generalization of the direct linearization method for the kadomtsev petviashvili kp equation and its lattice analogues such as the two dimensional toda equation the generalization consists of a riemann hilbert type of integral transform which relates solutions of the associated spectral problem to any given solution of the spectral problem by dimensional reduction we obtain the integral transform for the korteweg de vries kdv equation and its lattice analogues the integral transform is well suited for the investigation of the finite matrix generalizations of the above mentioned equations such finite matrix generalizations may be of use in connection with partial difference equations for spin correlation functions in the two dimensional ising model

notes on poles of autoregressive type model part ii robust singular pole abstract the non robust singular pole of a scalar t ar model which is defined by truncating the taylor expansion of physical ar ma model has been introduced in the previous paper this journal a two dimensional t ar model is obtained when two state variables are observed from a linear gauss markovian system described with three degrees of freedom the vector t ar model has a robust singular pole which has no direct correspondence to poles and or zeros of the original vector ar ma model the comparison of pole locations between t ar model and ar model is studied in a simple example

closed form analytical results for the rejection of narrow band interference in pn spread spectrum systems part ii linear interpolation filters the performance of pn spread spectrum communication systems in the presence of narrow band interference is studied when linear interpolation filters are employed for the estimation and subsequent suppression of the interference closed form analytical expressions for the system s performance are established for a broad class of interference processes the advantages of linear interpolation filters over predictive filters with identical number of taps are examined analytically and some unexpected results are obtained the analytical results are illustrated by examples

the structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions we complete classification of discrete abelian or finite group actions on injective type iii1 factors up to cocycle conjugacy we also give a proof for connes characterization of the ker mod and cnt m for an injective factor m of type iii 0 introduction the purpose of this paper is to give a proof of connes announcement on approximately inner automorphisms and centrally trivial automorphisms of an injective 1980 mathematics subject classification 1985 revision 46l40

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

the statistics of interacting dumbbells on a 2 n lattice space a set theoretic argument is utilizied to determine a 31 term recursion that describes exactly the composite nearest neighbor degeneracy for indistinguishable dumbbell particles distributed on a rectangular 2 n lattice space the associated generating functions the expectation of the lattice coverage and the density of occupied nearest neighbor pairs are also determined

fast algorithms for linear prediction and system identification filters with linear phase a general finite impulse response fir filter can be used as a linear prediction filter if given only an input sample sequence or as a system identification model if given the input and output sequences from an unknown system with known correlation the coefficients of the fir filter that minimize the mean square error in both applications are found by solution of a set of normal equations with toeplitz structure using only data samples the coefficients that yield the least squared error in both applications are found by solution of a set of normal equations with near to toeplitz structure computationally efficient fast algorithms have been published to solve for the coefficients from both types of normal equation structures if the fir filter is constrained to have a linear phase then the impulse response must be symmetric this then leads to normal equations with toeplitz plus hankel or near to toeplitz plus hankel structure fast algorithms for solving these normal equations for the filter coefficients are developed in this paper they have computational complexity proportional to m2and parameter storage proportional to m where m is the filter order an application of one of these algorithms for spectral estimation concludes the paper

efficient inversion of toeplitz block toeplitz matrix an iterative algorithm for the inversion of a toeplitz block toeplitz matrix consisting of m m blocks of size p p is described the algorithm presented exploits the structure of the toeplitz block toeplitz matrix and outperforms akaike s algorithm by a factor of max 2 p m 2 the use of this algorithm for an iterative solution of a toeplitz block toeplitz set of linear equations is also presented

a new algorithm for computing orthogonal polynomials the aim of this paper is to present an algorithm for computing orthogonal polynomials the fast fourier transform completes the connection given by draux between the three term recurrence relationship and the euclidian algorithm applications to hankel systems and numerical examples illustrate our purpose

euclid algorithm orthogonal polynomials and generalized routh hurwitz algorithm this paper is concerned with the relations between the euclid algorithm the theory of orthogonal polynomials and the problem of locating the zeros of a complex polynomial with respect to the imaginary axis in particular a simple generalized routh hurwitz algorithm is proposed which allows one to determine in any situation the numbers of zeros of an arbitrary complex polynomial in the right half plane on the imaginary axis and hence in the left half plane moreover it turns out that this algorithm yields as a side result a well defined factorization of the considered polynomial furthermore as a straightforward consequence of the adopted approach two presumably original algorithms are put into light which involve linear arithmetic operations only a polynomial nonnegativity test on the real axis and a characterization of positive real functions

maximally robust 2 d channel estimation for ofdm systems two dimensional minimum mean square error mmse channel estimation for orthogonal frequency division multiplexing ofdm systems is known to perform better than the least squares as well as the conventional 1 d mmse estimation owing to its ability of exploiting both the time and the frequency correlations among the channel frequency response cfr coefficients its superior performance comes however at the price of increased requirements the knowledge of observation noise power and that of the channel frequency as well as time correlation functions in practical transmission scenarios where channel correlation functions are not known or cannot be easily estimated it is desirable to have an estimator that is robust to mismatches between the assumed and the actual channel correlation function while such a robust estimator for the case of an infinite number of observations is well known for various uncertainty classes not much attention has been paid to the practical case of a finite number of observations we derive in this paper the maximally robust mr 2 d channel estimator for the case of a finite number of pilot observations under some realistic constraints on the uncertainty class to which the 2 d channel correlation sequence belongs we demonstrate that the correlation sequence associated with the mr estimator can be obtained by a simple semi definite optimization procedure and is interestingly different from the well known heuristic proposals simulation results establish the superiority of the proposed mr estimator over commonly employed heuristic robust estimator by as much as 3 db in terms of the worst case estimation mse and around 1 db in terms of the average ber performance under different practical transmission scenarios of interest

pointwise inner automorphisms of von neumann algebras an automorphism of a von neumann algebra m is called pointwise inner if for all m there is a unitary u m such that u u we analyse such automorphisms in particular we show that if m is a factor of type iii 0 1 with separable predual then an automorphism is pointwise inner if and only if there are an inner automorphism and an extended modular automorphism gsc in the sense of connes and takesaki such that gsc

order selection for and design of iir filters the design of infinite impulse response digital filters can be viewed as a spectral factorization problem when one knows what the numerator and denominator orders are this design problem is greatly simplified selection of the appropriate orders has long been a significant problem in recursive filter design recent work by gray et al suggests a general method by which the orders may be selected prior to design in this paper infinite impulse response digital filters are designed from finite impulse response prototypes using the gray technique to first select the order once the order has been determined the recursive filter coefficients are determined directly from the finite impulse filter because of the wealth of knowledge available concerning order lengths for nonrecursive filters the procedures used here permit direct comparison between the two filter methods

superfast tikhonov regularization of toeplitz systems toeplitz structured linear systems arise often in practical engineering problems correspondingly a number of algorithms have been developed that exploit toeplitz structure to gain computational efficiency when solving these systems the earliest fast algorithms for toeplitz systems required o n 2 operations while more recent superfast algorithms reduce the cost to o n log n 2 or below in this work we present a superfast algorithm for tikhonov regularization of toeplitz systems using an extension and transformation technique our algorithm translates a tikhonov regularized toeplitz system into a type of specialized polynomial problem known as tangential interpolation under this formulation we can compute the solution in only o n log n 2 operations we use numerical simulations to demonstrate our algorithm s complexity and verify that it returns stable solutions

a rohlin property for one parameter automorphism groups we define a rohlin property for one parameter automorphism groups of unital simplec algebras and show that for such an automorphism group any cocycle is almost a coboundary we apply the same method to the single automorphism case and show that if an automorphism of a unital simplec algebra with a certain condition has a central sequence of approximate eigen unitaries for any complex number of modulus one then any cocycle is almost a coboundary or the automorphism has the stability we also show that if a one parameter automorphism group of a unital separable purely infinite simplec algebra has the rohlin property then the crossed product is simple and purely infinite

transport in disordered media with spatially nonuniform fields the theoretical treatment of transport in a disordered system in the presence of a system wide force field mathcal f mathbf x or spatially varying macroscopic velocity field mathbf v mathbf x is developed in the framework of continuous time random walk ctrw the physical basis of ctrw and related fractional derivative equations relies on a mapping of the aggregate of transition rates w mathbf s mathbf s ensuremath between sites mathbf s and mathbf s ensuremath in the master equation describing the system kinetics onto a joint probability distribution function ensuremath psi mathbf s t this distribution is calculated from the ensemble average of a position dependent functional of w mathbf s mathbf s ensuremath the procedure is effective when the scale of heterogeneities is much smaller than the system size however statistical homogeneity does not hold in the presence of large heterogeneities which control the macroscopic mathbf v mathbf x or in the case of an interaction of mathcal f mathbf x with the transition rates the transport equation incorporating large scale heterogeneity involves the use of a local ensemble average to obtain a position dependent ensuremath psi mathbf s t mathbf x this determines a memory function m t mathbf x which is convoluted with the advection dispersion operator a prototype transport equation for a system with statistical inhomogeneity is developed as an integrodifferential equation it is solved numerically for particles migrating with a steady state darcy velocity mathbf v mathbf x determined for different permeability fields and boundary conditions the nature of the solutions as a function of key transport parameters e g a characteristic time t c is explored and solutions are also compared to those of the advection dispersion equation for mathbf v mathbf x and to a laboratory experiment this transport equation is in contrast to the fractional fokker planck equation which is based on a decoupling of mathcal f mathbf x or mathbf v mathbf x with the transition rates w mathbf s mathbf s ensuremath further an analytic expression for the effect of a variance of the ensemble average on the solution of the ctrw transport equation is derived

random walks with infinite spatial and temporal moments the continuous time random walk of montroll and weiss has been modified by scher and lax to include a coupled spatial temporal memory we treat novel cases for the random walk and the corresponding generalized master equation when combinations of both spatial and temporal moments of the memory are infinite the asymptotic properties of the probability distribution for being at any lattice site as a function of time and its variance are calculated the resulting behavior includes localized diffusive wavelike and levy s stable laws for the appropriate scaled variable we show that an infinite mean waiting time can lead to long time diffusive behavior while a finite mean waiting time is not sufficient to ensure the same

fast subsampled updating stabilized fast transversal filter fsu sftf rls algorithm for adaptive filtering we present a new doubly fast algorithm for recursive least squares rls adaptive filtering that uses displacement structure and subsampled updating the fast subsampled updating stabilized fast transversal filter fsu sftf algorithm is mathematically equivalent to the classical fast transversal filter ftf algorithm the ftf algorithm exploits the shift invariance that is present in the rls adaptation of an fir filter the ftf algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the levinson 1947 algorithm in the subsampled updating approach we accumulate the rotation matrices over some time interval before applying them to the filters it turns out that the successive rotation matrices themselves can be obtained from a schur type algorithm that once properly initialized does not require inner products the various convolutions that appear in the algorithm are done using the fast fourier transform fft the resulting algorithm is doubly fast since it exploits ftf and ffts the roundoff error propagation in the fsu sftf algorithm is identical to that in the sftf algorithm a numerically stabilized version of the classical ftf algorithm the roundoff error generation on the other hand seems somewhat smaller for relatively long filters the computational complexity of the new algorithm is smaller than that of the well known lms algorithm rendering it especially suitable for applications such as acoustic echo cancellation

toeplitz properties of the block matrices encountered in the processing of spatiotemporal signals various signal processing applications such as system identification fir finite impulse response wiener filtering linear prediction and spectral estimation are known to lead to the solution of toeplitz systems for the case of one dimensional signals and to toeplitz block toeplitz systems for the case of two dimensional signals the authors investigate such systems for the case of l dimensional signals with l 2 and emphasize their block and persymmetrical nature such important characteristics allow the use of fast algorithms for signals of any dimension the case of three dimensional signals is treated in detail not only because it is of special interest for video applications but also because the reasoning used for this case can be straightforwardly applied to higher dimension signals

notes on poles of autoregressive type model part iii general case abstract pole locations of a multivariate autoregressive ar type model for a gaussian markovian process are examined by using the rouches theorem the formalism of the previous papers by the authors j math anal appl 124 1987 98 116 123 1987 480 493 is generalized it is shown that when the order of the ar type model becomes large poles of the ar type model can be classified into three types 1 poles distributing almost equally spaced on circles which are centered at the origin with radiuses equal to the absolute value of zeros 2 system poles inside the smallest circle and 3 robust and non robust singular poles which were introduced in the papers referenced above

a hermitian toeplitz matrix is unitarily similar to a real toeplitz plus hankel matrix two unitary matrices are presented that transform a hermitian toeplitz matrix into a real toeplitz plus hankel matrix and vice versa additional properties and consequences of these unitary transformations are also presented for a certain class of n dimensional toeplitz plus hankel systems of equations an efficient method of solution is presented an example is given to illustrate the similarity transforms toeplitz plus hankel systems arise in a wide variety of applications such as linear filtering theory discrete inverse scattering and discretization of certain integral equations arising in mathematical physics

efficient construction of canonical ladder forms for vector autoregressive processes the paper treats the problem of constructing canonical ladder realizations for vector autoregressive ar processes specified by their characteristic matrix polynomials the difficulty of this problem is rooted in the fact that the backward matrix polynomial corresponding to a given vector ar process is a nontrivial function of the forward matrix polynomial the construction calls for solving a discrete lyapunov equation in block controller form two efficient procedures for solving this equation are presented both requiring a number of operations that is proportional to at most the square of the model order applications of the new procedures to stability tests simulation of ar processes and model reduction are described

human ankle joint stiffness over the full range of muscle activation levels abstract system identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels subjects lay supine on an experimental table with their left foot encased in a rigid low inertia cast which was fixed to an electro hydraulic actuator operating as a position servo subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions mvc during repeated presentations of a stochastic ankle angular position perturbation compliance impulse response functions irf were determined from every 2 5 s perturbation sequence the gain g natural freqency n and damping parameters of the second order model providing the best fit to each irf were determined and used to compute the corresponding inertial i viscous b and elastic k stiffness parameters the behaviour of these parameters with mean torque was found to follow two simple rules first the elastic parameter k increased in proportion to mean ankle torque as it was varied from rest to mvc these changes were considerable involving increases of more than an order of magnitude second the damping parameter remained almost invariant over the entire range of contractions despite the dramatic changes in k

the density of occupied nearest neighbor pairs on a rectangular 2 n lattice space utilizing a 15 term recursion that describes exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space 11 the expectation of the normalized number of occupied nearest neighbor pairs is calculated as a function of coverage and the reduced interaction potential

transport equation evaluation of coupled continuous time random walks the transport behavior of a migrating particle in a disordered medium is exhibited in the solution of a transport equation derived from a coupled continuous time random walk ctrw a core aspect of ctrw is the spectrum of transitions in displacement s and time t s t that characterizes the disordered system which determine the transport in many applications the ctrw approach has successfully accounted for the anomalous or non fickian nature of the particle plume propagation based on a power law dependence t in a decoupled p s t approximation to s t for example this power law dependence in t derives from the complex darcy flow fields in geological formations recently the fully coupled ctrw was analyzed using a particle tracking approach demonstrating that the decoupled approximation is valid only for a compact distribution of s in this paper we solve the nonlocal in time transport equation with a s t containing a power law dependence in both s a levy like distribution and t which necessitates the strong s t coupling we show enhanced transport behavior relative to the plume propagation behavior reported in the literature that derives from the rare large displacements in s limited by the transition t the interplay between the two coupled power laws is clearly shown in the changes in the breakthrough curves in the arrival times dispersion and dependence on the velocity v s t distribution similar enhancements are exhibited in the particle tracking results