automated approach to very high order aeroacoustic computations computational aeroacoustics requires efficient high resolution simulation tools for smooth problems this is best accomplished with very high order in space and time methods on small stencils however the complexity of highly accurate numerical methods can inhibit their practical application especially in irregular geometries this complexity is reduced by using a special form of hermite divided difference spatial interpolation on cartesian grids and a cauchy kowalewski recursion procedure for time advancement in addition a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries these procedures are used to develop automatically and to implement very high order methods 15 for solving the linearized euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point the accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries

fast coupled adaptation for sparse impulse responses using a partial haar transform this work presents a novel scheme for identifying the impulse response of a sparse channel the scheme consists of two adaptive filters operating sequentially the first adaptive filter adapts using a partial haar transform of the input and yields an estimate of the location of the peak of the sparse impulse response the second adaptive filter is then centered about this estimate both filters are short in comparison to the delay uncertainty of the unknown channel the principle advantage of this scheme is that two short adaptive filters can be used instead of one long adaptive filter resulting in faster overall convergence and reduced computational complexity and storage the scheme is analyzed in detail for a least mean squares lms lms lms type of structure although it can be implemented using any combination of adaptive algorithms monte carlo simulations are shown to be in good agreement with the theoretical model for the behavior of the peak estimating filter as well as for the mean square error mse behavior of the second filter

performance advantage of complex lms for controlling narrow band adaptive arrays in narrow band adaptive array applications the mean square convergence of the discrete time real least mean square lms algorithm is slowed by image frequency noises generated in the lms loops the complex lms algorithm proposed by widrow et al is shown to eliminate these noises yielding convergence of the mean squared error mse at slightly over twice the rate this paper includes a comprehensive analysis of the mse of adaptation for lms the analysis is based upon the method developed in the 1968 dissertation by k d senne and it represents the most complete treatment of the subject published to date

a novel kurtosis driven variable step size adaptive algorithm a new variable step size lms filter is introduced the time varying step size sequence is adjusted utilizing the kurtosis of the estimation error therefore reducing performance degradation due to the existence of strong noise the convergence properties of the algorithm are analyzed and an adaptive kurtosis estimator that takes into account noise statistics and optimally adapts itself is also presented simulation results confirm the algorithm s improved performance and flexibility

on the optimum gain parameter in lms adaptation in this correspondence the optimum selection of the adaptation parameter in lms adaptive estimation is discussed for a white data covarianee matrix it is shown via analysis and numerical evaluation that the optimum selection of is a complicated function of the number of filter taps the initial weight setting the wiener weights and the number of learning samples is not chosen in general to yield the most rapid transient response for most cases of interest a smaller value of will be selected for slower adaptation and smaller misadjustment error at the end of the learning phase

adaptive nonlinear system identification in the short time fourier transform domain in this paper we introduce an adaptive algorithm for nonlinear system identification in the short time fourier transform stft domain the adaptive scheme consists of a parallel combination of a linear component represented by crossband filters between subbands and a quadratic component which is modeled by multiplicative cross terms we adaptively update the model parameters using the least mean square lms algorithm and derive explicit expressions for the transient and steady state mean square error mse in frequency bins for white gaussian inputs we show that estimation of the nonlinear component improves the mse performance only when the power ratio of nonlinear to linear components is relatively high furthermore as the number of crossband filters increases a lower steady state mse may be obtained at the expense of slower convergence experimental results support the theoretical derivations

adaptive lms l filters for noise suppression in images several adaptive least mean squares lms l filters both constrained and unconstrained ones are developed for noise suppression in images and compared in this paper first the location invariant lms l filter for a nonconstant signal corrupted by zero mean additive white noise is derived it is demonstrated that the location invariant lms l filter can be described in terms of the generalized linearly constrained adaptive processing structure proposed by griffiths and jim 1982 subsequently the normalized and the signed error lms l filters are studied a modified lms l filter with nonhomogeneous step sizes is also proposed in order to accelerate the rate of convergence of the adaptive l filter finally a signal dependent adaptive filter structure is developed to allow a separate treatment of the pixels that are close to the edges from the pixels that belong to homogeneous image regions

orthogonal weight perturbation algorithms in partially adaptive arrays single port adaptive algorithms have been proposed to circumvent the need to implement a separate receiver for each adaptive element in an adpative antenna in this paper transient and steady state performance of a bounded single port perturbation algorithm is obtained and compared with that of the least mean square lms algorithm results are developed both with and without a hardlimiter on one input to the correlator techniques for adaptively changing both the algorithm step size and perturbation amplitude are given simulation results are presented and compared with theoretical results

optimal gain derivation for the lms algorithm using a visual fidelity criterion this paper analytically derives the optimal feedback gain parameter 0 for the least mean squares lms algorithm used in a video compression application and subject to a visual fidelity criteria experimental results are presented which show these analytically derived values of 0 to be in excellent agreement with experimentally derived 0 over a wide range of filter and data parameters

improved block interface conditions for aeroacoustic problems with grid discontinuities aeroacoustic simulations are extremely sensitive to numerical errors to achieve a high order of accuracy optimized finite difference schemes such as the well known dispersion relation preservation schemes and multiblock structured meshes are often used challenges appear in communicating the flow information near grid discontinuities between neighboring blocks and sophisticated interface treatments are required the characteristic interface condition has been successful in applications in previous publications and yet limitations exist that are identified in the present study this paper proposes a new interface treatment based on the analogy between finite difference and finite volume discretizations one sided finite difference schemes are used to calculate the spatial derivatives in the normal direction and the residuals are reconstructed from a finite volume perspective applications to several benchmark cases show an encouraging improvement as compared to the previous characteristic interface

finite difference schemes on regular triangular grids the phase error and isotropy properties of various finite difference schemes on grids consisting of regular triangles are compared with similar schemes on square grids the comparisons are based on a fourier analysis of semidiscrete solutions to the two dimensional linear convection equation the finite difference schemes presented on the triangular grid include a second order method a compact fourth order method and a modified compact method designed to extend the accurate wave number range of the numerical approximation all of the schemes considered are centered and hence nondissipative in each case the finite difference scheme on the triangular grid reduces the anisotropy of the phase error in comparison with a similar scheme on the square grid

steady state mse convergence of lms adaptive filters with deterministic reference inputs with applications to biomedical signals we analyze the steady state mean square error mse convergence of the lms algorithm when deterministic functions are used as reference inputs a particular adaptive linear combiner is presented where the reference inputs are any set of orthogonal basis functions the adaptive orthogonal linear combiner aolc several authors have applied this structure always considering in the analysis a time average behavior over one signal occurrence we make a more precise analysis using the deterministic nature of the reference inputs and their time variant correlation matrix two different situations are considered in the analysis orthogonal complete expansions and incomplete expansions the steady state misadjustment is calculated using two different procedures with equivalent results the classical one analyzing the transient behavior of the mse and as the residual noise at the output of the equivalent time variant transfer function of the system the latter procedure allows a very simple formalism being valid for colored noise as well the derived expressions for steady state misadjustment are contrasted with experimental results in electrocardiographic ecg signals giving exact concordance for any value of the step size

isotropic finite volume discretization finite volume methods traditionally employ dimension by dimension extension of the one dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured cartesian mesh in multiple dimensions this simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution the resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines in this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions respectively it is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next nearest and next next nearest neighbors in three dimensions use of these isotropic expressions alone in a standard finite volume framework however is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and or spatially non uniform the rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms while preserving the formal order of accuracy and discrete conservation of the original finite volume method are developed numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method prominent anisotropic errors such as spurious asymmetric distortions on a circular reaction diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization furthermore for a given spatial resolution a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization c 2014 elsevier inc all rights reserved

on error saturation nonlinearities in lms adaptation the effect of a saturation type error nonlinearity in the weight update equation in least mean squares lms adaptation is investigated for a white gaussian data model nonlinear difference equations are derived for the eight first and second moments which include the effect of an error function erf saturation type nonlinearity on the error sequence driving the algorithm a nonlinear difference equation for the mean norm is explicitly solved using a differential equation approximation and integration by quadratures the steady state second moment weight behavior is evaluated exactly for the erf nonlinearity using the above results the tradeoff between the extent of error saturation steady state excess mean square error and rate of algorithm convergence is studied the tradeoff shows that 1 starting with a sign detector the convergence rate is increased by nearly a factor of two for each additional bit and 2 as the number of bits is increased further the additional bit by very little in convergence speed asymptotically approaching the behavior of the linear algorithm

nonlinear quantization effects in the frequency domain complex scalar lms adaptive algorithm nonlinear quantization effects in the frequency domain complex scalar lms adaptive algorithm are analyzed by using conditional expectations the probability density function of the quantizer input conditioned on the weight is derived the density is applied to finding the conditional characteristic function and the mth conditional moment at the quantizer output the first and second conditional moments of the quantizer output are used to derive difference equations that approximate the dynamical behavior of the first and second weight moments these difference equations are solved numerically and compare favorably to simulation results a model of the quantizer as an additive noise source is of no analytical value since the quantizatian noise has negligible effect on the mean square error when the model is valid finally a design approach is proposed for selecting the number of bits in the weight accumulator the moment equations are also used to determine the algorithm mean square error for different quantizer step sizes and the optimum algorithm step size when a fixed amount of input data is available for adaptation

analysis of error gradient adaptive linear estimators for a class of stationary dependent processes in many applications the training data to be processed by an adaptive linear estimator can be assumed to have a finite correlation length an exact analysis for this class of problems that yields the coefficient bias coefficient correlation matrix and mean square estimation error is obtained via a stochastic imbedding procedure a power series expansion in the gain parameter is used to obtain simplified expressions of order one for the above statistical moments these new expressions are shown to contain the terms that would result from an analysis based upon the assumption of independent training data plus additional terms arising from data correlation algorithm convergence properties are studied by identifying the appropriate matrix eigenvalues from the first order theory

on an approximate subspace method for eigenfilter computation a method has been proposed for estimating the frequencies of sinusoids in additive white gaussian noise the method is an approximation to kumaresan s improved pisarenko method which can be thought of as the computation of an fir notch filter with zeros at the signal frequencies the new algorithm consists of subtracting a small e from the

a new extrapolation algorithm for band limited signals using the regularization method the ill posedness of the extrapolation problem in the presence of noise is considered a stable algorithm is constructed by solving a fredholm equation based on a regularization method the algorithm appears relatively robust since the noise eta sub delta t is taken as a function in l sup 2 t t t 0 such that the error energy integral mod eta sub delta t mod sup 2 dt

efficient subspace based algorithm for adaptive bearing estimation and tracking in some practical applications of array processing the directions of the incident signals should be estimated adaptively and or the time varying directions should be tracked promptly in this paper an adaptive bearing estimation and tracking abest algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow band signals impinging on a uniform linear array ula based on the subspace based method without eigendecomposition sumwe where a linear operator is obtained from the array data to form a basis for the null space by exploiting the array geometry and its shift invariance property specifically the null space is estimated using the least mean square lms or normalized lms nlms algorithm and the directions are updated using the approximate newton method the transient analyses of the lms and nlms algorithms are studied where the weight i e the linear operator is in the form of a matrix and there is a correlation between the additive noise and input data that involve the instantaneous correlations of the received array data in the updating equation and the step size stability conditions are derived explicitly in addition the analytical expressions for the mean square error mse and mean square deviation msd learning curves of the lms algorithm are clarified the effectiveness of the abest algorithm is verified and the theoretical analyses are corroborated through numerical examples simulation results show that the abest algorithm is computationally simple and has good adaptation and tracking abilities

distribution free confidence intervals for a parameter of wilcoxon mann whitney type for ordered categories and progressive censoring halperin gilbert and lachin 1987 biometrics 43 71 80 obtain confidence intervals for pr x less than y based on the two sample wilcoxon statistic for continuous data their approach is applied here to ordered categorical data and right censored continuous data using the generalization zeta pr x less than y 1 2pr x y to account for ties deviations from nominal coverage probability for various sample sizes and values of zeta are obtained via simulation of either three or six ordered categories based on underlying poisson or exponential distributions the simulation results indicate that the proposed method performs quite well and it is apparently superior to the approach of hochberg 1981 communications in statistics theory and methods a10 1719 1732 for values of zeta far from 1 2

convergence and performance analysis of the normalized lms algorithm with uncorrelated gaussian data it is demonstrated that the normalized least mean square nlms algorithm can be viewed as a modification of the widely used lms algorithm the nlms is shown to have an important advantage over the lms which is that its convergence is independent of environmental changes in addition the authors present a comprehensive study of the first and second order behavior in the nlms algorithm they show that the nlms algorithm exhibits significant improvement over the lms algorithm in convergence rate while its steady state performance is considerably worse

bias removal in equation error adaptive iir filters in the equation error formulation of adaptive iir filters the estimated parameters contain bias when there is noise in the desired response a method that can eliminate this bias is investigated the idea is to maintain a quadratic constraint on the feedback coefficients so that the noise contributes only a constant term to the mean square error this term does not affect minimization and thus the bias is eliminated a quadratically constrained stochastic gradient search method is applied for optimization and convergence behavior when the noise is white is analyzed adaptation of the feedback fir filter in second order cascade form useful for stability monitoring is also considered when the noise is nonwhite the technique requires an adaptive whitening filter simulation results are included to demonstrate the bias removal capability of the method corroborate the theoretical developments and compare with existing techniques

tracking of time varying mobile radio channels 1 the wiener lms algorithm adaptation algorithms with constant gains are designed for tracking smoothly time varying parameters of linear regression models in particular channel models occurring in mobile radio communications in a companion paper an application to channel tracking in the is 136 tdma system is discussed the proposed algorithms are based on two key concepts first the design is transformed into a wiener filtering problem second the parameters are modeled as correlated arima processes with known dynamics this leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information the algorithms can be realized as wiener filters called learning filters or as lms newton updates complemented by filters that provide predictions or smoothing estimates the simplest algorithm named the wiener lms is presented all parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known the computational complexity is of the same order of magnitude as that of lms for regressors which are either white or have autoregressive statistics the tracking performance is however substantially improved

numerical diffraction by a uniform grid in this report we analyze the influence of a spatial discretization on the propagation of a wave generated by a harmonic point source we consider finite element and finite difference schemes on a uniform grid for the wave equation we study the asymptotic behavior in space of the elementary solution of the associated helmholtz equation this study permits us to define the notions of asymptotic wave fronts a w f and asymptotic amplitude diagrams a a d we point out some results about the anisotropy and the dispersion of numerical scheme which complete those obtained from the more classical plane wave analysis see r m alford r kelly and d m boore accuracy of finite modeling of the acoustic wave equation biophysics 6 1974 pp 834 842 a bamberger g chavent and p lailly etude de schemas numeriques des equations de l elastodynamique lineaire rapport inria no 41 october 1980 t belytschko and r mullen dispersion analysis of finite element semi discretizations of the two dimen

microstatistic lms filtering adaptive microstatistic filters are developed for applications in which the second order statistics of the thresholded signals are not known or may be nonstationary a multilevel threshold decomposition such that real valued stochastic processes can be filtered is used and the computational complexity of the algorithm can be arbitrarily specified by the designer the adaptation uses the least mean squares error approach of the least mean square lms algorithm the convergence of the adaptive algorithm is proved due to the nonhomogeneous statistical characteristic of the threshold signals a different step size adaptation parameter can be assigned to each threshold level simple design guidelines are developed for finding the set of nonhomogeneous step sizes which in practice yield better convergence characteristics

a u statistics based approach to sample size planning of two arm trials with discrete outcome criterion aiming to establish either superiority or noninferiority in current practice the most frequently applied approach to the handling of ties in the mann whitney wilcoxon mww test is based on the conditional distribution of the sum of mid ranks given the observed pattern of ties starting from this conditional version of the testing procedure a sample size formula was derived and investigated by zhao et al stat med 2008 in contrast the approach we pursue here is a nonconditional one exploiting explicit representations for the variances of and the covariance between the two u statistics estimators involved in the mann whitney form of the test statistic the accuracy of both ways of approximating the sample sizes required for attaining a prespecified level of power in the mww test for superiority with arbitrarily tied data is comparatively evaluated by means of simulation the key qualitative conclusions to be drawn from these numerical comparisons are as follows with the sample sizes calculated by means of the respective formula both versions of the test maintain the level and the prespecified power with about the same degree of accuracy despite the equivalence in terms of accuracy the sample size estimates obtained by means of the new formula are in many cases markedly lower than that calculated for the conditional test perhaps a still more important advantage of the nonconditional approach based on u statistics is that it can be also adopted for noninferiority trials copyright 2016 john wiley sons ltd

a variable step size lms algorithm a least mean square lms adaptive filter with a variable step size is introduced the step size increases or decreases as the mean square error increases or decreases allowing the adaptive filter to track changes in the system as well as produce a small steady state error the convergence and steady state behavior of the algorithm are analyzed the results reduce to well known results when specialized to the constant step size case simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual lms algorithm and another variable step size algorithm they show that its performance compares favorably with these existing algorithms

tracking properties and steady state performance of rls adaptive filter algorithms adaptive signal processing algorithms derived from ls least squares cost functions are known to converge extremely fast and have excellent capabilities to track an unknown parameter vector this paper treats analytically and experimentally the steady state operation of rls recursive least squares adaptive filters with exponential windows for stationary and nonstationary inputs a new formula for the estimation noise has been derived involving second and fourth order statistics of the filter input as well as the exponential windowing factor and filter length furthermore it is shown that the adaptation process associated with lag effects depends solely on the exponential weighting parameter in addition the calculation of the excess mean square error due to the lag for an assumed markov channel provides the necessary information about tradeoffs between speed of adaptation and steady state error it is also the basis for comparison to the simple lms algorithm in a simple case of channel identification it is shown that the lms and rls adaptive filters have the same tracking behavior finally in the last part we present new rls restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise namely finite precision arithmetic

partial update lms algorithms partial updating of lms filter coefficients is an effective method for reducing computational load and power consumption in adaptive filter implementations this paper presents an analysis of convergence of the class of sequential partial update lms algorithms s lms under various assumptions and shows that divergence can be prevented by scheduling coefficient updates at random which we call the stochastic partial update lms algorithm spu lms specifically under the standard independence assumptions for wide sense stationary signals the s lms algorithm converges in the mean if the step size parameter spl mu is in the convergent range of ordinary lms relaxing the independence assumption it is shown that s lms and lms algorithms have the same sufficient conditions for exponential stability however there exist nonstationary signals for which the existing algorithms s lms included are unstable and do not converge for any value of spl mu on the other hand under broad conditions the spu lms algorithm remains stable for nonstationary signals expressions for convergence rate and steady state mean square error of spu lms are derived the theoretical results of this paper are validated and compared by simulation through numerical examples

simplified analysis of the lms adaptive filter using a transfer function approximation a simple approximation to the behavior of the lms adaptive filter as a discrete transfer function is developed this representation is a valid description for both deterministic inputs and for the expected results with random inputs including correlated inputs the results are shown to be exact for some classes of input including periodic signals one result of this analysis is the demonstration that the lms filter can produce results which are biased from the least squares solution under the combined conditions of a nonzero mean primary and a correlated reference input

on the joint characteristic function of the complex scalar lms adaptive weight in this paper the joint characteristic function of the single weight complex scalar lms adaptive algorithm is studied an integral equation is derived for the joint characteristic function of the real and imaginary parts of the weight this integral equation is used to obtain the weight moments and is approximately solved for a sufficiently small adaptation parameter it is shown that for small and in steady state the real and imaginary parts of the weights are statistically independent gaussian random variables with means equal to the wiener weight these results are applied to a detection problem using the weight magnitude square as the detection statistic assuming the weight is also gaussian during the transient phase of adaptation the detection performance is optimized over for a fixed number of data samples and a known observation interval the optimum selection of approaches zero so that the adaptation process reduces to a cross correlation operation when the observation interval is not known a priori a bounded away from zero is required this detector is shown to be 3 db degraded from the optimum narrow band envelope detector using the same number of data samples

finite difference schemes for long time integration a general method for constructing finite difference schemes for longtime integration problems is presented it is demonstrated for discretizations of first and second space derivatives however the approach is not limited to these cases the schemes are constructed so as to minimize the global truncation error taking into account the initial data the resulting second order compact schemes can be used for integration times fourfold or more longer than previously studied schemes with similar computational complexity a similar approach was used to obtain improved integration schemes

a note on the convergence analysis of lms adaptive filters with gaussian data necessary and sufficient conditions for the convergence of lms least mean squares adaptive filters with gaussian data have been established by l l horowitz and k d senne 1981 with the recent support of a feuer and e weinstein 1985 a feature of both of these studies is the necessity to investigate bounds on the roots of rather unwieldy characteristic equations the authors show how such an investigation can be avoided through the use of a theorem of f r gantmacher 1959 in formally applying this theorem similar results to those of the above studies are obtained in a precise and straightforward manner

power and sample size calculations for exact conditional tests with ordered categorical data we develop an algorithm for computing sample sizes equal or unequal for categorical data we illustrate its use in the two sample setting using the wilcoxon rank sum statistic but the algorithm accommodates the entire class of linear rank statistics and can be extended to include nonlinear rank statistics as well the sample size determinations can be based on either exact power or on a very precise monte carlo estimate of it to reduce the computations further power can be computed as a function of asymptotic critical values when the number of categories is not too small for the wilcoxon statistic we show that this approximation works well if there are more than five response categories

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

finite difference approximations of first derivatives for three dimensional grid singularities explicit finite difference approximations of first derivatives are developed for two dimensional three way and five way grid singularities the schemes for three way singularities also apply for six way singularities the development objectives are such that the finite difference schemes are non dissipative and compatible with regular difference approximations for convection dominated phenomena special emphasis is given to the directional dependency of numerical phase speeds and stability limits for explicit time integration for that purpose free coefficients are used to minimize the isotropy error of the numerical phase velocity it is shown that numerical phase speeds and stability limits are almost isotropic hence employment of the proposed schemes is nearly independent of the local orientation of the differencing stencil the time step limits are greater than those of regular finite differences indicating that the overall time step of a computation is not reduced by employing the proposed schemes the developed schemes for three way singularities are of second fourth and sixth order of accuracy whereas the five way difference approximations are second and fourth order accurate respectively the spectral characteristics the formal order of accuracy and the stability limits of the proposed schemes imply that they can favorably be used in combination with regular difference approximations of the same order of accuracy on block structured grids

alpha stable signals and adaptive filtering let d sub k x sub k be jointly stationary symmetric spl alpha stable processes with index 1 spl alpha 2 we first consider the problem of optimal fir linear and regression filters we then consider the signed error and sign sign adaptive filtering algorithms for the estimation of the desired signal d sub j on the basis of the input vector x sub j various convergence results are established for the signal and tap weights estimation errors

adaptive stack filtering with application to image processing with the aid of threshold decomposition it is shown that optimal stack filters under the mean absolute error mae criterion are equal to optimal or bayesian classifiers subject to stacking constraints under the mean classification error mce criterion nonadaptive and adaptive constrained least mean absolute lma algorithms are developed for the esti mation of stack filters through the linearization of the unit step function in the objective function the convergence of the al gorithms is proven under certain conditions although the methods do not generally give optimal stack filters under the mae criterion these algorithms have several distinct merits compared to other stack filter optimization methods 1 the op timization problem has a unique solution that approximates the optimal stack filters in the least mean square sense 2 the meth ods can be implemented in the binary and real domains and 3 for stack filters defined by linearly separable positive boolean functions pbf s or weighted order statistic wos filters the number of the parameters to be estimated is reduced to the window width of the filter a comparison between images re stored by the new algorithms and the stack filtering algorithm optimal under the mae criterion confirms the effectiveness of the proposed algorithms

comments on subband coding of images the commenter feels that an equation in the above named work by j w woods and s o neil ibid vol assp 34 pp 1278 1288 oct 1986 is incorrect as given a corrected version is provided along with another equation which together allow one to obtain another equation as originally stated the analysis following the equation remains valid

convergence analysis of adaptive linear estimation for dependent stationary processes the convergence properties of an adaptive linear mean square estimator that uses a modified lms algorithm are established for generally dependent processes bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated it is shown that the mean square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation the present findings extend earlier results in the literature obtained for independent and m dependent input data

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

the composite regressor algorithm for iir adaptive systems an adaptive iir algorithm called the composite regressor algorithm cra is developed the algorithm is a generalization of the common equation error a priori output error and a posteriori output error adaptive iir algorithms the cra is analyzed for convergence in a noiseless environment and for bias in a stochastic setting it is determined that by using a parameter called the regressor composition parameter a tradeoff can be obtained between the automatic convergence but large bias results of the equation error algorithm and the difficult convergence condition but small bias results of the output error algorithms in proving results for the cra it is shown that the a posteriori output error algorithm produces estimates with nonzero bias when the adaptive gain is small but bounded away from zero a convergence condition for the a priori output error algorithm is derived for the first time

optimized compact finite difference schemes with maximum resolution direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high resolution characteristics in the evaluation of spatial derivatives compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders an analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes based on the idea of the minimization of dispersive phase errors in the wave number domain and these are applied to the analytic optimization of multidiagonal compact schemes actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases respectively from these comparisons the usefulness of an optimized high order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed for the optimized high order spatial schemes the feasibility of using classical high order runge kutta time advancing methods is investigated

performance analysis of the deficient length lms adaptive algorithm in almost all analyzes of the least mean square lms finite impulse response fir adaptive algorithm it is assumed that the length of the adaptive filter is equal to that of the unknown system impulse response however in many practical situations a deficient length adaptive filter whose length is less than that of the unknown system is employed and analysis results for the sufficient length lms algorithm are not necessarily applicable to the deficient length case therefore there is an essential need to accurately quantify the behavior of the lms algorithm for realistic situations where the length of the adaptive filter is deficient in this paper we present a performance analysis for the deficient length lms adaptive algorithm for correlated gaussian input data and using the common independence assumption exact expressions that completely characterize the transient and steady state mean square performances of the algorithm are developed which lead to new insights into the statistical behavior of the deficient length lms algorithm simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm

power and sample size evaluation for the cochran mantel haenszel mean score wilcoxon rank sum test and the cochran armitage test for trend the power of a chi square test and thus the required sample size are a function of the noncentrality parameter that can be obtained as the limiting expectation of the test statistic under an alternative hypothesis specification herein we apply this principle to derive simple expressions for two tests that are commonly applied to discrete ordinal data the wilcoxon rank sum test for the equality of distributions in two groups is algebraically equivalent to the mann whitney test the kruskal wallis test applies to multiple groups these tests are equivalent to a cochran mantel haenszel mean score test using rank scores for a set of c discrete categories although various authors have assessed the power function of the wilcoxon and mann whitney tests herein it is shown that the power of these tests with discrete observations that is with tied ranks is readily provided by the power function of the corresponding cochran mantel haenszel mean scores test for two and r 2 groups these expressions yield results virtually identical to those derived previously for rank scores and also apply to other score functions the cochran armitage test for trend assesses whether there is an monotonically increasing or decreasing trend in the proportions with a positive outcome or response over the c ordered categories of an ordinal independent variable for example dose herein it is shown that the power of the test is a function of the slope of the response probabilities over the ordinal scores assigned to the groups that yields simple expressions for the power of the test copyright 2011 john wiley sons ltd

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

convergence analysis of the sign algorithm for adaptive filtering we consider the convergence analysis of the sign algorithm for adaptive filtering when the input processes are uncorrelated and gaussian and a fixed step size spl mu 0 is used exact recursive equations for the covariance matrix of the deviation error are established for any step size spl mu 0 asymptotic time averaged convergence for the mean absolute deviation error mean square deviation error and for the signal mean square estimation error are established these results are shown to hold for arbitrary step size spl mu 0

an approximate statistical analysis of the widrow lms algorithm with application to narrow band interference rejection the widrow lms algorithm is considered for the implementation of an adaptive prewhitening filter in a direct sequence ds spread spectrum receiver exact expressions for the steady state tapweight covariance matrix and resulting average excess mean square error are developed for the real lms algorithm when the input contains a random binary sequence used to model a pseudonoise spreading sequence it is shown here that the output samples of the adaptive filter possess approximately gaussian statistics under the conditions of slow convergence and a large number of filter taps using this approximation expressions for the resulting bit error rate ber when the adaptive algorithm is used to suppress a fading gone jammer are developed and numerical results obtained from these expressions are compared to simulation results for the ds receiver

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

a normalized frequency domain lms adaptive algorithm a scheme is presented for obtaining an input power estimate for setting the algorithm gain parameter separately in each frequency bin in the frequency domain lms adaptive algorithm this is particularly important if the input has large spectral variations and a single feedback parameter set on the broad band power could result in instability in the adaptive filters in some frequency bins the estimate is incorporated directly into the algorithm as a data dependent time varying stochastic n using a gaussian data model and sample to sample data independence first order linear difference equations are derived and solved for the mean and misadjustment errors the performance of the scheme is compared to the case for which the input power level is known a priori for the same transient response only about ten samples need be averaged to yield the same misadjustment error

sample size determination for some common nonparametric tests abstract the article discusses the problem of determining the number of observations required by some common nonparametric tests so that the tests have power at least 1 against alternatives that differ sufficiently from the hypothesis being tested it is shown that the number of observations depends on certain simple probabilities a method is suggested for fixing the value of the appropriate probability when determining sample size

sample size calculation for the wilcoxon mann whitney test adjusting for ties in this paper we study sample size calculation methods for the asymptotic wilcoxon mann whitney test for data with or without ties the existing methods are applicable either to data with ties or to data without ties but not to both cases while the existing methods developed for data without ties perform well the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties we propose a new method which has a closed form formula and therefore is very easy to calculate in addition the new method can be applied to both data with or without ties simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers

recursive nonlinear system identification by a stochastic gradient algorithm stability performance and model nonlinearity considerations a parameter estimation problem in a class of nonlinear systems is considered where the input output relation of a nonlinear system is approximated by a polynomial model e g a volterra series a least mean squares lms type algorithm is utilized for the recursive estimation of the polynomial coefficients and its resulting mean square error mse convergence properties are investigated conditions for the algorithm stability in the mean square sense are established steady state mse bounds are obtained and the convergence rate is discussed in addition modeling accuracy versus steady state performance is examined it is found that an increase of the modeling accuracy may result in a deterioration of the asymptotic performance that is yielding a larger steady state mse linear system identification is studied as a special case

size and power estimation for the wilcoxon mann whitney test for ordered categorical data we derive an exact variance method for the size and power calculation for the wilcoxon mann whitney test for ordered categorical data the o brien castelloe approximation implemented in sas version 9 2 sas institute inc cary nc usa is simplified simulation studies show that the exact variance approach tends to be more accurate than the o brien castelloe approximation and the zhao rahardja qu method derived under local alternatives copyright 2011 john wiley sons ltd

constrained adaptive filtering algorithms asymptotic convergence properties for dependent data the convergence properties of constrained adaptive filtering algorithms are established the constraint is in the form of a bounded set in which the filter s coefficients must lie a recursive procedure that converges to the deterministic solution of the constrained linear mean square estimation problem is obtained using an appropriate contraction mapping the recursion is used to derive the adaptive algorithm for the filter coefficients bounds on the mean square error of the coefficients bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated the algorithms use a moving window of size n on the data from one adaptation step to the next however tighter bounds can be obtained when a skipped sampling mechanism is used

analytic behavior of the lms adaptive line enhancer for sinusoids corrupted by multiplicative and additive noise the least mean squares adaptive line enhancer lms ale has been widely used for the enhancement of coherent sinusoids in additive wideband noise this paper studies the behavior of the lms ale when applied to the enhancement of sinusoids that have been corrupted by both colored multiplicative and white additive noise the multiplicative noise decorrelates the sinusoid spreads its power spectrum and acts as an additional corrupting noise closed form expressions are derived for the optimum wiener filter ale output snr as a function of the residual coherent sine wave power the noncoherent sine wave power spectrum and the background additive white noise when the coherent to noncoherent sine wave power ratio is sufficiently small it is shown that a nonlinear e g square law transformation of the ale input results in a larger optimum ale output snr

optimized prefactored compact schemes the numerical simulation of aeroacoustic phenomena requires high order accurate numerical schemes with low dispersion and dissipation errors in this paper we describe a strategy for developing high order accurate prefactored compact schemes requiring very small stencil support these schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes the prefactorization strategy splits the central implicit schemes into forward and backward biased operators using fourier analysis we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components this ensures that when the forward and backward stencils are added the original central compact scheme is recovered to extend the resolution characteristic of the schemes an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh the resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth and eighth order compact schemes making them more suitable for high resolution numerical simulations in gas dynamics and computational aeroacoustics the efficiency accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems

test statistics and sample size formulae for comparative binomial trials with null hypothesis of non zero risk difference or non unity relative risk when it is required to establish a materially significant difference between two treatments or alternatively to show that two treatments are equivalent standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply this paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non zero difference or non unity relative risk methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine

nonlinear blind equalization schemes using complex valued multilayer feedforward neural networks among the useful blind equalization algorithms stochastic gradient iterative equalization schemes are based on minimizing a nonconvex and nonlinear cost function however as they use a linear fir filter with a convex decision region their residual estimation error is high in the paper four nonlinear blind equalization schemes that employ a complex valued multilayer perceptron instead of the linear filter are proposed and their learning algorithms are derived after the important properties that a suitable complex valued activation function must possess are discussed a new complex valued activation function is developed for the proposed schemes to deal with qam signals of any constellation sizes it has been further proven that by the nonlinear transformation of the proposed function the correlation coefficient between the real and imaginary parts of input data decreases when they are jointly gaussian random variables last the effectiveness of the proposed schemes is verified in terms of initial convergence speed and mse in the steady state in particular even without carrier phase tracking procedure the proposed schemes correct an arbitrary phase rotation caused by channel distortion

a global gradient noise covariance expression for stationary real gaussian inputs supervised parameter adaptation in many artificial neural networks is largely based on an instantaneous version of gradient descent called the least mean square lms algorithm this paper considers only neural models which are linear with respect to their adaptable parameters and has two major contributions first it derives an expression for the gradient noise covariance under the assumption that the input samples are real stationary gaussian distributed but can be partially correlated this expression relates the gradient correlation and input correlation matrices to the gradient noise covariance and explains why the gradient noise generally correlates maximally with the steepest principal axis and minimally with the one of the smallest curvature regardless of the magnitude of the weight error second a recursive expression for the weight error correlation matrix is derived in a straightforward manner using the gradient noise covariance and comparisons are drawn with the complex lms algorithm

using spectral estimation techniques in adaptive processing antenna systems improved spectral estimation techniques hold promise for becoming a valuable asset in adaptive processing array antenna systems their value lies in the considerable amount of additional useful information which they can provide about the interference environment utilizing a relatively small number of degrees of freedom dof the superresolution capabilities estimation of coherence and relative power level determination serve to complement and refine the data from faster conventional estimation techniques two conceptual application area examples for using such techniques are discussed partially adaptive low sidelobe arrays and fully adaptive tracking arrays for the partially adaptive area the information is utilized for efficient assignment of a limited number of dof in a beamspace constrained adaptive system in order to obtain a stable main beam retention of low sidelobes considerably faster response and reduction in overall cost these benefits are demonstrated via simulation examples computed for a 16 element linear array for the fully adaptive tracking array area the information is utilized in an all digital processing system concept to permit stable hulling of coherent interference sources in the main beam region efficient assignment control of the available dof and greater flexibility in time domain adaptive filtering strategy

a robust variable step size lms type algorithm analysis and simulations a number of time varying step size algorithms have been proposed to enhance the performance of the conventional lms algorithm experimentation with these algorithms indicates that their performance is highly sensitive to the noise disturbance this paper presents a robust variable step size lms type algorithm providing fast convergence at early stages of adaptation while ensuring small final misadjustment the performance of the algorithm is not affected by existing uncorrelated noise disturbances an approximate analysis of convergence and steady state performance for zero mean stationary gaussian inputs and for nonstationary optimal weight vector is provided simulation results comparing the proposed algorithm to current variable step size algorithms clearly indicate its superior performance for cases of stationary environments for nonstationary environments our algorithm performs as well as other variable step size algorithms in providing performance equivalent to that of the regular lms algorithm

analysis of stability and performance of adaptation algorithms with time invariant gains adaptation laws that track parameters of linear regression models are investigated the considered class of algorithms apply linear time invariant filtering on the instantaneous gradient vector and includes least mean squares lms as its simplest member the asymptotic stability and steady state tracking performance for prediction and smoothing estimators is analyzed for parameter variations described by stochastic processes with time invariant statistics the analysis is based on a novel technique that decomposes the inherent feedback of adaptation algorithms into one time invariant loop and one time varying loop the impact of the time varying feedback on the tracking error covariance can be neglected under certain conditions and the performance analysis then becomes straightforward performance analysis in the presence of a non negligible time varying feedback is performed for algorithms that use scalar measurements convergence in mean square error mse and the mse tracking performance is investigated assuming independent consecutive regression vectors closed form expressions for the tracking mse are thereafter derived without this independence assumption for a subclass of algorithms applied to finite impulse response fir models with white inputs this class includes wiener lms adaptation

leaky lms algorithm mse analysis for gaussian data despite the widespread usage of the leaky lms algorithm there has been no detailed study of its performance this paper presents an analytical treatment of the mean square error mse performance for the leaky lms adaptive algorithm for gaussian input data the common independence assumption regarding w n and x n is also used exact expressions that completely characterize the second moment of the coefficient vector and algorithm steady state excess mse are developed rigorous conditions for mse convergence are also established analytical results are compared with simulation and are shown to agree well

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

adaptive enhancement of finite bandwidth signals in white gaussian noise the steady state behavior of the adaptive line enhancer ale is analyzed for stationary inputs consisting of finite bandwidth signals embedded in a white gaussian noise wgn background analytic expressions for the weights and output of the lms adaptive filter are derived as functions of input signal bandwidth and snr as well as ale length and bulk delay the steady state gain in broad band snr from input to output is derived as a function of these same four variables for fixed ale parameters and input snr it is shown that this gain increases as the input signal becomes narrower and approaches the sinusoidal limit it is emphasized that because the correlation time of finite bandwidth signals is limited excessively large values of the ale bulk delay parameter result in diminished gain furthermore there is an optimal filter length whose value depends upon signal bandwidth and snr for which the broad band gain is maximized these results demonstrate the importance of including the effects of algorithm noise in analyzing the performance of real time adaptive processors

isotropic finite differences new finite differences called isotropic finite differences where the lowest order error terms are without any directional bias are proposed an accurate simulation of 6 fold symmetric dendritic solidification is presented using a numerical scheme based on these finite differences