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

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

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

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

an extension of the split levinson algorithm and its relatives to the joint process estimation problem it is shown that the split levinson algorithm the split schur algorithm and the split lattice algorithm to compute the reflection coefficients of the optimal linear prediction filter for a discrete time stationary stochastic process can be extended to the more general case of the joint process estimation problem the new algorithms are essentially based on well defined recurrence relations for symmetric prediction filters and symmetric estimation filters they are more economical than the standard methods in terms of storage space and number of arithmetic operations

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

the split levinson algorithm the classical levinson algorithm for computing the predictor polynomial relative to a real positive definite toeplitz matrix is shown to be redundant in complexity it can be broken down into two simpler algorithms either of which needs only to be processed this result can be interpreted in the framework of the theory of orthogonal polynomials on the real line as follows the symmetric and antisymmetric parts of the predictors relative to the sequence of toeplitz matrices constitute two families of polynomials orthogonal on the interval 1 1 with respect to some even weight functions it turns out that the recurrence relations for these orthogonal polynomials can be used efficiently to compute the desired predictor the resulting split levinson algorithm requires roughly one half the number of multiplications and the same number of additions as the classical levinson algorithm a simple derivation of cybenko s method for computing the pisarenko frequencies is obtained from the recurrence relations underlying the split levinson algorithm

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

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

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

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

a note on minimizing the prediction error when the zeros are restricted to the unit circle it is shown that the problem of minimizing the prediction error under the constraint that the zeros of the predictor polynomial be on the unit circle can be solved by using a modification of the levinson algorithm consequences of this result are discussed

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

random designs for estimating integrals of stochastic processes the integral of a second order stochastic process z over a d dimensional domain is estimated by a weighted linear combination of observations of z in a random design the design sample points are possibly dependent random variables and are independent of the process z which may be nonstationary necessary and sufficient conditions are obtained for the mean squared error of a random design estimator to converge to zero as the sample size increases towards infinity simple random stratified and systematic sampling designs are considered an optimal simple random design is obtained for fixed sample size and the mean squared errors of the estimators from these designs are compared it is shown for example that for any simple random design there is always a better stratified design 1 introduction we consider the problem of estimating the weighted average of a second order stochastic process z t t e a a c r d the process is assumed to be continuous in quadratic mean with covariance ro s t mean m t and second moment function r s t ro s t m s m t such that 0 fa r t t dt oo we wish to estimate

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

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

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

on the splitting of classical algorithms in linear prediction theory the levinson algorithm has been shown recently to be redundant in complexity it can be broken down into two simpler algorithms either of these split levinson algorithms needs only to be processed in the present paper it is shown that the schur algorithm the lattice algorithm and the normalized lattice algorithm for computing reflection coefficients can be broken down in a similar manner the number of multiplications in each of the resulting split algorithms is reduced with respect to the classical version by a factor lying between 1 5 and 2

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

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

a symmetric matrix method for schrodinger eigenstates it is shown how the one dimensional schrodinger eigenvalue equation can be transformed into a symmetric generalised matrix eigenproblem with a local truncation error of only delta 4 where delta is the step size as in the numerov algorithm standard sparse matrix library packages are available for the solution and it is demonstrated that groups of eigenvalues and their associated eigenvectors wavefunctions can be determined simultaneously with high precision and speed

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

symmetric matrix methods for schrodinger eigenvectors the one dimensional single particle schrodinger eigenvalue equation is represented by a generalized matrix eigenvalue equation of the form a psi ea psi where a is a symmetric matrix a is a symmetric positive definite matrix and psi is a column vector the local error in making the representation is proportional to delta 4 where delta is the step size several methods of solution which make use of the sparsity of the matrices are investigated

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

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

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

numerov method maximally adapted to the schro dinger equation abstract we construct and investigate the two step scheme which is maximally specialized for the schrodinger equation the new scheme is found to preserve all attractive features of the standard numerov method ease in programming flexibility in application speed in run etc with the important advantage of being more efficient for problems involving high values of energy its efficiency is actually found to be close to that of the piecewise perturbation methods a fact which strongly recommends it for further applications

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

a two step even odd split levinson algorithm for toeplitz systems abstract we use a two step durbin method rather than the single step version in the even odd split levinson algorithm for strongly nonsingular real symmetric toeplitz systems with arbitrary right hand side thereby slightly reducing the complexity of this algorithm to 19 8 n 2 o n flops on a sequential machine we also present extensive numerical results comparing several levinson type methods

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

locally lattice sampling designs for isotropic random fields for predicting g v x z x dx where v is a fixed known function and z is a stationary random field a good sampling design should have a greater density of observations where v is relatively large in absolute value designs using this idea when g 0 1 have been studied for some time for g a region in two dimensions very little is known about the statistical properties of cubature rules based on designs with varying density this work proposes a class of designs that are locally parallelogram lattices but whose densities can vary the asymptotic variance of the cubature error for these designs is obtained for a class of isotropic random fields and an asymptotically optimal sequence of cubature rules within this class is found i conjecture that this sequence of cubature rules is asymptotically optimal with respect to all cubature rules

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

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

solving the 1 2 and 3 dimensional schrodinger equation for multiminima potentials using the numerov cooley method an extrapolation formula for energy eigenvalues as demonstrated with examples the numerov cooley algorithm can be applied to more complicated potentials especially multiminima potentials there are no stability problems in the classically forbidden regions an extrapolation formula for energy eigenvalues is deduced which gets an additional accuracy of 2 4 digits for energy eigenvalues this formula is checked as follows for one state of a double minimum potential which is used to approximate hydrogen bond potentials an analytical solution is given this solution is compared with numerical results also the accuracy of the eigenfunctions is checked computer dependent rounding errors cdc cyber 995 are estimated the eigenfunctions corresponding to 1 dimensional potentials v x x and v y y are used as basis functions for a perturbed 2 dimensional multiminima potential v x x v y y email protected x y for a 63 minima potential as an example the accuracy of the eigenvalues is 4 6 digits depending on the perturbation dv x y the computer time depending on the accuracy is tabulated for different potentials

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

predicting integrals of random fields using observations on a lattice for a stationary random field z on r d this work studies the asymptotic behavior of predictors of v x z x dx based on observations on a lattice as the distance between neighbors in the lattice tends to 0 under a mild condition on the spectral density of z an asymptotic expression for the mean squared error of a predictor of v x z x dx based on observations on an infinite lattice is derived for predicting integrals over the unit cube a simple predictor based just on observations in the unit cube is shown to be asymptotically optimal if v is sufficiently smooth and z is not too smooth modified predictors extend this result to smoother processes

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

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

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