an evd algorithm for para hermitian polynomial matrices an algorithm for computing the eigenvalue decomposition of a para hermitian polynomial matrix is described this amounts to diagonalizing the polynomial matrix by means of a paraunitary similarity transformation the algorithm makes use of elementary paraunitary transformations and constitutes a generalization of the classical jacobi algorithm for conventional hermitian matrix diagonalization a proof of convergence is presented the application to signal processing is highlighted in terms of strong decorrelation and multichannel data compaction some simulated results are presented to demonstrate the capability of the algorithm

the equation for time like extremal surfaces in minkowski space r2 n in this paper we investigate the equation for time like extremal surfaces in the minkowski space r2 n and show that this kind of equation enjoys many interesting properties nonstrict hyperbolicity constant multiplicity of eigenvalues boundedness of characteristic propagation speeds linear degeneracy of all characteristic fields richness etc without any smallness assumption of initial data we give the necessary and sufficient condition on the global existence of classical solutions of the cauchy problem based on this we prove some global existence theorems on classical solutions of the dirichlet problem and neumann problem for this kind of equation finally we present an explicit exact representation involving two independent arbitrary functions of general solution

block iterative surrogate projection methods for convex feasibility problems abstract a unified framework is presented for studying the convergence of projection methods for finding a common point of finitely many closed convex sets in r n every iteration approximates each set by a half space given either by an approximate projection of the current iterate or by an aggregate inequality derived from the convex inequalities describing this set the next iterate is found by projecting the current one on a surrogate half space formed by taking a convex combination of the half space inequalities convergence to a solution is established under weak conditions that allow various acceleration techniques and choices of aggregating weights the resulting methods are block iterative and hence lend themselves to parallel implementation we show that the idea of forming cut maps via surrogate inequalities encompasses many classical as well as recently proposed methods for set intersection problems and convex feasibility problems with nondifferentiable inequalities and linear equations and inequalities

theory and design of signal adapted fir paraunitary filter banks we study the design of signal adapted fir paraunitary filter banks using energy compaction as the adaptation criterion we present some important properties that globally optimal solutions to this optimization problem satisfy in particular we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi infinite programming sip problem the remaining filters are related to the first through a matrix eigenvector decomposition we discuss uniqueness and sensitivity issues the sip problem is solved using a discretization method and a standard simplex algorithm we also show how regularity constraints may be incorporated into the design problem to obtain globally optimal in the energy compaction sense filter banks with specified regularity we also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be dct based such constraints may also be incorporated into our optimization algorithm therefore we are able to obtain globally optimal filter banks subject to regularity and or computational complexity constraints numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters as well as the effects of the various constraints the conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for fir filter banks

on factorization of m channel paraunitary filterbanks we systematically investigate the factorization of causal finite impulse response fir paraunitary filterbanks with given filter length based on the singular value decomposition of the coefficient matrices of the polyphase representation a fundamental order one factorization form is first proposed for general paraunitary systems then we develop a new structure for the design and implementation of paraunitary system based on the decomposition of hermitian unitary matrices within this framework the linear phase filterbank and pairwise mirror image symmetry filterbank are revisited their structures are special cases of the proposed general structures compared with the existing structures more efficient ones that only use approximately half the number of free parameters are derived the proposed structures are complete and minimal although the factorization theory with or without constraints is discussed in the framework of m channel filterbanks the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems

on optimal analysis synthesis filters for coding gain maximization we consider the use of pre and postfilters in conjunction with m channel uniform band paraunitary orthonormal filter banks we show that given any orthonormal filter bank the pre and postfilters that maximize the coding gain are determined entirely by the power spectrum of the input process regardless of the details of the orthonormal filter blank which could be fir iir or even the ideal brickwall filter bank the optimized coding gain however depends on the prefilter as well as the sandwiched orthonormal filter bank the coding gain improvement due to pre and postfiltering is often significant as we demonstrate with numerical examples and comparisons the validity of our results depends strongly on the orthonormality property of the filter bank in between the pre and postfilters in the nonorthonormal case most of these results are not true as is demonstrated

parallel projected aggregation methods for solving the convex feasibility problem convergence conditions are established for new sequential and parallel projected aggregation methods pams that find a feasible point of a large system of convex inequalities and linear equations

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

optimum nonnegative integer bit allocation for wavelet based signal compression and coding in this paper first a new optimum nonnegative integer bit allocation oniba algorithm is proposed for transform coding with lower computational complexity compared to the existing algorithms the algorithm is extended for the cases in which the variances of some sources are zero then an oniba algorithm is developed for wavelet based subband coding finally the algorithm is modified for adaptive subband coding computer simulations demonstrate considerable superiority of the proposed subband coding algorithm over the existing ones

rational subspace estimation using adaptive lossless filters rational models have been studied as a tractable attempt to account for frequency dependencies using a finite parameter description in this context the following problem is addressed given time domain measurements estimate rational orthonormal spanning vectors for the signal and noise subspaces it is shown that the problem can be rephrased as adapting a lossless transfer matrix so as to maximize the power split between two sets of output bins an efficient and numerically robust adaptive filtering algorithm is derived for lossless multivariable lattice filters and the system can be programmed in real time using cordic processors the adaptive filter equations are consistent with the proper subspace identification if the subspace filter satisfies a sufficient order condition in under modeled scenarios the stable stationary points are characterized by a minimized rayleigh quotient which leads to good subspace fits the proposed adaptive filter makes real time rational subspace estimation an accessible alternative to computationally expensive offline techniques

integrable graded manifolds and nonlinear equations a method is proposed for the classification of integrable embeddings of 2 2 dimensional supermanifoldsv2 2 into an enveloping superspace supplied with the structure of a lie superalgebra the approach is first applied to the even part of the scheme i e for the embeddings of 2 dimensional manifoldsv2 into riemannian or non riemannian enveloping space the general consideration is also illustrated by the example of superspaces supplied with the structure of the series sl n n 1 whose integrable supermanifolds are described by supersymmetrical 2 dimensional toda lattice type equations in particular forn 1 they are described by the supersymmetrical liouville and sine gordon equations

on the optimality of ideal filters for pyramid and wavelet signal approximation the reconstructed lowpass component in a quadrature mirror filter qmf bank provides a coarser resolution approximation of the input signal since the outputs of the two qmf branches are orthogonal the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error this property is used as a common strategy for the optimization of qmf banks orthogonal wavelet transforms and least squares pyramids a general solution is derived for the qmf bank that provides the optimal decomposition of an arbitrary wide sense stationary process this approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate in particular it is shown that the sine wavelet transform is optimal for the representation at all scales of signals with non increasing spectral density

iterative greedy algorithm for solving the fir paraunitary approximation problem in this paper a method for approximating a multi input multi output mimo transfer function by a causal finite impulse response fir paraunitary pu system in a weighted least squares sense is presented using a complete parameterization of fir pu systems in terms of householder like building blocks an iterative algorithm is proposed that is greedy in the sense that the observed mean squared error at each iteration is guaranteed to not increase for certain design problems in which there is a phase type ambiguity in the desired response which is formally defined in the paper a phase feedback modification is proposed in which the phase of the fir approximant is fed back to the desired response with this modification in effect it is shown that the resulting iterative algorithm not only still remains greedy but also offers a better magnitude type fit to the desired response simulation results show the usefulness and versatility of the proposed algorithm with respect to the design of principal component filter bank pcfb like filter banks and the fir pu interpolation problem concerning the pcfb design problem it is shown that as the mcmillan degree of the fir pu approximant increases the resulting filter bank behaves more and more like the infinite order pcfb consistent with intuition in particular this pcfb like behavior is shown in terms of filter response shape multiresolution coding gain noise reduction with zeroth order wiener filtering in the subbands and power minimization for discrete multitone dmt type transmultiplexers

pohlmeyer reduction for superstrings in ads space the pohlmeyer reduced equations for strings moving only in the ads subspace of ads5 s5 have been used recently in the study of classical euclidean minimal surfaces for wilson loops and some semiclassical three point correlation functions we find an action that leads to these reduced superstring equations for example for a bosonic string in adsn such an action contains a liouville scalar part plus a k k gauged wzw model for the group k so n 2 coupled to another term depending on two additional fields transforming as vectors under k solving for the latter fields gives a non abelian toda model coupled to the liouville theory for n 5 we generalize this bosonic action to include the s5 contribution and fermionic terms the corresponding reduced model for the ads2 s2 truncation of the full ads5 s5 superstring turns out to be equivalent to super liouville theory our construction is based on taking a limit of the previously found reduced theory actions for bosonic strings in adsn s1 and superstrings in ads5 s5 this new action may be useful as a starting point for possible quantum generalizations or deformations of the classical pohlmeyer reduced theory we give examples of simple extrema of this reduced superstring action which represent strings moving in the ads5 part of the space expanding near these backgrounds we compute the corresponding fluctuation spectra and show that they match the spectra found in the original superstring theory

on non integrability of classical strings in p brane backgrounds we investigate the question of possible integrability of classical string motion in curved p brane backgrounds for example the d3 brane metric interpolates between the flat and the ads5 s5 regions in which string propagation is integrable we find that while the point like string geodesic equations are integrable the equations describing an extended string in the complete d3 brane geometry are not the same conclusion is reached for similar brane intersection backgrounds interpolating between flat space and adsk sk we consider in particular the case of the ns 5 brane fundamental string background to demonstrate non integrability we make a special pulsating string ansatz for which the string equations reduce to an effective one dimensional system expanding near this simple solution leads to a linear differential equation for small fluctuations that cannot be solved in quadratures implying non integrability of the original set of string equations

design of fir paraunitary filter banks for subband coding using a polynomial eigenvalue decomposition the problem of paraunitary pu filter bank design for subband coding has received considerable attention in recent years not least because of the energy preserving property of this class of filter banks in this paper we consider the design of signal adapted finite impulse response fir pu filter banks using polynomial matrix evd pevd techniques modifications are proposed to an iterative time domain pevd method known as the sequential best rotation sbr2 algorithm which enables its effective application to the problem of fir orthonormal filter bank design for efficient subband coding by choosing an optimization scheme that maximizes the coding gain at each stage of the algorithm it is shown that the resulting filter bank behaves more and more like the infinite order principle component filter bank pcfb the proposed method is compared to state of the art techniques namely the iterative greedy algorithm iga the approximate evd aevd standard sbr2 and a fast algorithm for fir compaction filter design called the window method wm we demonstrate that for the calculation of the subband coder the wm approach offers a low cost alternative at lower coding gains while at moderate to high complexity the proposed approach outperforms the benchmarkers in terms of run time complexity aevd performs well at low orders while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios

on the spectral factor ambiguity of fir energy compaction filter banks this paper focuses on the design of signal adapted finite impulse response fir paraunitary pu filter banks optimized for energy compaction ec the design of such filter banks has been shown in the literature to consist of the design of an optimal fir compaction filter followed by an appropriate karhunen loe spl grave ve transform klt despite this elegant construction ec optimal filter banks have been shown to perform worse than common nonadapted filter banks for coding gain contrary to intuition here it is shown that this phenomenon is most likely due to the nonuniqueness of the compaction filter in terms of its spectral factors this nonuniqueness results in a finite set of ec optimal filter banks by choosing the spectral factor yielding the largest coding gain it is shown that the resulting filter bank behaves more and more like the infinite order principal components filter bank pcfb in terms of numerous objectives such as coding gain multiresolution noise reduction with zeroth order wiener filters in the subbands and power minimization for discrete multitone dmt type nonredundant transmultiplexers

multidimensional paraunitary principal component filter banks in this correspondence the one dimensional 1 d principal component filter banks pcfb s derived by tsatsatsanis and giannakis 1995 are generalized to higher dimensions as presented by tsatsatsanis and giannakis pcfb s minimize the mean squared error mse when only q out of p subbands are retained previously two dimensional 2 d pcfb s were proposed by tirakis et al 1995 the work by tirakis et al was limited to 2 d signals and separable resampling operators the formulation presented here is general in that it can easily accommodate signals of arbitrary yet finite dimension and nonseparable sampling a major result presented in this paper is that in addition to minimizing mse when reconstructing from q out of p subbands the pcfb s result in maximizing theoretical coding gain tcg thereby performing optimally in a energy compaction sense

inconsistent signal feasibility problems least squares solutions in a product space presents parallel projection methods to find least squares solutions to inconsistent convex set theoretic signal synthesis problems the problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the cartesian product of the original sets a solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space the convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated

convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections solving a convex set theoretic image recovery problem amounts to finding a point in the intersection of closed and convex sets in a hilbert space the projection onto convex sets pocs algorithm in which an initial estimate is sequentially projected onto the individual sets according to a periodic schedule has been the most prevalent tool to solve such problems nonetheless pocs has several shortcomings it converges slowly it is ill suited for implementation on parallel processors and it requires the computation of exact projections at each iteration we propose a general parallel projection method emopsp that overcomes these shortcomings at each iteration of emopsp a convex combination of subgradient projections onto some of the sets is formed and the update is obtained via relaxation the relaxation parameter may vary over an iteration dependent extrapolated range that extends beyond the interval 0 2 used in conventional projection methods emopsp not only generalizes existing projection based schemes but it also converges very efficiently thanks to its extrapolated relaxations theoretical convergence results are presented as well as numerical simulations

estimation of time differences of arrival by pole decomposition time differences of arrival tdoa s of emitter wave fronts to a spatially distributed array of sensors can be used to determine the source location in this paper we suggest a new method of tdoa estimation for multiple unknown autoregressive moving average arma sources and additive noise that may be correlated between the sensors we derive a theoretical formula that only uses the receiver cross spectra and the source poles for the tdoa determination the poles are estimated by a least squares technique and two methods are suggested for the estimation of the cross spectra which allow tradeoffs between computational complexity and accuracy a new time delay model is derived and used to show the applicability of the methods for noninteger tdoa s results from simulations illustrate the performance of the algorithm by monte carlo trials and compare it to the cramer rao bound

corrections to on the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix presents corrections to the paper on the existence and uniqueness of the eigenvalue decomposition of a paraher mitian matrix weiss s et al ieee trans signal process vol 66 no 10 pp 2659 2672 may 2018

new optimal z complementary code sets based on generalized paraunitary matrices the concept of paraunitary pu matrices arose in the early 1990 s in the study of multi rate filter banks these matrices have found wide applications in cryptography digital signal processing and wireless communications existing pu matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice motivated by this for the first time we introduce a novel concept called z paraunitary zpu matrix whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value we show that there exists an equivalence between a zpu matrix and a z complementary code set when the latter is expressed as a matrix with polynomial entries furthermore we investigate some important properties of zpu matrices which are useful for the extension of matrix sizes and sequence lengths we propose a new construction framework for optimal zpu matrices which includes existing pu matrices as special cases finally we give the enumeration formula for the constructed z complementary sequences from the optimal zpu matrices

modeling analysis and optimum design of quantized m band filter banks this paper provides a rigorous modeling and analysis of quantization effects in m band subband codecs followed by optimal filter bank design and compensation the codec is represented by a polyphase decomposition of the analysis synthesis filter banks and an embedded nonlinear gain plus additive noise model for the pdf optimized scalar quantizers we construct an equivalent time invariant but nonlinear structure operating at the slow clock rate that allows us to compute the exact expression for the mean square quantization error in the reconstructed output this error is shown to consist of two components a distortion component and a dominant random noise component uncorrelated with the input signal we determine the optimal paraunitary and biorthogonal fir filter coefficients compensators and integer bit allocation to minimize this mse subject to the constraints of filter length average bit rate and perfect reconstruction pr in the absence of quantizers the biorthogonal filter bank results in a smaller mse but the filter coefficients are very sensitive to signal statistics and to average bit constraints by comparison the paraunitary structure is much more robust we also show that the null compensated design that eliminates the distortion component is more robust than the optimally compensated case that minimizes the total mse but only at nominal conditions both modeling and optimal design are validated by simulation in the two channel case

a state space approach to the design of globally optimal fir energy compaction filters we introduce a new approach for the least squared optimization of a weighted fir filter of arbitrary order n under the constraint that its magnitude squared response be nyquist m although the new formulation is general enough to cover a wide variety of applications the focus of the paper is on optimal energy compaction filters the optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks pcfbs the newly proposed method finds the optimum product filter f sub opt z h sub opt z h sub opt z sup 1 corresponding to the compaction filter h sub opt z by expressing f z in the form d z d z sup 1 we show that the compaction problem can be completely parameterized in terms of the state space realization of the causal function d z for a given input power spectrum the resulting filter f sub opt z is guaranteed to be a global optimum solution due to the convexity of the new formulation the new algorithm is universal in the sense that it works for any m arbitrary filter length n and any given input power spectrum furthermore additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem finally obtaining h sub opt z from f sub opt z does not require an additional spectral factorization step the minimum phase spectral factor h sub min z can be obtained automatically by relating the state space realization of d sub opt z to that of h sub opt z

broad band signal subspace spatial spectrum bass ale estimation an approach to spatial spectrum estimation of broadband sources is described the approach termed broadband signal subspace spatial spectrum bass ale estimation is based on the eigenstructure of a broadband spatial temporal covariance matrix and is justified by identifying the low rank character of spatial temporal observations of broadband sources bass ale estimators are described which incorporate source focusing spatial temporal noise decorrelating a signal or noise only subspace generated from the eigenstructure of the transformed spatial temporal covariance matrix and broadband source models through discussion and simulation bass ale estimators are compared to the coherent signal subspace processor a similar subspace method and relative advantages of the two are identified

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

the role of gtd in optimizing perfect reconstruction filter banks filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications in this paper we propose gtd generalized triangular decomposition filter banks as a subband coder for optimizing the theoretical coding gain we focus on perfect reconstruction orthonormal gtd filter banks and biorthogonal gtd filter banks we show that in both cases there are two fundamental properties in the optimal solutions namely total decorrelation and spectrum equalization the optimal solutions can be obtained by performing the frequency dependent gtd on the cholesky factor of the input power spectrum density matrices we also show that in both theory and numerical simulations the optimal gtd subband coders have superior performance than optimal traditional subband coders in addition the uniform bit loading scheme can with no loss of optimality be used in the optimal biorthogonal gtd coders which solves the granularity problem in the conventional optimum bit loading formula we then extend the use of gtd filter banks to wireless communication systems where linear precoding and zero forcing decision feedback equalization is used in frequency selective channels we consider the quality of service qos problem of minimizing the transmitted power subject to the bit error rate and total bit rate constraints optimal systems with orthonormal precoder and unconstrained precoder are both derived and shown to be related to the frequency dependent gtd of the channel frequency response

signal analysis using a multiresolution form of the singular value decomposition this paper proposes a multiresolution form of the singular value decomposition svd and shows how it may be used for signal analysis and approximation it is well known that the svd has optimal decorrelation and subrank approximation properties the multiresolution form of svd proposed here retains those properties and moreover has linear computational complexity by using the multiresolution svd the following important characteristics of a signal may he measured at each of several levels of resolution isotropy sphericity of principal components self similarity under scaling and resolution of mean squared error into meaningful components theoretical calculations are provided for simple statistical models to show what might be expected results are provided with real images to show the usefulness of the svd decomposition

application of benveniste s convergence results in the study of adaptive iir filtering algorithms it is shown that the weak convergence results of a benveniste et al ieee trans automat contr vol ac 25 p 1042 58 dec 1980 can be used to prove convergence of some adaptive infinite impulse response iir filtering algorithms the association of the algorithms with some ordinary differential equations for constant gains which parallels the theory of l ljung et al 1983 is suitable for constant gain adaptive filtering applications convergence proofs for a prefiltering algorithm for a simple constant gain version of the recursive maximum likelihood algorithm and for the well known simple hyperstable adaptive recursive filter sharf algorithm are given as examples

principal component filter banks for optimal multiresolution analysis an important issue in multiresolution analysis is that of optimal basis selection an optimal p band perfect reconstruction filter bank prfb is derived in this paper which minimizes the approximation error in the mean square sense between the original signal and its low resolution version the resulting prfb decomposes the input signal into uncorrelated low resolution principal components with decreasing variance optimality issues are further analyzed in the special case of stationary and cyclostationary processes by exploiting the connection between discrete time filter banks and continuous wavelets an optimal multiresolution decomposition of l sub 2 r is obtained analogous results are also derived for deterministic signals some illustrative examples and simulations are presented

an algorithm for calculating the qr and singular value decompositions of polynomial matrices in this paper a new algorithm for calculating the qr decomposition qrd of a polynomial matrix is introduced this algorithm amounts to transforming a polynomial matrix to upper triangular form by application of a series of paraunitary matrices such as elementary delay and rotation matrices it is shown that this algorithm can also be used to formulate the singular value decomposition svd of a polynomial matrix which essentially amounts to diagonalizing a polynomial matrix again by application of a series of paraunitary matrices example matrices are used to demonstrate both types of decomposition mathematical proofs of convergence of both decompositions are also outlined finally a possible application of such decompositions in multichannel signal processing is discussed

particle swarm algorithm for solving systems of nonlinear equations solving systems of nonlinear equations is one of the most difficult problems in all of numerical computation and in a diverse range of engineering applications newton s method for solving systems of nonlinear equations can be highly sensitive to the initial guess of the solution in this study a new particle swarm optimization algorithm is proposed to solve systems of nonlinear equations some standard systems are presented to demonstrate the efficiency of this method

results on principal component filter banks colored noise suppression and existence issues we have made explicit the precise connection between the optimization of orthonormal filter banks fbs and the principal component property the principal component filter bank pcfb is optimal whenever the minimization objective is a concave function of the subband variances of the fb this explains pcfb optimality for compression progressive transmission and various hitherto unnoticed white noise suppression applications such as subband wiener filtering the present work examines the nature of the fb optimization problems for such schemes when pcfbs do not exist using the geometry of the optimization search spaces we explain exactly why these problems are usually analytically intractable we show the relation between compaction filter design i e variance maximization and optimum fbs a sequential maximization of subband variances produces a pcfb if one exists but is otherwise suboptimal for several concave objectives we then study pcfb optimality for colored noise suppression unlike the case when the noise is white here the minimization objective is a function of both the signal and the noise subband variances we show that for the transform coder class if a common signal and noise pcfb klt exists it is optimal for a large class of concave objectives common pcfbs for general fb classes have a considerably more restricted optimality as we show using the class of unconstrained orthonormal fbs for this class we also show how to find an optimum fb when the signal and noise spectra are both piecewise constant with all discontinuities at rational multiples of spl pi

global weak and smooth solutions of the equation for timelike extremal surface in minkowski space abstract the time like extremal surface is an interesting model which may be viewed as simple but nontrivial examples of membrane in field theory in this paper we first consider the global weak solutions to the timelike extremal surface in minkowski space r 1 1 n furthermore we can get global smooth solutions to the timelike extremal hypersurface for initial data sufficiently close to the arbitrary time like plane a 0 t a 1 x 1 a n x n b 0 in minkowski space r 1 n 1 but not in the initial plane t 0

generalized triangular decomposition in transform coding a general family of optimal transform coders tcs is introduced here based on the generalized triangular decomposition gtd developed by jiang this family includes the karhunen loeve transform klt and the generalized version of the prediction based lower triangular transform plt introduced by phoong and lin as special cases the coding gain of the entire family with optimal bit allocation is equal to that of the klt and the plt even though the original plt introduced by phoong is not applicable for vectors that are not blocked versions of scalar wide sense stationary processes the gtd based family includes members that are natural extensions of the plt and therefore also enjoy the so called minlab structure of the plt which has the unit noise gain property other special cases of the gtd tc are the geometric mean decomposition gmd and the bidiagonal decomposition bid transform coders the gmd tc in particular has the property that the optimum bit allocation is a uniform allocation this is because all its transform domain coefficients have the same variance implying thereby that the dynamic ranges of the coefficients to be quantized are identical

bezout space time precoders and equalizers for mimo channels the transmitter receiver diversities in p input q output multiple input multiple output mimo channels will play a key role in future high rate wireless communication the major challenge in mimo signal recovery is the mitigation of the inevitable intersymbol interference isi and interchannel interference ici in multipath mimo channels the bezout system theory provides a simple solution for isi ici cancellation and thus can serve as a powerful mathematical foundation for mimo systems if p q and the mimo system h d is left coprime the system is perfectly recoverable via a bezout precoder assuming the channel information is available at the transmitter for a robust channel design a quantitative analysis of signal to noise ratio snr of the optimal bezout equalizer precoder can be derived from the bezout null space compared with the alamouti see ieee j select areas commun vol 16 p 1451 58 oct 1998 space time coding the bezout precoder is shown to be more appealing in slowly time varying channels where the feedback of the channel information induces minor overhead the bezout system can work well jointly with the space time block coding stbc the stbc can be adopted to artificially construct a larger q spl times p q p virtual transfer function without the channel information a necessary and sufficient condition is provided for perfect recoverability pr for the stbc induced virtual mimo systems based on the virtual transfer function both channel independent and channel dependent precoding strategies are feasible via a singular value decomposition svd analysis the bezout precoder can be shown to outperform the orthogonal frequency division multiplexing ofdm precoder in bit error rate ber transmission rate and receiver implementation the interplay of the two design parameters n and spl rho is analyzed to provide a simple guideline for an optimal configuration the combined stbc and bezout equalization techniques offer a broader spectrum of transceiver system configuration to achieve optimal design tradeoff among ber transmission rate and implementation complexity

general solutions of nonlinear equations in the geometric theory of the relativistic string general solutions for the system of nonlinear equations in the second order partial derivatives with two independent variables are obtained they determine the basic differential forms of the two dimensional minimal surface embedded inton dimensional pseudo euclidean space

minimum mean squared error reconstruction for generalized undersampling of cyclostationary processes the generalized sampling problem is considered using a filter bank model with a stochastic process framework a signal reconstruction solution minimizing the time averaged mean squared error is found using a filter bank optimization technique for cyclostationary signals the use of a stochastic model approach to find a minimized error solution rather than a perfect reconstruction solution allows consideration of sampling problems that deterministic approaches cannot solve for instance a particular sampling density is not required allowing reconstruction optimization in cases of undersampling an extension is also presented for optimal reconstruction in the presence of additive noise and interference the result is a generalized sampling model which can be used for an extensive variety of scenarios combining aspects of undersampling multiple input multiple output mimo sampling and periodic nonuniform sampling

minlab minimum noise structure for ladder based biorthogonal filter banks we introduce a minimum noise structure for ladder based biorthogonal minlab filter bank the minimum noise structure ensures that the quantization error has a unity noise gain even though the filter bank is biorthogonal the coder has a very low design and implementation cost the perfect reconstruction property is structurally preserved optimal bit allocation and coding gain formulas are derived we show that the coding gain of the optimal minlab coder is always greater than or equal to unity for both ar 1 process and ma 1 process the minlab coder with two taps has a higher coding gain than the optimal orthonormal coder with an infinite number of taps in addition to its superior decorrelation ability it has many other desired features that make it a potentially valuable and attractive alternative to the orthonormal coder especially for a high fidelity compression

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

signal adapted multiresolution transform for image coding the authors consider the problem of designing multiresolution transforms that are adapted to the given image signal in the sense that they maximize the coding gain at each resolution level a simple alternating optimization algorithm is derived for solving this problem in the framework of the lattice realization of para unitary quadrature mirror filters the resulting large coding scheme is discussed in some detail and its performance is compared with that of the discrete cosine transform jpeg technique and with that of some nonadapted multiresolution transforms

chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations abstract this study proposes a novel chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations different chaotic maps are introduced to enhance the effectiveness and robustness of the algorithm several benchmark studies are carried out logistic map gives the best results and is utilized in solving nonlinear equation sets nine well known problems are solved with our algorithm and results are compared with quantum behaved particle swarm optimization intelligent tuned harmony search gravitational search algorithm and literature studies comparison results reveal that the proposed algorithm can cope with the highly non linear problems and outperforms many algorithms which exist in the literature

a new flexible bi orthogonal filter design for multiresolution filterbanks with application to image compression we propose a new fast method with great potential for multiresolution pyramid decomposition of signals and images the method allows unusual flexibility in choosing a filter for any task involving the multiresolution analysis and synthesis using our method one can choose any low pass filter for the multiresolution filtering this method enabled us to choose the best filters for set partitioning in hierarchical trees spiht image compression for the corresponding support sizes the compression results for our seven tap filters are better than those of the 9 7 wavelet filters and approximately the same as those of the 10 18 filters while at the same time our seven tap filters are faster than 10 18 filters

wronskians geometry and some general solutions to the nonlinear liouville like pde s the formal properties of n dimensional wronskians and their geometric interpretation enable one to construct explicit analytic solutions to some nonlinear partial differential equations pde s that generalize the liouville equation xy e2 the studied pde s are a lmf const b lmf g lmg f and c lm lmf const where lm is the nonlinear differential operation lmf det kx lyf with k l 0 1 m some nontrivial formal properties of the composition of the lm s are established

efficient design of orthonormal wavelet bases for signal representation the efficient representation of a signal as a linear combination of elementary atoms or building blocks is central to much signal processing theory and many applications wavelets provide a powerful flexible and efficiently implementable class of such atoms in this paper we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized since the squared error is not an explicit function of the design parameters some form of approximation of this objective is required if conventional optimization techniques are to be used previous approximations have resulted in nonconvex optimization problems which require delicate management of local minima in this paper we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved constraints on the smoothness of the wavelet can be efficiently incorporated into the design we show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows in our examples we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods

superposition formulas for exterior differential systems abstract in this article we solve an inverse problem in the theory of quotients for differential equations we characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original the fact that a system can be written as a quotient can be used to find the general solution to these equations some examples are given to demonstrate the theory

on the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix this paper addresses the extension of the factorization of a hermitian matrix by an eigenvalue decomposition evd to the case of a parahermitian matrix that is analytic at least on an annulus containing the unit circle such parahermitian matrices contain polynomials or rational functions in the complex variable z and arise e g as cross spectral density matrices in broadband array problems specifically conditions for the existence and uniqueness of eigenvalues and eigenvectors of a parahermitian matrix evd are given such that these can be represented by a power or laurent series that is absolutely convergent at least on the unit circle permitting a direct realization in the time domain based on an analysis of the unit circle we prove that eigenvalues exist as unique and convergent but likely infinite length laurent series the eigenvectors can have an arbitrary phase response and are shown to exist as convergent laurent series if eigenvalues are selected as analytic functions on the unit circle and if the phase response is selected such that the eigenvectors are holder continuous with alpha frac 1 2 on the unit circle in the case of a discontinuous phase response or if spectral majorisation is enforced for intersecting eigenvalues an absolutely convergent laurent series solution for the eigenvectors of a parahermitian evd does not exist we provide some examples comment on the approximation of a parahermitian matrix evd by laurent polynomial factors and compare our findings to the solutions provided by polynomial matrix evd algorithms

light likeness of boundaries of extremal surfaces of mixed type in physical space times abstract in this paper we prove the light likeness of boundaries of smooth extremal surfaces of mixed type in general physical space time r 1 n n 1 in particular we improve gu s theorem on the light likeness of boundaries of extremal surfaces in r 1 2 and prove the light likeness of boundaries of smooth extremal surfaces of mixed type in general physical space times as a consequence we show that a curve moving in a physical space time keeps its like property and the boundary only exists when its world sheet at the initial time has light like points this implies that any extremal surface of mixed type is generated by an initial curve of mixed type

theory of optimal orthonormal subband coders the theory of the orthogonal transform coder and methods for its optimal design have been known for a long time we derive a set of necessary and sufficient conditions for the coding gain optimality of an orthonormal subband coder for given input statistics we also show how these conditions can be satisfied by the construction of a sequence of optimal compaction filters one at a time several theoretical properties of optimal compaction filters and optimal subband coders are then derived especially pertaining to behavior as the number of subbands increases significant theoretical differences between optimum subband coders transform coders and predictive coders are summarized finally conditions are presented under which optimal orthonormal subband coders yield as much coding gain as biorthogonal ones for a fixed number of subbands

filterbank optimization with convex objectives and the optimality of principal component forms this paper proposes a general framework for the optimization of orthonormal filterbanks fbs for given input statistics this includes as special cases many previous results on fb optimization for compression it also solves problems that have not been considered thus far fb optimization for coding gain maximization for compression applications has been well studied before the optimum fb has been known to satisfy the principal component property i e it minimizes the mean square error caused by reconstruction after dropping the p weakest lowest variance subbands for any p we point out a much stronger connection between this property and the optimality of the fb the main result is that a principal component fb pcfb is optimum whenever the minimization objective is a concave function of the subband variances produced by the fb this result has its grounding in majorization and convex function theory and in particular explains the optimality of pcfbs for compression we use the result to show various other optimality properties of pcfbs especially for noise suppression applications suppose the fb input is a signal corrupted by additive white noise the desired output is the pure signal and the subbands of the fb are processed to minimize the output noise if each subband processor is a zeroth order wiener filter for its input we can show that the expected mean square value of the output noise is a concave function of the subband signal variances hence a pcfb is optimum in the sense of minimizing this mean square error the above mentioned concavity of the error and hence pcfb optimality continues to hold even with certain other subband processors such as subband hard thresholds and constant multipliers although these are not of serious practical interest we prove that certain extensions of this pcfb optimality result to cases where the input noise is colored and the fb optimization is over a larger class that includes biorthogonal fbs we also show that pcfbs do not exist for the classes of dft and cosine modulated fbs

relativistic string model in a space time of a constant curvature the relativistic string model is investigated in a space time of a constant curvature de sitter universe the fundamental differential quadratic forms of the world surface of the string are considered as the dynamical variables the coefficients of these forms obey two nonlinear equations varphi 11 varphi 22 e varphi cos theta ke varphi theta 11 theta 22 e varphi sin theta the lax representation for this system is obtained

fast image recovery using dynamic load balancing in parallel architectures by means of incomplete projections this paper formulates an incomplete projection algorithm that is applied to the image recovery problem the algorithm allows an easy implementation of dynamic load balancing for parallel architectures furthermore the local computation communication load ratio can be adjusted since each processor performs a finite number of iterations of any projection type technique and this number can be provided as a parameter of the algorithm numerical results compare favorably with those obtained by the extrapolated method of parallel subgradient projections

prediction based lower triangular transform a new nonunitary transform called the prediction based lower triangular transform plt is introduced for signal compression the new transform has the same decorrelation property as the kahurnen loeve transform klt but its implementational cost is less than one half of klt compared with the klt the design cost of an m spl times m plt is much lower and is only of the order of o m sup 2 moreover the plt can be factorized into simple building blocks using two different factorizations we introduce two minimum noise structures that have roughly the same complexity as the direct implementation of plt these minimum noise structures have the following properties 1 its noise gain is unity even though the transform is nonunitary 2 perfect reconstruction is structurally guaranteed 3 it can be used for both lossy lossless compression we show that the coding gain of plt implemented using the minimum noise structure is the same as that of klt furthermore universal transform coders using plt are derived for ar 1 process the m spl times m plt has a closed form and needs only m 1 multiplications and additions

rate distortion optimal subband coding without perfect reconstruction constraints we investigate the design of subband coders without the traditional perfect reconstruction constraint on the filters the coder uses scalar quantizers and its filters and bit allocation are designed to optimize a rate distortion criterion using convexity analysis we show that optimality can be achieved using filterbanks that are the cascade of a paraunitary principal component filterbank for the input spectral process and a set of pre and postfilters surrounding each quantizer analytical expressions for the pre and postfilters are then derived an algorithm for computing the globally optimal filters and bit allocation is given we also develop closed form solutions for the special case of two channel coders under an exponential rate distortion model finally we investigate a constrained length version of the filter design problem which is applicable to practical coding scenarios while the optimal filterbanks are nearly perfect reconstruction at high rates we demonstrate an apparently surprising advantage of optimal fir filterbanks they significantly outperform optimal perfect reconstruction fir filterbanks at all bit rates

sequential matrix diagonalization algorithms for polynomial evd of parahermitian matrices for parahermitian polynomial matrices which can be used for example to characterize space time covariance in broadband array processing the conventional eigenvalue decomposition evd can be generalized to a polynomial matrix evd pevd in this paper a new iterative pevd algorithm based on sequential matrix diagonalization smd is introduced at every step the smd algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation a proof of convergence is provided and it is demonstrated that smd establishes diagonalization faster and with lower order operations than existing pevd algorithms

image restoration by the method of convex projections part 2 applications and numerical results the image restoration theory discussed in a previous paper by youla and webb 1 is applied to a simulated image and the results compared with the well known method known as the gerchberg papoulis algorithm the results show that the method of image restoration by projection onto convex sets by providing a convenient technique for utilizing a priori information performs significantly better than the gerchberg papoulis method

initial boundary value problem for the equation of timelike extremal surfaces in minkowski space this paper investigate the mixed initial boundary value problem for the equation of timelike extremal surfaces in minkowski space r1 1 n in the first quadrant under the assumptions that the initial data are bounded and the boundary data are small we prove the global existence and uniqueness of the c2 solutions of the initial boundary value problem for this kind of equation based on the existence results on global classical solutions we also show that as t tends to infinity the first order derivatives of the solutions approach c1 traveling wave under the appropriate conditions on the initial and boundary data geometrically this means the extremal surface approaches a generalized cylinder which is an exact solution

perfect discrete multitone modulation with optimal transceivers previously discrete fourier transform dft based discrete multitone modulation dmt systems have been widely applied to various applications in this paper we study a broader class of dmt systems using more general unitary matrices instead of dft matrices for this class we show how to design optimal dmt systems over frequency selective channels with colored noise in addition asymptotical performance of dft based and optimal dmt systems are studied and shown to be equivalent however for a moderate number of bands the optimal dmt system offers significant gain over the dft based dmt system as is demonstrated by examples

algebraic theory of optimal filterbanks we introduce an optimality theory for finite impulse response fir filterbanks using a general algebraic point of view we consider an admissible set spl lscr of fir filterbanks and use scalability as the main notion based on which performance of the elements in spl lscr are compared we show that quantification of scalability leads naturally to a partial ordering on the set spl lscr an optimal solution is therefore represented by the greatest element in spl lscr it turns out that a greatest element does not necessarily exist in spl lscr hence one has to settle with one of the maximal elements that exist in spl lscr we provide a systematic way of finding a maximal element by embedding the partial ordering at hand in a total ordering this is done by using a special class of order preserving functions known as schur convex there is however a price to pay for achieving a total ordering there are infinitely many possible choices for schur convex functions and the optimal solution specified in spl lscr depends on this subjective choice an interesting aspect of the presented algebraic theory is that the connection between several concepts namely principal component filterbanks pcfbs filterbanks with maximum coding gain and filterbanks with good scalability is clearly revealed we show that these are simply associated with different extremal elements of the partial ordering induced on spl lscr by scalability

the qrd and svd of matrices over a real algebra abstract recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool in this article we show how to generalise the qr decomposition and svd to a wide class of real algebras including all finite dimensional semi simple algebras twisted group algebras and clifford algebras two approaches are described for computing the qrd svd one jacobi method with a generalised givens rotation and one based on the artin wedderburn theorem

two dimensional exactly and completely integrable dynamical systems monopoles instantons dual models relativistic strings lund regge model generalized toda lattice etc an investigation of two dimensional exactly and completely integrable dynamical systems associated with the local part of an arbitrary lie algebra mathfrak g whose grading is consistent with an arbitrary integral embedding of 3d subalgebra in mathfrak g has been carried out we have constructed in an explicit form the corresponding systems of nonlinear partial differential equations of the second order and obtained their general solutions in the sense of a goursat problem a method for the construction of a wide class of infinite dimensional lie algebras of finite growth has been proposed

stable and efficient lattice algorithms for adaptive iir filtering previous attempts at applying lattice structures to adaptive infinite impulse response iir filtering have met with gradient computations of o n sup 2 complexity to overcome this computational burden two new lattice based algorithms are proposed for adaptive iir filtering and system identification with both algorithms of o n complexity the first algorithm is a reinterpretation of the steiglitz mcbride method 1965 while the second is a variation on the output error method state space models are employed to make the derivations transparent and the methods can be extended to other parameterizations if desired the set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct form versions of the steiglitz mcbride and output error methods whose properties are well studied the derived algorithms are as computationally efficient as existing direct form based algorithms while overcoming the stability problems associated with time varying direct form filters

canonical coordinates for transform coding of noisy sources based on the additive white quantization noise model linear transform coders are derived for gaussian sources corrupted by noise there are two alternative design objectives minimizing the trace of the error correlation matrix and thus minimizing the mean squared error or minimizing the determinant of the error correlation matrix and thus maximizing information rate it is shown that a solution to both problems is to first transform the noisy observations into canonical coordinates quantize and apply a wiener filter in this coordinate system and then transform the result back to the original coordinates canonical coordinates are uncorrelated and quantization and wiener filtering are applied to each component independently the type of canonical coordinate system depends on the design objective quantization in half canonical coordinates minimizes the mean squared error and quantization in full canonical coordinates maximizes information rate finally it is also demonstrated in this paper that majorization is the fundamental principle underlying proofs of optimal transform coding

the dynamics of relativistic strings moving in the minkowski space mathbb r 1 n in this paper we investigate the dynamics of relativistic in particular closed strings moving in the minkowski space mathbb r 1 n n ge 2 we first derive a system with n nonlinear wave equations of born infeld type which governs the motion of the string this system can also be used to describe the extremal surfaces in mathbb r 1 n we then show that this system enjoys some interesting geometric properties based on this we give a sufficient and necessary condition for the global existence of extremal surfaces without space like point in mathbb r 1 n with given initial data this result corresponds to the global propagation of nonlinear waves for the system describing the motion of the string in mathbb r 1 n we also present an explicit exact representation of the general solution for such a system moreover a great deal of numerical analyses are investigated and the numerical results show that in phase space various topological singularities develop in finite time in the motion of the string finally some important discussions related to the theory of extremal surfaces of mixed type in mathbb r 1 n are given