a higher density discrete wavelet transform this paper describes a new set of dyadic wavelet frames with two generators the construction is simple yet the wavelets cover the time frequency plane in an arrangement that provides a higher sampling in both time and frequency specifically the spectrum of the first wavelet is concentrated halfway between the spectrum of the second wavelet and the spectrum of its dilated version in addition the second wavelet is translated by half integers rather than whole integers in the frame construction this arrangement leads to an expansive wavelet transform that is approximately shift invariant and has intermediate scales the wavelet frames presented in this paper are compactly supported and have vanishing moments

partially stable lq optimal control by spectral factorization this paper presents a method for solving by spectral factorization the linear quadratic optimal control of a linear time invariant stabilizable system with an incompletely detectable state in the output in the integral of the cost function and a terminal partial stabilization constraint the solution by state feedback has been given by willems and callier 1983 the new method extends the polynomial matrix spectral factorization technique developed by kucera 1981 for the standard lq regulator with stabilization constraint an example and several comments add perspective to the results which are mainly intended to discover the correct spectral factorization equation

polynomial j spectral factorization several algorithms are presented for the j spectral factorization of a para hermitian polynomial matrix the four algorithms that are discussed are based on diagonalization successive factor extraction interpolation and the solution of an algebraic riccati equation respectively the paper includes a special algorithm for the factorization of unimodular para hermitian polynomial matrices and deals with canonical noncanonical and nearly noncanonical factorizations

optimal robust stabilization and dissipativity synthesis by behavioral interconnection given a nominal plant together with a fixed neighborhood of this plant the problem of robust stabilization is to find a controller that stabilizes all plants in that neighborhood in an appropriate sense if a controller achieves this design objective we say that it robustly stabilizes the nominal plant in this paper we formulate the robust stabilization problem in a behavioral framework with control as interconnection we also formulate a relevant behavioral mathcal h infty synthesis problem which will be instrumental in solving the robust stabilization problem we use both rational and polynomial representations for the behaviors under consideration necessary and sufficient conditions for the existence of robustly stabilizing controllers are obtained using the theory of dissipative systems we will also find the optimal stability radius i e the smallest upper bound on the radii of the neighborhoods for which there exists a robustly stabilizing controller this smallest upper bound is expressed in terms of certain storage functions associated with nominal control system

the extended bethe ansatz for infinite s 1 2 quantum spin chains with non nearest neighbor interaction it is shown that the description of the states of infinites 1 2 interacting spin systems with the hamiltonian open image in new window can be performed by studying the hyperbolic calogero sutherland eigenvalue problem the construction of multimagnon wave functions in eachn magnon sector is based on solutions of the set of linear algebraic equations which determine also the structure of zonal spherical functions on symmetric spacesxn sl n h sp n of negative curvature the usual bethe ansatz for the xxx heisenberg model corresponds to asymptotic forms of these wave functions at small values ofa 1 or large distances between spins turned over the ferromagnetic ground state

discrete j spectral factorization of possibly singular polynomial matrices we develop two state space algorithms for discrete time j spectral factorization of possibly singular possibly non column reduced and with possible zeros at the origin para hermitian matrices by assignment of matrices in optimal lq return difference equality the column degrees of the spectral factor equal the column degrees of the given matrix and the dimension of a discrete time algebraic riccati system equals the sum of the column degrees necessary and sufficient condition for the least order property of our state space realizations is column reduction of the given matrix

rational sampling filter banks based on iir filters the problem of splitting the spectrum of a digital signal by using nonuniform infinite impulse response iir filter banks is addressed near perfect reconstruction npr is considered the method uses the modulation of different iir prototypes the cancellation of the main aliasing components constrains the prototypes to be dependent on each other by using this approach linear phase prototypes are needed and noncausal filtering is required numerical examples of filter bank design are given and the computational complexity is compared with the finite impulse response fir case

every storage function is a state function it is shown that for linear dynamical systems with quadratic supply rates a storage function can always be written as a quadratic function of the state of an associated linear dynamical system this dynamical system is obtained by combining the dynamics of the original system with the dynamics of the supply rate

on the connection between the one dimensional s 1 2 heisenberg chain and haldane shastry model extra integrals of motion and the lax representation are found for interacting spin systems with the hamiltonianh j 2 j k 1 j k n p j k j k where one of the periods of the weierstrassp function is equal ton the heisenberg and haldane shastry chains appear as limiting cases of these systems at some values of the second period the simplest eigenvectors and eigenvalues ofh corresponding to the scattering of two spin waves are presented explicitly for these finite dimensional systems and for their infinite dimensional version

on polynomial matrix spectral factorization by symmetric extraction we revise the 1963 davis algorithm 2 for the spectral factorization of a para hermitian nonnegative polynomial matrix phi by symmetric factor extraction this algorithm is careless about zeros at infinity by introducing the notion of diagonal reducedness of phi we obtain an easy sufficient test for the absence of zeros at infinity we show then how to get phi diagonally reduced by diagonal excess reduction steps similar to the oono and yasuura steps removing all zeros at infinity and then how to remove synunetrically finite zeros while keeping el diagonally reduced hence free of zeros at infinity this results in a revised symmetric extraction spectral factorization algorithm with monotone degree control an example shows the didactical conceptual simplicity of the method appropriate symmetric extraction is discovered by revising and discovering important particular one sided factor extraction properties of polynomial matrices

algorithm of j spectral factorization of polynomial matrices numerical algorithms for the canonical j factorization of polynomial matrices with respect to the imaginary axis are given the factorization problems for the non regular polynomial matrices and for polynomials whose determinants have zero roots are considered the constructed algorithms are not connected to the finding of roots of the polynomial the basic calculation procedure is the construction of the stabilizing solution of the matrix algebraic riccati equation

algorithms for multidimensional spectral factorization and sum of squares in this paper algorithms are developed for the problems of spectral factorization and sum of squares of polynomial matrices with n indeterminates and a natural interpretation of the tools employed in the algorithms is given using ideas from the theory of lossless and dissipative systems these algorithms are based on the calculus of 2n variable polynomial matrices and their associated quadratic differential forms and share the common feature that the problems are lifted from the original n variable polynomial context to a 2n variable polynomial context this allows to reduce the spectral factorization problem and the sum of squares problem to linear matrix inequalities lmi s to the feasibility of a semialgebraic set or to a linear eigenvalue problem

brief papers new results in state estimation and regulation an alternative technique to design linear state estimators and regulators is presented this technique is based on transfer matrix considerations the optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices this approach provides further insight displays the duality of estimation and control nicely and bridges the state space and frequency domain techniques the resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form

theory of regular m band wavelet bases orthonormal m band wavelet bases have been constructed and applied by several authors this paper makes three main contributions first it generalizes the minimal length k regular 2 band wavelets of daubechies 1988 to the m band case by deriving explicit formulas for k regular m band scaling filters several equivalent characterizations of k regularity are given and their significance explained second two approaches to the construction of the m 1 wavelet filters and associated wavelet bases are described one relies on a state space characterization with a novel technique to obtain the unitary wavelet filters the other uses a factorization approach third this paper gives a set of necessary and sufficient condition on the m band scaling filter for it to generate an orthonormal wavelet basis the conditions are very similar to those obtained by cohen 1990 and lawton 1990 for 2 band wavelets

new solution to the inverse regulator problem by the polynomial matrix method abstract this paper gives a new criterion for the inverse regulator problem in terms of polynomial matrix fractions the generalized kalman equation in polynomial matrix form leads to a necessary and sufficient condition for a stable feedback law to be optimal for some unknown quadratic performance index this criterion consists of i a symmetric factorizability of a polynomial matrix and ii a polynomial type criterion that guarantees detectability the relationship between the riccati and kalman equations is also established finally an example is given to illustrate the new result in contrast with the existing result

on a schur algorithm approach to spectral factorization state space formulae abstract in some earlier publications 10 13 we indicated how the classical schur algorithm can be used as a method to solve a spectral factorization problem in the present paper indicate how to obtain a state space formulation of the theory and formulae for an iterative algorithm for spectral factorization using state space representations

large strain inelastic state variable theory abstract a precise format for the construction of three dimensional large strain inelastic state variable models through the continuum modeling of micromechanism is proposed this general theory is based on a concept of state wherein each material element in its present configuration is regarded as a black box which converts possible future stimuli deformations into future response stress and internal energy fundamental considerations suggest that state is determined by the instantaneous spatial distribution of the material bonds the parameterization of the accessible states with n tuples of tensor state variables is considered and the explicit assumptions which make it possible to reduce causal functional forms to response and incremental evolution equations are enumerated the specific restrictions associated with material frame invariance and material symmetry are specified at each step of this development the presentation concludes by considering some important specialized theories which contain virtually all successful models in the field of inelasticity

dissipativity of pseudorational behaviors this paper studies dissipativity for a class of infinite dimensional systems called pseudorational in the behavioral context extending the finite dimensional counterpart we show that a pseudorational behavior is dissipative if and only if it admits a storage function or a dissipation function for its proof we derive a new necessary and sufficient condition for entire functions of exponential type in the so called paley wiener class to allow a symmetric factorization characterization of dissipative behaviors and linear quadratic optimal behaviors are also given

spectral factorization with imaginary axis zeros abstract we examine the problem of the existence and calculation of hermitian solutions p of a linear matrix inequality corresponding to the spectral factorization of a proper rational spectral density in particular zeros are permitted on the finite imaginary axis or at infinity as part of our construction of solutions we show explicitly that each such imaginary axis eigenvalue either finite or infinite defines a fixed part of all solutions p

an elementary proof of the polynomial matrix spectral factorization theorem a very simple and short proof of the polynomial matrix spectral factorization theorem on the unit circle as well as on the real line is presented which relies on elementary complex analysis and linear algebra

an analytic wavelet transform with a flexible time frequency covering we develop a rational dilation wavelet transform for which the dilation factor the q factor and the redundancy can be easily specified the introduced transform contains hilbert transform pairs of atoms therefore it is also suitable for oscillatory signal processing the transform may be modified to obtain a tight chirplet frame for discrete time signals a fast implementation that makes use of an equivalent filter bank makes the transform suitable for long signals examples on natural signals are provided to demonstrate the utility of the transform

paper efficient algorithm for matrix spectral factorization an algorithm is presented for the spectral factorization of polynomial or rational matrices arising in optimal control and filtering theory as well as in network theory there are two versions of the algorithm one applicable to continuous time problems the other to discrete time ones both versions are based on newton s method feature quadratic convergence and provide a significant improvement in efficiency over the existing methods

on linear h sup spl infin equalization of communication channels as an alternative to existing techniques and algorithms we investigate the merit of the h sup spl infin approach to the linear equalization of communication channels we first give the formulation of all causal h sup spl infin equalizers using the results of and then look at the finite delay ease we compare the risk sensitive h sup spl infin equalizer with the mmse equalizer with respect to both the average and the worst case ber performances and illustrate the improvement due to the use of the h sup spl infin equalizer

discrete j spectral factorization abstract this paper deals with the j spectral factorization for general discrete rational matrices a simple approach based on the kalman filtering in krein space is proposed the main idea is to construct a stochastic state space filtering model in krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized the spectral factor is then easily derived by using the generalized kalman filtering in krein space which is similar to the h 2 spectral factorization our approach unifies the treatment of the h 2 spectral factorization and the j spectral factorization the applications of the derived results in h and risk sensitive estimation for both nonsingular and singular systems are demonstrated

the properties of reduced order minimum variance filters for systems with partially perfect measurements the problem of the finite time reduced order minimum variance full state estimation of linear continuous time invariant systems is considered in cases where the output measurement is partially free of corrupting white noise components the structure of the optimal filter is obtained and a link between this structure and the structure of the system invariant zeros is established using expressions that are derived in closed form for the invariant zeros of the system simple sufficient conditions are obtained for the existence of the optimal filter in the stationary case the structure and the transmission properties of the stationary filter for general left invertible systems are investigated a direct relation between the optimal filter and a particular minimum order left inverse of the system is obtained a simple explicit expression for the filter transfer function matrix is also derived the expression provides an insight into the mechanism of the optimal estimation

on kublanovskaya s approach to the solution of the generalized latent value problem for functional lambda matrices in siam j numer anal 7 1970 pp 532 537 kublanovskaya proposed a quadratically convergent algorithm for computing the eigenvalues of the generalized latent value problem for lambda matrices in this contribution we show that kublanovskaya s algorithm does not constitute a newton iteration though it can be justified through its equivalence with the generalized rayleigh quotient an alternative iteration scheme that can provide a higher order of convergence is proposed

deformation analysis for finite elastic plastic strains in a lagrangean type description abstract a general concept is presented to analyse the deformation of structures undergoing arbitrarily large elastic and arbitrarily large plastic strains based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions the kinematics of two superposed finite non coaxial deformations are investigated lagrangean type elastic and plastic stretch tensors are introduced and multiplicative decompositions of the total stretch into these elastic and plastic stretches are derived it is shown that the result is independent of any decomposition of the total rotation into an elastic and a plastic rotation for the second superposed deformation the total lagrangean logarithmic hencky strain tensor with corresponding elastic and plastic logarithmic strains is defined if in a large deformation analysis the first deformation is updated such that the second deformation is constrained to be moderately large then the total logarithmic strain tensor of the second deformation can be additively decomposed into purely elastic and purely plastic parts this enables an appropriate formulation of constitutive equations for isotropic hyperelastic material behavior with associated flow rule and evolution laws for combined isotropic kinematic hardening work conjugate to the elastic logarithmic strain tensor is a back rotated kirchhoff stress tensor the rotational change of its reference configuration during the update is given explicitly finally the principle of virtual work with corresponding equilibrium equations and static and geometric boundary conditions is given the virtual work functional is transformed to deliver the consistent tangent stiffness matrix as basis for a finite element solution algorithm

brief polynomial j spectral factorization in minimal state space by a specific choice of matrices in optimal lq return difference equality we develop a simple state space algorithm for polynomial j spectral factorization for this purpose we solve a minimal order algebraic riccati equation the order obtained by solving an integer linear programming ilp problem an example that cannot be solved by the existing algorithms illustrates our algorithm

rational spectral factorization using state space methods abstract we describe a state space based algorithm to find the minimum phase spectral factor of any rational spectral density whether it be proper improper or polynomial

on a hardy space approach to the analysis of spectral factors the paper presents a study of several problems related to spectral factorizations we assume only a very weak form of coercivity for the p x p spectral function phi and look at the set wm of all rectangular p x m spectral factors the main object is the arithmetization of the geometry of the set of minimal stable spectral factors by employing hardy space techniques and the arithmetic of inner functions particular attention is paid to the study of various partial orders associated with the set of spectral factors

wavelet transform with tunable q factor this paper describes a discrete time wavelet transform for which the q factor is easily specified hence the transform can be tuned according to the oscillatory behavior of the signal to which it is applied the transform is based on a real valued scaling factor dilation factor and is implemented using a perfect reconstruction over sampled filter bank with real valued sampling factors two forms of the transform are presented the first form is defined for discrete time signals defined on all of z the second form is defined for discrete time signals of finite length and can be implemented efficiently with ffts the transform is parameterized by its q factor and its oversampling rate redundancy with modest oversampling rates e g three to four times overcomplete being sufficient for the analysis synthesis functions to be well localized

a parametrisation for dissipative behaviours the matrix case we study linear time invariant dynamical systems that are dissipative with respect to a generalised power defined by a quadratic differential form we address several cases in an increasing order of complexity and show how dissipative systems can be parametrised in this process we also establish a number of results for polynomial matrices that are of independent interest the present article is a generalisation of our earlier work that dealt with single input single output dissipative systems pendharkar i and pillai h k 2004 a parametrization for dissipative behaviours systems and control letters 51 123 132

least squares approximation of perfect reconstruction filter banks designing good causal filters for perfect reconstruction pr filter banks is a challenging task due to the unusual nature of the design constraints we present a new least squares ls design methodology for approximating prfbs that avoids most of these difficult constraints the designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters then given some desired reconstruction delay this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a prfb this technique is built on a multi input multi output mimo system model for filter banks derived from the filter bank polyphase representation using this model we frame the ls approximation problem for prfbs as a causal ls equalization problem for mimo systems we derive the causal ls solution to this design problem and present an algorithm for computing this solution the resulting algorithm includes a mimo spectral factorization that accounts for most of the complexity and computational cost for this design technique finally we consider some design examples and evaluate their performance

brief positive polynomial matrices and improved lmi robustness conditions recently several new lmi conditions for stability of linear systems have been proposed introducing additional slack variables to reduce the gap between conservative convex quadratic stability conditions and intractable non convex robust stability conditions in this paper we show that these improved lmi conditions can be derived with the help of some basic results on positive polynomial matrices the approach allows us to derive in a unifying way results in the state space and polynomial frameworks applications to robust stability analysis and robust stabilization of systems with multi linear parametric uncertainty are fully described

overcomplete discrete wavelet transforms with rational dilation factors this paper develops an overcomplete discrete wavelet transform dwt based on rational dilation factors for discrete time signals the proposed overcomplete rational dwt is implemented using self inverting fir filter banks is approximately shift invariant and can provide a dense sampling of the time frequency plane a straightforward algorithm is described for the construction of minimal length perfect reconstruction filters with a specified number of vanishing moments whereas in the nonredundant rational case no such algorithm is available the algorithm is based on matrix spectral factorization the analysis synthesis functions discrete time wavelets can be very smooth and can be designed to closely approximate the derivatives of the gaussian function

perfect reconstruction filter banks with rational sampling factors an open problem namely how to construct perfect reconstruction filter banks with rational sampling factors is solved such filter banks have n branches each one having a sampling factor of p i qi and their sum equals one in this way the well known theory of filter banks with uniform band splitting is extended to allow for nonuniform divisions of the spectrum this can be very useful in the analysis of speech and music the theory relies on two transforms the first transform leads to uniform filter banks having polyphase components as individual filters the other results in a uniform filter bank containing shifted versions of same filters this in turn introduces dependencies in design and is left for future work as an illustration several design examples for the 2 3 1 3 case are given filter banks are then classified according to the possible ways in which they can be built it is shown that some cases cannot be solved even with ideal filters with real coefficients

on the factorization of rational discrete time spectral densities in this paper we consider an arbitrary matrix valued rational spectral density phi z we show with a constructive proof that phi z admits a factorization of the form phi z w top z 1 w z where w z is stochastically minimal moreover w z and its right inverse are analytic in regions that may be selected with the only constraint that they satisfy some symplectic type conditions by suitably selecting the analyticity regions this extremely general result particularizes into a corollary that may be viewed as the discrete time counterpart of the matrix factorization method devised by youla in his celebrated work 48

generalized lqr control and kalman filtering with relations to computations of inner outer and spectral factorizations we investigate the generalized linear quadratic regulator lqr control where the dimension of the control input is strictly greater than the dimension of the controlled output and the weighting matrix on the control signal is singular the dual problem is the generalized kalman filtering where the dimension of the input noise process is strictly smaller than the dimension of the output measurement and the covariance of the observation noise is singular these two problems are intimately related to inner outer factorizations for nonsquare stable transfer matrices with square inners of the smaller size such inner outer factorizations are in turn related to spectral factorizations for power spectral density psd matrices whose normal ranks are not full we propose iterative algorithms and establish their convergence for inner outer and spectral factorizations which in turn solve the generalized lqr control and kalman filtering

on the lyapunov equation coinvariant subspaces and some problems related to spectral factorizations a geometric approach to stochastic realization theory and hence to spectral factorization problems has been developed by lindquist and picci 1985 1991 and lindquist et al 1995 most of this work was done abstractly fuhrmann and gombani 1998 adopted an entirely hardy space approach to this set of problems studying the set of rectangular spectral factors of given size for a weakly coercive spectral function the parametrization of spectral factors in terms of factorizations of related inner functions as developed in fuhrmann 1995 had to be generalized this led to a further understanding of the partial order introduced by lindquist and picci in the set of stable spectral factors in the present paper we study the geometry of finite dimensional coinvariant subspaces of a vectorial hardy space h 2 via realization theory emphasizing the role of the lyapunov equation in lifting the hardy space metric to the statespace domain we follow this by deriving state space formulas for rectangular spect

lossless and dissipative distributed systems this paper deals with linear shift invariant distributed systems by this we mean systems described by constant coefficient linear partial differential equations we define dissipativity with respect to a quadratic differential form i e a quadratic functional in the system variables and their partial derivatives the main result states the equivalence of dissipativity and the existence of a storage function or a dissipation rate the proof of this result involves the construction of the dissipation rate we show that this problem can be reduced to hilbert s 17th problem on the representation of a nonnegative rational function as a sum of squares of rational functions

spectral factorization by symmetric extraction for distributed parameter systems the spectral factorization problem of a scalar coercive spectral density is considered in the framework of the callier desoer algebra of distributed parameter system transfer functions criteria are given for the infinite product representation of a meromorphic coercive spectral density of finite order and for the convergence of infinite product representations of spectral factors i e for the convergence of the symmetric extraction method for solving the spectral factorization problem of such spectral density these convergence criteria are applied to the solution of the linear quadratic optimal control problem by spectral factorization for a specific class of semigroup hilbert state space systems with a riesz spectral generator the speed of convergence of the symmetric extraction method is also considered as an example a damped vibrating string model is handled

a coprime factorisation and its application in ℋ2 control given a plant transfer matrix as a fraction of two polynomial matrices we present a doubly coprime factorisation identity over the proper stable rational matrices of the plant transfer matrix and

iterated filter banks with rational rate changes connection with discrete wavelet transforms some properties of two band filter banks with rational rate changes rational filter banks are first reviewed focusing then on iterated rational filter banks compactly supported limit functions are obtained in the same manner as previously done for dyadic schemes allowing a characterization of such filter banks these functions are carefully studied and the properties they share with the dyadic case are highlighted they are experimentally observed to verify a shift property strictly verified in the dyadic ease up to an error which can be made arbitrarily small when their regularity increases in this case the high pass outputs of an iterated filter bank can be very close to samples of a discrete wavelet transform with the same rational dilation factor straightforward extension of the formalism of multiresolution analysis is also made finally it is shown that if one is ready to put up with the loss of the shift property rational iterated filter banks can be used in the same manner as if they were dyadic filter banks with the advantage that rational dilation factors can be chosen closer to 1

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

a toeplitz algorithm for polynomial j spectral factorization a block toeplitz algorithm is proposed to perform the j spectral factorization of a para hermitian polynomial matrix the input matrix can be singular or indefinite and it can have zeros along the imaginary axis the key assumption is that the finite zeros of the input polynomial matrix are given as input data the algorithm is based on numerically reliable operations only namely computation of the null spaces of related block toeplitz matrices polynomial matrix factor extraction and linear polynomial matrix equations solving

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

design of two band critically sampled rational rate filter banks with multiple regularity orders and associated discrete wavelet transforms an approach for designing two band rational rate critically sampled nonorthogonal filter banks with perfect reconstruction and multiple regularity orders is proposed this approach relies on an updated result on the relationship between the filters in the filter bank to achieve all the desired properties filter responses are optimized to approximate ideal brick wall responses subject to linear and nonlinear constraints derived from regularity and perfect reconstruction conditions respectively the obtained designs are approximately shift invariant as a result of strong frequency selectivity and multiple regularity orders two methods for solving the nonconvex optimization design problem are presented and the results from the proposed approach are compared against existing designs in the literature

elastic shadow flow and its theoretical implications for inelastic solids microstructural considerations have led to a constitutive format for the modeling of inelastic solids which does not make use of a fixed material reference in the usual sense a principal motivation for this eulerian type theoretical structure stems from a belief that large deformation inelastic flow phenomena such as that encountered in certain metal forming processes will one day prove amenable to numerical techniques of the sort common to the field of fluid mechanics unfortunately virtually all established theoretical results of a general nature have been developed in a lagrangian or referential context and are not readily adapted to this new format here this difficulty is partially overcome through the introduction of an instantaneous local reference corresponding to a material element s so called shadow elastically unstretched configuration a related state variable transformation and the definition of a shadow frame time derivative analogous to the corotational time derivative are then shown to facilitate a far more tractable theoretical reformulation throughout three equivalent variants of this general theory are presented one expressed in terms of a gradient type cell placement tensor a second involving symmetric elastic stretch and orthogonal cell orientation tensors and a third in which the aforementioned elastic stretch is replaced by the elastic natural log strain tensor in each case the theoretical simplifications appropriate for various types of materials are enumerated it is noteworthy that the latter two forms are instantly specialized for the most common class of structurally isotropic materials by merely dropping dependence on the cell orientation tensor in all forms basic thermodynamic considerations second law result in general expressions for true stress response in terms of energy derivatives the rate of mechanical dissipation and to necessary conditions in the form of constitutive inequalities for il iushin stability finally the specific circumstances under which these inequalities reduce to the familiar drucker like forms are identified

exact multimagnon states in one dimensional ferromagnetic spin chains with a short range interaction the authors propose the procedure of constructing the exact wavefunctions of m magnons on an infinite one dimensional lattice in the one parameter model with an exponentially decreasing interaction between spins for m or 4 the problem is solved explicitly the bethe wavefunctions in the heisenberg xxx chain appear in the limit of nearest neighbour interaction

plastic potential theory in large strain elastoplasticity abstract the classical theory of isotropie rate independent strain hardening elastoplasticity based on the invariance of elastic properties is reformulated as an incremental state variable theory in this eulerian spatial formulation state is described in terms of a scalar work hardening parameter and a single finite strain elastic deformation tensor that fixes the elastic stretch ellipsoid in the current configuration this theoretically efficient formulation proves amenable to the consideration of material stability as the postulate of il iushin is shown to rigorously extend the classical plastic potential theory into the larger strain deformation regime in virtually identical form special care is taken to establish the precise connection between these theoretical forms and those of lee as well as the more general forms of green and naghdi small strain linearization then serves to justify a particularly convenient frame invariant generalization of the classical prandtl reuss equations

a new design algorithm for two band orthonormal rational filter banks and orthonormal rational wavelets we present a new algorithm for the design of orthonormal two band rational filter banks owing to the connection between iterated rational filter banks and rational wavelets this is also a design algorithm for orthonormal rational wavelets it is basically a simple iterative procedure which explains its exponential convergence and adaptability under various linear constraints e g regularity although the filters obtained from this algorithm are suboptimally designed they show excellent frequency selectivity after an in depth account of the algorithm we discuss the properties of the rational wavelets generated by some designed filters in particular we stress the possibility to design almost shift error free wavelets which allows the implementation of a rational wavelet transform

frequency domain design of overcomplete rational dilation wavelet transforms the dyadic wavelet transform is an effective tool for processing piecewise smooth signals however its poor frequency resolution its low q factor limits its effectiveness for processing oscillatory signals like speech eeg and vibration measurements etc this paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied the new wavelet transform can attain higher q factors desirable for processing oscillatory signals or the same low q factor of the dyadic wavelet transform the new wavelet transform is modestly overcomplete and based on rational dilations like the dyadic wavelet transform it is an easily invertible constant q discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for l2 r the wavelet can be made to resemble a gabor function and can hence have good concentration in the time frequency plane the construction of the new wavelet transform depends on the judicious use of both the transform s redundancy and the flexibility allowed by frequency domain filter design