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

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 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

the role of linear semi infinite programming in signal adapted qmf bank design we consider the problem of designing a perfect reconstruction fir quadrature mirror filter qmf bank h g adapted to input signal statistics with the coding gain as the adaptation criterion maximization of the coding gain has so far been viewed as a difficult nonlinear constrained optimization problem it is shown that the coding gain depends only on the product filter p z h z h z sup 1 and this transformation leads to a stable class of linear optimization problems having finitely many variables and infinitely many constraints termed linear semi infinite programming sip problems the sought for original filter h z is obtained by deflation and spectral factorization of p z with the sip formulation every locally optimal solution is also globally optimal and can be computed using reliable numerical algorithms the natural regularity properties inherent in the sip formulation enhance the performance of these algorithms we present a comprehensive theoretical analysis of the sip problem and its dual characterize the optimal filters and analyze uniqueness and sensitivity issues all these properties are intimately related to those of the input signal and bring considerable insight into the nature of the adaptation process we present discretization and cutting plane algorithms and apply both methods to several examples

theory of rate distortion optimal constrained filterbanks application to iir and fir biorthogonal designs we design filterbanks that are best matched to input signal statistics in m channel subband coders using a rate distortion criterion previous research has shown that unconstrained length paraunitary filterbanks optimized under various energy compaction criteria are principal component filterbanks that satisfy two fundamental properties total decorrelation and spectral majorization in this paper we first demonstrate that the two properties above are not specific to the paraunitary case but are satisfied for a much broader class of design constraints our results apply to a broad class of rate distortion criteria including the conventional coding gain criterion as a special case a consequence of these properties is that optimal perfect reconstruction pr filterbanks take the form of the cascade of principal component filterbanks and a bank of pre and post conditioning filters the proof uses variational techniques and is applicable to a variety of constrained design problems in the second part of this paper we apply the theory above to practical filterbank design problems we give analytical expressions for optimal iir biorthogonal filterbanks our analysis validates a conjecture by several researchers we then derive the asymptotic limit of optimal fir biorthogonal filterbanks as filter length tends to infinity the performance loss due to fir constraints is quantified theoretically and experimentally the optimal filters are quite different from traditional filters finally a sensitivity analysis is presented

a chain observer for nonlinear systems with multiple time varying measurement delays this paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time varying delays a modular approach is followed where subobservers are connected in cascade to achieve a desired exponential convergence rate chain observer when the delay is small a single step observer is sufficient to carry out the goal two or more subobservers are needed in the the presence of large delays the observer employs delay dependent time varying gains to achieve the desired exponential error decay the proposed approach allows to deal with vector output measurements where each output component can be affected by a different delay relationships among the error decay rate the bound on the measurement delays the observer gains and the lipschitz constants of the system are presented the method is illustrated on the synchronization problem of continuous time hyperchaotic systems with buffered measurements

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

linear quadratic regulation for linear time varying systems with multiple input delays this paper studies the classic linear quadratic regulation lqr problem for both continuous time and discrete time systems with multiple input delays for discrete time systems the lqr problem for systems with single input delay has been studied in existing literature whereas a solution to the multiple input delay case is not known to our knowledge for continuous time systems with multiple input delays the lqr problem has been tackled via an infinite dimensional system theory approach and a frequency time domain approach the objective of the present paper is to give an explicit solution to the lqr problem via a simple and intuitive approach the main contributions of the paper include a fundamental result of duality between the lqr problem for systems with multiple input delays and a smoothing problem for an associated backward stochastic system the duality allows us to obtain a solution to the lqr problem via standard projection in linear space the lqr controller is simply constructed by the solution of one backward riccati difference for the discrete time case or differential for the continuous time case equation of the same order as the plant ignoring the delays

memoryless approach to the lq and lqg problems with variable input delay this note studies the lq and lqg problems for linear time invariant systems with a single time varying input delay and instantaneous memoryless state feedback we extend the memoryless state feedback solution proposed in 1 in two directions we prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay for which we provide a sufficient and sometimes strict bound moreover we show that this memoryless control is optimal also in the case of time varying delays and that the quadratic cost functional has the same value as in the case without delay for time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous finally we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case but with a larger cost than the delay less lqg solution

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

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

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

construction of e s 2 optimal supersaturated designs booth and cox proposed the e s 2 criterion for constructing two level supersaturated designs nguyen technometrics 38 1996 69 73 and tang and wu canad j statist 25 1997 191 201 independently derived a lower bound for e s 2 this lower bound can be achieved only when m is a multiple of n 1 where m is the number of factors and n is the run size we present a method that uses difference families to construct designs that satisfy this lower bound we also derive better lower bounds for the case where the nguyen tang wu bound is not achievable our bounds cover more cases than a bound recently obtained by butler mead eskridge and gilmour j r stat soc ser b stat methodol 63 2001 621 632 new e s 2 optimal designs are obtained by using a computer to search for designs that achieve the improved bounds

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

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

quadratic control of evolution equations with delays in control the quadratic cost problem of evolution equations with delays in control is considered a semigroup model which involves no explicit delays in control but contains an unbounded control operator is introduced with the aid of a family of approximating systems it is shown that the optimal feedback control and the minimum cost are characterized by the solution of a riccati equation three examples are given to illustrate the theory the filtering problem of evolution equations with observation delays is also solved through the duality relation

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

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

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

some theory for constructing minimum aberration fractional factorial designs summary minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution minimum aberration designs for n runs and n 2 m n factors have previously been constructed using the novel idea of complementary designs in this paper an alternative method of construction is developed by relating the wordlength pattern of designs to the so called confounding between experimental runs this allows minimum aberration designs to be constructed for n runs and 5n 16 m n 2 factors as well as for n 2 m n

truncated predictor feedback control for exponentially unstable linear systems with time varying input delay abstract the stabilization of exponentially unstable linear systems with time varying input delay is considered in this paper we extend the truncated predictor feedback tpf design method which was recently developed for systems with all poles on the closed left half plane to be applicable to exponentially unstable linear systems assuming that the time varying delay is known and bounded the design approach of a time varying state feedback controller is developed based on the solution of a parametric lyapunov equation an explicit condition is derived for which the stability of the closed loop system with the proposed controller is guaranteed it is shown that for the stability of the closed loop system the maximum allowable time delay in the input is inversely proportional to the sum of the unstable poles in the plant the effectiveness of the proposed method is demonstrated through numerical examples

k circulant supersaturated designs a class of supersaturated designs called k circulant designs is explored these designs are constructed from cyclic generators by cycling k elements at a time the class of designs includes many es2 optimal designs some of which are already known and some of which are more efficient than known designs for model estimation under factor sparsity generators for the most efficient designs are listed and projection properties of some of the designs are explored we also illustrate that some k circulant supersaturated designs can be augmented with interaction columns to produce efficient designs for a larger number of factors or for estimating interactions

a new class of supersaturated designs supersaturated designs are useful in situations in which the number of active factors is very small compared to the total number of factors being considered in this article a new class of supersaturated designs is constructed using half fractions of hadamard matrices when a hadamard matrix of order n is used such a design can investigate up to n 2 factors in n 2 runs results are given for n 60 extension to larger n is straightforward these designs are superior to other existing supersaturated designs and are easy to construct an example with real data is used to illustrate the ideas

stabilization and robustness analysis for time varying systems with time varying delays using a sequential subpredictors approach we provide a new sequential predictors approach for the exponential stabilization of linear time varying systems our method circumvents the problem of constructing and estimating distributed terms in the control laws and allows arbitrarily large input delay bounds pointwise time varying input delays and uncertainties instead of using distributed terms our approach to handling longer delays is to increase the number of predictors we obtain explicit formulas to find lower bounds for the number of required predictors the formulas involve bounds on the delays and on the derivatives of the delays we illustrate our method in three examples

construction properties and analysis of group orthogonal supersaturated designs in this article we propose a new method for constructing supersaturated designs that is based on the kronecker product of two carefully chosen matrices the construction method leads to a partitio

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

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

approximating the linear quadratic optimal control law for hereditary systems with delays in the control a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator quadratic cost problem associated with time varying functional differential equations with control delays the approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law general properties of the volterra factors of hilbert schmidt operators are then used to obtain convergence results for the controls trajectories and feedback kernels two algorithms are derived from the basic approximation scheme including a fast algorithm in the time invariant case a numerical example is also considered

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

the linear quadratic optimal control problem with delays in state and control variables a state space approach this paper generalizes the results of vinter and kwong to a control operator with a more general delay structure than the one in a ichikawa and to delay systems with both finite and infinite memories the linear quadratic optimal control problem over both finite and infinite time horizons is treated several forms of associated abstract riccati differential and algebraic equations are presented the properties of the kernel of the solution are studied and a coupled set of matrix ordinary and partial differential equations is obtained

predictor based control of stochastic systems with nonlinear diffusions and input delay abstract we consider the problem of state feedback control of linear continuous time stochastic systems with nonlinear diffusion terms affected by time varying input delays or equivalently by time varying state measurement delays we propose a finite dimensional control law based on closed loop predictors and derive sufficient delay bounds for the exponential stability in mean and exponential mean square stability with prescribed rate

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

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

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

predictor based control of linear systems with large and variable measurement delays this paper concerns the problem of the control of linear systems by means of feedback from delayed output where the delay is known and time varying the main advantage of the approach is that it can be applied to systems with any delay bound i e not only small delays the predictor is based on a combination of finite dimensional elementary predictors whose number can be suitably chosen to compensate any delay the single predictor element is an original proposal and the class of delays to which the schema can be applied includes but it is not limited to continuous delay functions

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

a twofold spline approximation for finite horizon lqg control of hereditary systems in this paper an approximation scheme is developed for the solution of the linear quadratic gaussian lqg control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay the solution here proposed is achieved by means of two approximating subspaces the first one to approximate the riccati equation for control and the second one to approximate the filtering equations since the approximating subspaces have finite dimension the resulting equations can be implemented the convergence of the approximated control law to the optimal one is proved simulation results are reported on a wind tunnel model showing the high performance of the method

blocked regular fractional factorial designs with minimum aberration this paper considers the construction of minimum aberration ma blocked factorial designs based on coding theory the concept of minimum moment aberration due to xu 2003 for unblocked designs is extended to blocked designs the coding theory approach studies designs in a row wise fashion and therefore links blocked designs with nonregular and supersaturated designs a lower bound on blocked wordlength pattern is established it is shown that a blocked design has ma if it originates from an unblocked ma design and achieves the lower bound it is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros sufficient conditions are given for constructing ma blocked designs from unblocked ma designs the theory is then applied to construct ma blocked designs for all 32 runs 64 runs up to 32 factors and all 81 runs with respect to four combined wordlength patterns

new e s2 optimal supersaturated designs constructed from incomplete block designs we present a method for constructing two level supersaturated designs ssds from incomplete block designs a lower bound of e s2 that also covers the case of odd run sizes is given this bound is attained by ssds constructed from balanced incomplete block designs we study ssds that can be constructed from regular graph designs when balanced incomplete block designs do not exist a computer search is conducted to find ssds with 5 n 50 and n m 2n that can be constructed from regular graph designs where m is the number of factors and n is the run size many ssds derived from regular graph designs are optimal the best e s2 optimal ssds with respect to additional optimality criteria are tabulated some notes on the construction of saturated designs also are given

improved technique for design of perfect reconstruction fir qmf banks with lossless polyphase matrices a technique is developed for the design of analysis filters in an m channel maximally decimated perfect reconstruction finite impulse response quadrature mirror filter fir qmf bank that has a lossless polyphase component matrix e z the aim is to optimize the parameters characterizing e z until the sum of the stopband energies of the analysis filters is minimized there are four novel elements in the procedure reported here the first is a technique for efficient initialization of one of the m analysis filters as a spectral factor of an mth band filter the factorization itself is done in an efficient manner using the eigenfilters approach without the need for root finding techniques the second element is the initialization of the internal parameters which characterize e z based on the above spectral factor the third element is a modified characterization mostly free from rotation angles of the fir e z the fourth is the incorporation of symmetry among the analysis filters so as to minimize the number of unknown parameters being optimized the resulting design procedure always gives better filter responses than earlier ones for a given filter length and converges much faster

fir principal component filter banks two dimensional 2 d principal component filter banks pcfbs of finite impulse response fir are proposed for 2 d signals among all uniform paraunitary fir analysis synthesis filter banks the fir pcfbs have the most energy compaction and maximize the arithmetic mean to geometric mean ratio am gm ratio of subband variances which is the theoretic coding gain tcc of the systems under proper assumptions the theoretic proof and design techniques are provided several special cases are discussed experimental results show the potential power of the fir pcfbs

optimal supersaturated designs we consider screening experiments where an investigator wishes to study many factors using fewer observations our focus is on experiments with two level factors and a main effects model with intercept since the number of parameters is larger than the number of observations traditional methods of inference and design are unavailable in 1959 box suggested the use of supersaturated designs and in 1962 booth and cox introduced measures for efficiency of these designs including e s2 which is the average of squares of the off diagonal entries of the information matrix ignoring the intercept for a design to be e s2 optimal the main effect of every factor must be orthogonal to the intercept factors are balanced and among all designs that satisfy this condition it should minimize e s2 this is a natural approach since it identifies the most nearly orthogonal design and orthogonal designs enjoy many desirable properties including efficient parameter estimation factor balance in an e s2 optimal d

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

a general method of constructing e s2 optimal supersaturated designs there has been much recent interest in supersaturated designs and their application in factor screening experiments supersaturated designs have mainly been constructed by using the e s 2 optimality criterion originally proposed by booth and cox in 1962 however until now e s 2 optimal designs have only been established with certainty for n experimental runs when the number of factors m is a multiple of n 1 and in adjacent cases where m q n 1 r r 2 q an integer a method of constructing e s 2 optimal designs is presented which allows a reasonably complete solution to be found for various numbers of runs n including n 8 12 16 20 24 32 40 48 64

construction of optimal multi level supersaturated designs author s xu hongquan wu cfj abstract a supersaturated design is a design whose run size is not large enough for estimating all the main effects the goodness of multi level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by xu and wu 2001 optimal supersaturated designs are shown to have a periodic property and general methods for constructing optimal multilevel supersaturated designs are proposed inspired by the addelman kempthorne construction of orthogonal arrays optimal multi level supersaturated designs are given in an explicit form columns are labeled with linear or quadratic polynomials and rows are points over a finite field additive characters are used to study the properties of resulting designs some small optimal supersaturated designs of 3 4 and 5 levels are listed with their properties

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

construction of supersaturated designs through partially aliased interactions summary an n x n hadamard matrix can be used to construct a saturated 2 n 1 design with n runs furthermore if an interaction column for two of the columns of the matrix is not fully aliased with any column of the matrix this interaction column can be used as a supplementary column for studying an additional factor for some small hadamard matrices studied by plackett burman 1946 the number of such interaction columns is very large thus allowing the construction of supersaturated designs whose number of factors far exceeds the number of runs a general method of construction along these lines is proposed the efficiency of the constructed designs is studied by using three criteria

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

optimal control of linear systems with large and variable input delays abstract this paper proposes an optimal control law for linear systems affected by input delays specifically we prove that when the delay functions are known it is possible to generate the optimal control for arbitrarily large delay values by using a dde without distributed terms the solution can be seen as a chain of predictors whose size depends on the maximum delay

on asymptotic stabilizability of linear systems with delayed input this paper examines the asymptotic stabilizability of linear systems with delayed input by explicit construction of stabilizing feedback laws it is shown that a stabilizable and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open loop system is not exponentially unstable i e all the open loop poles are on the closed left half plane a simple example shows that such results would not be true if the open loop system is exponentially unstable it is further shown that such systems when subject to actuator saturation are semiglobally asymptotically stabilizable by linear state or output feedback

output feedback control of linear systems with input state and output delays by chains of predictors abstract in this paper we consider the control problem of linear systems with state time delays when the control signal is affected by a possibly time varying delay the problem is solved by a chain of predictors under the assumption that a stabilizing control exists for the case of no input delay this solution is then extended to the case of partial information when only delayed output is available both the input and the output delays may have arbitrary bounds with respect to previous approaches to the same problem appeared recently in the literature the method proposed here has a simpler structure and in particular it does not need the computation of distributed terms as a by product we show that it is possible to derive an observer for a system with state and output delays from an observer for the same system without output delays

minimum aberration construction results for nonregular two level fractional factorial designs summary nonregular two level fractional factorial designs are designs which cannot be specified in terms of a set of defining contrasts the aliasing properties of nonregular designs can be compared by using a generalisation of the minimum aberration criterion called minimum g2 aberration until now the only nontrivial designs that are known to have minimum g2 aberration are designs for n runs and m n 5 factors in this paper a number of construction results are presented which allow minimum g2 aberration designs to be found for many of the cases with n 16 24 32 48 64 and 96 runs and m n 2 2 factors