optimization for training neural nets various techniques of optimizing criterion functions to train neural net classifiers are investigated these techniques include three standard deterministic techniques variable metric conjugate gradient and steepest descent and a new stochastic technique it is found that the stochastic technique is preferable on problems with large training sets and that the convergence rates of the variable metric and conjugate gradient techniques are similar

estimation of input pulse locations from the response of an all pole transfer system using tapered rank reduction when ordinary rank reduction is used to remove the characteristics of the transfer system and to estimate the multipulse input time series the nonsignificant singular values are sharply cut off by low order truncation if the system q quality factor is high and then a large ripple occurs around each pulse location in order to avoid these difficulties a method is proposed in which the multipulse time series is estimated by a rank reduction using a tapering window in order to suppress the ripple due to the low order sharp truncation and then by applying the pole estimation method to the inverse fourier transform of the resultant time series thus the pulse locations are accurately estimated by using the pulse locations as the initial estimates the maximum likelihood estimates of the pulse locations are obtained from simulation experiments these principles are confirmed

minimum mean squared error transform coding and subband coding knowledge of the power spectrum of a stationary random sequence can be used for quantizing the signal efficiently and with minimum mean squared error a multichannel filter is used to transform the random sequence into an intermediate set of variables that are quantized using independent scalar quantizers and then inverse filtered producing a quantized version of the original sequence equal word length and optimal word length quantization at high bit rates is considered an analytical solution for the filter that minimizes the mean squared quantization error is obtained in terms of its singular value decomposition the performance is characterized by a set of invariants termed second order modes which are derived from the eigenvalue decomposition of the matrix valued power spectrum a more general rank reduced model is used for decreasing distortion by introducing bias the results are specialized to the case when the vector valued time series is obtained from a scalar random sequence which gives rise to a filter bank model for quantization the asymptotic performance of such a subband coder is derived and shown to coincide with the asymptotic bound for transform coding quantization employing a single scalar pre and postfilter traditional transform coding using a square linear transformation and subband coding in filter banks arise as special cases of the structure analyzed here

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

estimation of the number of signals from features of the covariance matrix a supervised approach the purpose of this paper is to provide a fast and simplified detection test for use in the presence of a small number of sources from 0 2 which is able to accommodate correlated paths and nonwhite noise conventional eigenvalue based criteria are unable to do so for a uniform linear array using common sense arguments a small set of significant features of the covariance matrix are used as inputs to a neural net the nonlinear transfer function of the neural net is adjusted by supervised training to provide the discriminant functions for order selection in its outputs results from the net are then compared with conventional criteria and demonstrate superior performance in particular for correlated sources and small sample sizes training may be introduced for known nonwhite noise which serves to maintain high performance for reasonable correlation lengths

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

a software package for lie algebraic computations the paper presents a computer algebra package that facilitates lie algebraic symbolic computations required in the solution of a variety of problems such as the solution of right invariant differential equations evolving on lie groups lie theory is a powerful tool helpful in the analysis and design of modern nonlinear control laws nonlinear filters and the study of particle dynamics the practical application of lie theory often results in highly complex symbolic expressions that are difficult to handle efficiently without the aid of a computer software tool the aim of the package is to facilitate and encourage further research relying on lie algebraic computations

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

sufficient conditions for conservativity of minimal quantum dynamical semigroups abstract the conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a generalized subharmonic operator bounded from below by the dissipative part of the infinitesimal generator we discuss applications of this criteria in mathematical physics and quantum probability

second order analysis of improper complex random vectors and processes we present a comprehensive treatment of the second order theory of complex random vectors and wide sense stationary wss signals the main focus is on the improper case in which the complementary covariance does not vanish accounting for the information present in the complementary covariance requires the use of widely linear transformations based on these we present the eigenanalysis of complex vectors and apply it to the problem of rank reduction through principal components we also investigate joint properties of two complex vectors by introducing canonical correlations which paves the way for a discussion of the wiener filter and its rank reduced version we link the concepts of propriety and joint propriety to eigenanalysis and canonical correlation analysis respectively our treatment is extended to wss signals in particular we give a result on the asymptotic distribution of eigenvalues and examine the connection between wss proper and analytic signals

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

fast recursive low rank linear prediction frequency estimation algorithms a class of fast recursive low rank linear prediction algorithms for the tracking of time varying frequencies of multiple nonstationary sinusoids in noise is introduced realizations with o nn and o nn sup 2 arithmetic operations per time step are described where n is the model order and n is the number of independent sinusoids the key step towards an operations count that depends only linearly on the model order is fast eigensubspace tracking and the property that the coefficients of a high order n prediction filter itself constitute a perfectly or almost perfectly predictable sequence that can be annihilated using a low order 2n prediction error filter that carries the desired signal frequency information in its roots in this concept root tracking is limited to a low order filter polynomial even if the overmodeling factor n n is much larger than 1 for optimal noise suppression extraneous roots are not computed explicitly detailed simulation results confirm the tracking capabilities of the new algorithms

the dobrushin ergodicity coefficient and the ergodicity of noncommutative markov chains abstract in this paper we study the notion of the dobrushin ergodicity coefficient for positive contractions defined on the predual m of von neumann algebra m moreover in terms of this coefficient we prove ergodic type theorems for nonhomogeneous markov chains on m

on the use of singular value decomposition and decimation in discrete time band limited signal extrapolation the problem of extrapolating a band limited signal in discrete time is viewed as one of solving an underdetermined system of linear equations choosing the minimum norm least squares mnls solution is one criterion for singling out an extrapolation from all the possible solutions to the linear system use of the moore penrose inverse yields the mnls solution and singular value decomposition svd provides a means for implementing the moore penrose inverse an expression for the mean square error incurred in solving a linear system via svd is derived this can be used to estimate the number of singular values needed to form the inverse the error expression also indicates that decimation can be applied in the extrapolation problem to reduce the high computational cost of svd without degrading the extrapolation the results developed for the one dimensional case are extended to higher dimensions examples of the svd approach to extrapolation are given along with examples using other extrapolation techniques for comparison the svd approach compares favorably with known mnls extrapolation methods

the geometry of weighted low rank approximations the low rank approximation problem is to approximate optimally with respect to some norm a matrix by one of the same dimension but smaller rank it is known that under the frobenius norm the best low rank approximation can be found by using the singular value decomposition svd although this is no longer true under weighted norms in general it is demonstrated here that the weighted low rank approximation problem can be solved by finding the subspace that minimizes a particular cost function a number of advantages of this parameterization over the traditional parameterization are elucidated finding the minimizing subspace is equivalent to minimizing a cost function on the grassmann manifold a general framework for constructing optimization algorithms on manifolds is presented and it is shown that existing algorithms in the literature are special cases of this framework within this framework two novel algorithms a steepest descent algorithm and a newton like algorithm are derived for solving the weighted low rank approximation problem they are compared with other algorithms for low rank approximation as well as with other algorithms for minimizing a cost function on a grassmann manifold

a new method for low rank transform domain adaptive filtering this paper introduces a least squares matrix based framework for adaptive filtering that includes normalized least mean squares nlms affine projection ap and recursive least squares rls as special cases we then introduce a method for extracting a low rank underdetermined solution from an overdetermined or a high rank underdetermined least squares problem using a part of a unitary transformation we show how to create optimal low rank transformations within this framework for obtaining computationally competitive versions of our approach we use the discrete fourier transform dft we convert the complex valued dft based solution into a real solution the most significant bottleneck in the optimal version of the algorithm lies in having to calculate the full length transform domain error vector we overcome this difficulty by using a statistical approach involving the transform of the signal rather than that of the error to estimate the best low rank transform at each iteration we also employ an innovative mixed domain approach in which we jointly solve time and frequency domain equations this allows us to achieve very good performance using a transform order that is lower than the length of the filter thus we are able to achieve very fast convergence at low complexity using the acoustic echo cancellation problem we show that our algorithm performs better than nlms and ap and competes well with ftf rls for low snr conditions the algorithm lies in between affine projection and ftf rls both in terms of its complexity and its performance

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

minimum variance beamforming with soft response constraints soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming a quadratic constraint on the beamformer weights is used to control the mean squared error between a desired response and the actual response in the signal direction the constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation under the assumptions of known signal direction and spectral shape the signal to noise ratio is shown to be a nondecreasing function of the mean square distortion the distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired properties of this beamforming method and its relationship to linear constrained beamforming are discussed simulations verify analytic results and illustrate the utility of the soft constrained approach

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

rank reduction for modeling stationary signals rank reduction is developed as a general principle for trading off model bias and model variance in the analysis and synthesis of signals the principle is applied to three basic problems stationary time series modeling stationary time series whitening and vector quantization each problem brings its own surprises and insights

an iterative algorithm for the computation of the mvdr filter statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter or constraint vector and generates a sequence of filters that converges to the minimum variance distortionless response mvdr solution for any positive definite input autocorrelation matrix computationally the algorithm is a simple noninvasive recursive procedure that avoids any form of explicit autocorrelation matrix inversion decomposition or diagonalization theoretical analysis reveals basic properties of the algorithm and establishes formal convergence when the input autocorrelation matrix is replaced by a conventional sample average positive definite estimate the algorithm effectively generates a sequence of mvdr filter estimators the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample matrix inversion smi estimator in fact formal convergence of the estimator sequence to the smi estimate is established however for short data records it is the early nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean square estimation error constraint lms rls type orthogonal multistage decomposition as well as plain and diagonally loaded smi estimates an illustrative interference suppression example is followed throughout this presentation

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

low rank detection of multichannel gaussian signals using block matrix approximation the exact design of an m channel matched filter with l taps requires the solution of an ml spl times ml block system of linear equations with toeplitz entries practical cases where m 50 and l 100 are not uncommon when the individual sensors of an array are closely spaced the temporal and spatial correlation of the resulting vector noise process may be modeled in a separable fashion in this case the noise covariance block matrix attains a special structure where all block entries are just weighted versions of each other it is shown that in this case the complexity of the detector design can be reduced drastically by a factor of ml compared to a conventional multichannel matched filter design procedure it is further shown that the separable vector noise model facilitates a complete exploitation of the rank properties of noise and data matrices a constructive procedure for the design of low rank detectors in the multichannel case is derived these detectors consist of two consecutive blocks a data and noise dependent compression stage which maps the significant signal energy into a subspace of minimal dimension followed by a minimal set of independent matched filters which point in the subspace directions in which the signal is much stronger than the noise this low rank detector concept enables discrimination with little or no performance penalty at a minimal computational cost

a note on noncommutative unique ergodicity and weighted means abstract in this paper we study unique ergodicity of c dynamical system a t consisting of a unital c algebra a and a markov operator t a a relative to its fixed point subspace in terms of riesz summation which is weaker than cesaro one namely it is proven that a t is uniquely ergodic relative to its fixed point subspace if and only if its riesz means 1 p 1 p n k 1 n p k t k x converge to e t x in a for any x a as n here e t is an projection of a to the fixed point subspace of t it is also constructed a uniquely ergodic entangled markov operator relative to its fixed point subspace which is not ergodic

reduced rank adaptive filtering a novel rank reduction scheme is introduced for adaptive filtering problems this rank reduction method uses a cross spectral metric to select the optimal lower dimensional subspace for reduced rank adaptive filtering as a function of the basis vectors of the full rank space

bi iteration svd subspace tracking algorithms we present a class of fast subspace tracking algorithms that arise from a straightforward extension of bauer s 1957 classical bi iteration to the sequential processing case the bi iteration concept has an unexpected potential in subspace tracking our new bi svd subspace trackers are well structured and show excellent convergence properties they outperform the tqr svd subspace tracking algorithm detailed comparisons confirm our claims an application to rank and data adaptive signal reconstruction is also discussed

wiener filters in canonical coordinates for transform coding filtering and quantizing canonical correlations are used to decompose the wiener filter into a whitening transform coder a canonical filter and a coloring transform decoder the outputs of the whitening transform coder are called canonical coordinates these are the coordinates that are reduced in rank and quantized in our finite precision version of the gauss markov theorem canonical correlations are in fact cosines of the canonical angles between a source vector and a measurement vector they produce new formulas for error covariance spectral flatness and entropy

low rank adaptive filters we introduce a class of adaptive filters based on sequential adaptive eigendecomposition subspace tracking of the data covariance matrix these new algorithms are completely rank revealing and hence they can perfectly handle the following two relevant data cases where conventional recursive least squares rls methods fail to provide satisfactory results 1 highly oversampled smooth data with rank deficient of almost rank deficient covariance matrix and 2 noise corrupted data where a signal must be separated effectively from superimposed noise this paper contradicts the widely held belief that rank revealing algorithms must be computationally more demanding than conventional recursive least squares a spatial rls adaptive filter has a complexity of o n sup 2 operations per time step where n is the filter order the corresponding low rank adaptive filter requires only o nr operations per time step where r spl les n denotes the rank of the data covariance matrix thus low rank adaptive filters can be computationally less or even much less demanding depending on the order rank ratio n r or the compressibility of the signal simulation results substantiate our claims this paper is devoted to the theory and application of fast orthogonal iteration and bi iteration subspace tracking algorithms

adaptive reduced rank processing based on joint and iterative interpolation decimation and filtering we present an adaptive reduced rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems the proposed method is based on the concept of joint and iterative interpolation decimation and filtering we describe an iterative least squares ls procedure to jointly optimize the interpolation decimation and filtering tasks for reduced rank adaptive filtering in order to design the decimation unit we present the optimal decimation scheme and also propose low complexity decimation structures we then develop low complexity least mean squares lms and recursive least squares rls algorithms for the proposed scheme along with automatic rank and branch adaptation techniques an analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed we consider the application of the proposed algorithms to interference suppression in code division multiple access cdma systems simulations results show that the proposed algorithms outperform the best known reduced rank schemes with lower complexity

blind adaptive constrained constant modulus reduced rank interference suppression algorithms based on interpolation and switched decimation this work proposes a blind adaptive reduced rank scheme and constrained constant modulus ccm adaptive algorithms for interference suppression in wireless communications systems the proposed scheme and algorithms are based on a two stage processing framework that consists of a transformation matrix that performs dimensionality reduction followed by a reduced rank estimator the complex structure of the transformation matrix of existing methods motivates the development of a blind adaptive reduced rank constrained barc scheme along with a low complexity reduced rank decomposition the proposed barc scheme and a reduced rank decomposition based on the concept of joint interpolation switched decimation and reduced rank estimation subject to a set of constraints are then detailed the proposed set of constraints ensures that the multipath components of the channel are combined prior to dimensionality reduction we develop low complexity joint interpolation and decimation techniques stochastic gradient and recursive least squares reduced rank estimation algorithms a model order selection algorithm for adjusting the length of the estimators is devised along with techniques for determining the required number of switching branches to attain a predefined performance an analysis of the convergence properties and issues of the proposed optimization and algorithms is carried out and the key features of the optimization problem are discussed we consider the application of the proposed algorithms to interference suppression in ds cdma systems the results show that the proposed algorithms outperform the best known reduced rank schemes while requiring lower complexity

adaptive reduced rank interference suppression based on the multistage wiener filter a class of adaptive reduced rank interference suppression algorithms is presented based on the multistage wiener filter mswf the performance is examined in the context of direct sequence ds code division multiple access cdma unlike the principal components method for reduced rank filtering the algorithms presented can achieve near full rank performance with a filter rank much less than the dimension of the signal subspace we present batch and recursive algorithms for estimating the filter parameters which do not require an eigen decomposition the algorithm performance in a heavily loaded ds cdma system is characterized via computer simulation the results show that the reduced rank algorithms require significantly fewer training samples than other reduced and full rank algorithms

markov shift in non commutative probability abstract we consider a class of quantum dissipative semigroup on a von neumann algebra which admits a normal invariant state we investigate asymptotic behavior of the dissipative dynamics and their relation to that of the canonical markov shift in case the normal invariant state is also faithful we also extend the notion of quantum detailed balance introduced by frigerio gorini and prove that forward weak markov process and backward weak markov process are equivalent by an anti unitary operator

structured low rank approximation this paper concerns the construction of a structured low rank matrix that is nearest to a given matrix the notion of structured low rank approximation arises in various applications ranging from signal enhancement to protein folding to computer algebra where the empirical data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected in the original system the task to retrieve useful information while maintaining the underlying physical feasibility often necessitates the search for a good structured lower rank approximation of the data matrix this paper addresses some of the theoretical and numerical issues involved in the problem two procedures for constructing the nearest structured low rank matrix are proposed the procedures are flexible enough that they can be applied to any lower rank any linear structure and any matrix norm in the measurement of nearness the techniques can also be easily implemented by utilizing available optimization packages the special case of symmetric toeplitz structure using the frobenius matrix norm is used to exemplify the ideas throughout the discussion the concept rather than the implementation details is the main emphasis of the paper

robust adaptive beamforming based on low rank and cross correlation techniques this paper presents cost effective low rank techniques for designing robust adaptive beamforming rab algorithms the proposed algorithms are based on the exploitation of the cross correlation between the array observation data and the output of the beamformer first we construct a general linear equation considered in large dimensions whose solution yields the steering vector mismatch then we employ the idea of the full orthogonalization method fom an orthogonal krylov subspace based method to iteratively estimate the steering vector mismatch in a reduced dimensional subspace resulting in the proposed orthogonal krylov subspace projection mismatch estimation okspme method we also devise adaptive algorithms based on stochastic gradient sg and conjugate gradient cg techniques to update the beamforming weights with low complexity and avoid any costly matrix inversion the main advantages of the proposed low rank and mismatch estimation techniques are their cost effectiveness when dealing with high dimension subspaces or large sensor arrays simulations results show excellent performance in terms of the output signal to interference plus noise ratio sinr of the beamformer among all the compared rab methods

estimation of the number of signals in the presence of unknown correlated sensor noise a method for estimating the number of transmitted signals in the presence of spatially correlated sensor noise is proposed the procedure is developed under the assumption that the unknown noise covariance matrix is a band matrix in practice it is quite robust with respect to this finite correlation length assumption in sensor array processing this amounts to assuming that the noise field is locally correlated spatially since spatial stationarity of the noise is not necessary it also applies for instance to white noise with different power along the array simulations indicate that the asymptotic analysis holds for quite small sample sizes

multirate filter banks and transform coding gain an analytical derivation of quantization error in filter banks using additive and signal dependent noise models is presented the coding gain over pcm is derived for both noise models interesting properties of coding gain in optimized filter banks with an ar 1 input signal model asymptotic performance of multirate systems and the analytical constraints required to achieve such performance are discussed connections to the recent developments of optimal subband systems are presented

universal preparability of states and asymptotic completeness we introduce a notion of universal preparability for a state of a system more precisely for a normal state on a von neumann algebra it describes a situation where from an arbitrary initial state it is possible to prepare a target state with arbitrary precision by a repeated interaction with a sequence of copies of another system for mathcal b mathcal h we give criteria sufficient to ensure that all normal states are universally preparable which can be verified for a class of non commutative birth and death processes realized in particular by the interaction of a micromaser with a stream of atoms as a tool the theory of tight sequences of states and of stationary states is further developed and we show that in the presence of stationary faithful normal states universal preparability of all normal states is equivalent to asymptotic completeness a notion studied earlier in connection with the scattering theory of non commutative markov processes

estimation of structured covariance matrices and multiple window spectrum analysis a close relationship between low rank modeling and multiple window spectrum estimation is demonstrated by using maximum likelihood estimates of structured covariance matrices the power in a narrow spectral band is estimated by estimating the variances in a low rank signal plus noise covariance model this model is swept through the entire frequency band to obtain an estimate of power as a function of frequency the resulting spectrum estimates are given by weighted combinations of eigenspectra each eigenspectrum results from projecting the data onto an orthogonal component of the signal subspace and squaring the multiple window spectrum estimates of thomson 1982 correspond to a particular choice for the low rank signal model the low rank modeling and structured covariance matrix framework is also used to derive the maximum likelihood estimate for the center frequency of a signal in noise this estimate is also obtained from a weighted combination of eigenspectra

robust reduced rank adaptive algorithm based on parallel subgradient projection and krylov subspace in this paper we propose a novel reduced rank adaptive filtering algorithm exploiting the krylov subspace associated with estimates of certain statistics of input and output signals we point out that when the estimated statistics are erroneous e g due to sudden changes of environments the existing krylov subspace based reduced rank methods compute the point that minimizes a ldquowrongrdquo mean square error mse in the subspace the proposed algorithm exploits the set theoretic adaptive filtering framework for tracking efficiently the optimal point in the sense of minimizing the ldquotruerdquo mse in the subspace therefore compared with the existing methods the proposed algorithm is more suited to adaptive filtering applications a convergence analysis of the algorithm is performed by extending the adaptive projected subgradient method apsm numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for system identification problems

new methods and structures in the theory of the multi mode dicke laser model we base a treatment of the dissipative multi mode version of dicke laser model on the theory of completely positive dynamical semigroups and quantum markov processes this leads to new results at both the mathematical and physical levels on the physical side it provides a generalization of the hepp lieb model that admits both chaotic and polychromatic laser radiation on the mathematical side it extends the theory of dynamical semigroups to a regime where the generators are perturbed by unbounded derivations

blind adaptive constrained reduced rank parameter estimation based on constant modulus design for cdma interference suppression this paper proposes a multistage decomposition for blind adaptive parameter estimation in the krylov subspace with the code constrained constant modulus ccm design criterion based on constrained optimization of the constant modulus cost function and utilizing the lanczos algorithm and arnoldi like iterations a multistage decomposition is developed for blind parameter estimation a family of computationally efficient blind adaptive reduced rank stochastic gradient sg and recursive least squares rls type algorithms along with an automatic rank selection procedure are also devised and evaluated against existing methods an analysis of the convergence properties of the method is carried out and convergence conditions for the reduced rank adaptive algorithms are established simulation results consider the application of the proposed techniques to the suppression of multiaccess and intersymbol interference in ds cdma systems

minimum energy band limited predictor with dynamic subspace selection for time variant flat fading channels in this paper we develop and analyze the basic methodology for minimum energy me band limited prediction of sampled time variant flat fading channels this predictor is based on a subspace spanned by time concentrated and band limited sequences the time concentration of these sequences is matched to the length of the observation interval and the band limitation is determined by the support of the doppler power spectral density of the fading process slepian showed that discrete prolate spheroidal dps sequences can be used to calculate the me band limited continuation of a finite sequence we utilize this property to perform channel prediction we generalize the concept of time concentrated and band limited sequences to a band limiting region consisting of disjoint intervals for a fading process with constant spectrum over its possibly discontiguous support we prove that the me band limited predictor is identical to a reduced rank maximum likelihood predictor which is a close approximation of a wiener predictor in current cellular communication systems the time selective fading process is highly oversampled the essential dimension of the subspace spanned by time concentrated and band limited sequences is in the order of two to five only the prediction error mainly depends on the support of the doppler spectrum we exploit this fact to propose low complexity time variant flat fading channel predictors using dynamically selected predefined subspaces the subspace selection is based on a probabilistic bound on the reconstruction error we compare the performance of the me band limited predictor with a predictor based on complex exponentials for a prediction horizon of one eights of a wavelength the numerical simulation results show that the me band limited predictor with dynamic subspace selection performs better than or similar to a predictor based on complex exponentials with perfectly known frequencies for a prediction horizons of three eights of a wavelength the performance of the me band limited predictor approaches that of a wiener predictor with perfectly known doppler bandwidth

derivation of numerical methods using computer algebra the use of computer algebra systems in a course on scientific computation is demonstrated various examples such as the derivation of newton s iteration formula the secant method newton cotes and gaussian integration formulas as well as runge kutta formulas are presented for the derivations the computer algebra system maple is used

bandlimited extrapolation using time bandwidth dimension the problem of extrapolating discrete index bandlimited signals from a finite number of samples is addressed in this paper the algorithm presented in this paper exploits the fact that the set of bandlimited signals that are also essentially time limited is approximated well by a low dimensional linear subspace this fact which is well known for one dimensional 1 d signals with contiguous passbands and time concentration intervals is established for a more general class of multidimensional m d signals with discontiguous passbands and discontiguous time concentration regions a criterion is presented for determining the dimension of the approximating subspace and the minimax optimal subspace itself based on knowledge of the passband time concentration regions energy concentration factor and bounds on the tolerable extrapolation error the extrapolation is constrained to lie in this subspace and parameters characterizing the extrapolation are obtained from the data by solving a linear system of equations for certain sampling patterns the system is ill conditioned and a second rank reduction is needed to reduce the deleterious effects of observation noise and modeling error a novel criterion for rank selection based on known bounds on noise power and modeling error is presented the effectiveness of the new algorithm and the rank selection criterion are demonstrated by means of computer simulations

fir filter representations of reduced rank noise reduction we show that the reduced rank output signal computed via truncated q svd is identical to that from an array of parallelly connected analysis synthesis finite impulse response fir filter pairs the filter coefficients are determined by the q svd and the filters provide an explicit description of the reduced rank noise reduction algorithm in the frequency domain

stochastic mv pure estimator robust reduced rank estimator for stochastic linear model this paper proposes a novel linear estimator named stochastic mv pure estimator developed for the stochastic linear model and designed to provide improved performance over the linear minimum mean square error mmse wiener estimator in cases prevailing in practical real world settings where at least some of the second order statistics of the random vectors under consideration are only imperfectly known the proposed estimator shares its main mathematical idea and terminology with the recently introduced minimum variance pseudo unbiased reduced rank estimator mv pure developed for the linear regression model the proposed stochastic mv pure estimator minimizes the mean square error mse of its estimates subject to rank constraint and inducing minimum distortion to the target random vector therefore the stochastic mv pure combines the techniques of the reduced rank wiener filter named in this paper rr mmse and the distortionless constrained estimator named in this paper c mmse in order to achieve greater robustness against noise or model errors than rr mmse and c mmse furthermore to ensure that the stochastic mv pure estimator combines the reduced rank and minimum distortion approaches in the mse optimal way we propose a rank selection criterion which minimizes the mse of the estimates obtained by the stochastic mv pure as a numerical example we employ the stochastic mv pure rr mmse c mmse and mmse estimators as linear receivers in a mimo wireless communication system this example is chosen as a typical signal processing scenario where the statistical information on the data on which the estimates are built is only imperfectly known we verify that the stochastic mv pure achieves the lowest mse and symbol error rate ser in such settings by employing the proposed rank selection criterion

low rank estimation of higher order statistics low rank estimators for higher order statistics are considered in this paper the bias variance tradeoff is analyzed for low rank estimators of higher order statistics using a tensor product formulation for the moments and cumulants in general the low rank estimators have a larger bias and smaller variance than the corresponding full rank estimator and the mean squared error can be significantly smaller this makes the low rank estimators extremely useful for signal processing algorithms based on sample estimates of the higher order statistics the low rank estimators also offer considerable reductions in the computational complexity of such algorithms the design of subspaces to optimize the tradeoffs between bias variance and computation is discussed and a noisy input noisy output system identification problem is used to illustrate the results

subharmonic projections for a quantum markov semigroup this article introduces a concept of subharmonic projections for a quantum markov semigroup in view of characterizing the support projection of a stationary state in terms of the semigroup generator these results together with those of our previous article j math phys 42 1296 2001 lead to a method for proving the existence of faithful stationary states this is often crucial in the analysis of ergodic properties of quantum markov semigroups the method is illustrated by applications to physical models

source number estimators using transformed gerschgorin radii we introduce effective uses of gerschgorin radii of the unitary transformed covariance matrix for source number estimation there are two approaches likelihood and heuristic used for developing the detection criteria the likelihood approach combines the gerschgorin radii to the well known source number detectors and improves their detection performances for gaussian and white noise processes it is verified that the gerschgorin likelihood estimators gle are consistent the gerschgorin aic yields a consistent estimate and the gerschgorin mdl criterion does not tend to underestimate for small or moderate data samples the heuristic approach applying the gerschgorin disk estimator gde developed from the projection concept overcomes the problem in cases of small data samples an unknown noise model and data dependency furthermore the detection performances of both approaches through the suggested rotations and averaging can be further improved finally the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data

on the existence of stationary states for quantum dynamical semigroups we provide two criteria on the existence of stationary states for quantum dynamical semigroups the first one is based on the semigroup itself while the second criterion is based on the generator which is in general unbounded and interpreted as a sesquilinear form these results are illustrated by physical examples drawn from quantum optics

embedded explicit runge kutta type methods for directly solving special third order differential equations y f x y abstract in this paper three pairs of embedded runge kutta type methods for directly solving special third order ordinary differential equations odes of the form y f x y denoted as rkd methods are presented the first is the rkd4 3 pair which is third order embedded in fourth order method has the property first same as last fsal whereby the last row of the coefficient matrix is equal to the vector output the second method is the rkd5 4 pair followed by the rkd6 5 pair the methods are derived with the strategies such that the higher order methods are very accurate and the lower order methods will give the best error estimates variables stepsize codes are developed based on the methods and used to solve a set of special third order problems numerical results are compared with the existing embedded runge kutta pairs which require the problems to be reduced into a system of first order odes numerical results have clearly shown the advantage and the efficiency of the new rkd pairs

rank reduction and james stein estimation this correspondence addresses the problem of estimating the signal in a signal plus gaussian noise model when it is known that the signal lies in a given subspace an alternative to rank reduction is presented the new estimator has the remarkable property of having a smaller mean square error than that of the maximum likelihood also least squares estimator for all parameter values