a computational algorithm for pole assignment of linear single input systems an efficient computational algorithm for pole assignment of linear multiinput systems is proposed a preliminary stage of the algorithm is a reduction of the system matrices into orthogonal canonical form the gain matrix elements are then found by orthogonal transformation of the closed loop system matrix into upper quasi triangular form whose diagonal blocks correspond to the desired poles the algorithm is numerically stable the computed gain matrix being exact for a system with slightly perturbed matrices it works equally well with real and complex distinct and multiple poles and is applicable to ill conditioned and high order problems

representation of images through group delay functions in this correspondence we propose a new representation for images through the use of group delay functions we provide algorithms for the computation of the group delay functions and for the recovery of images from them we give several examples to show that most of the perceptually significant information of an image is retained in this representation we derive the minimum phase equivalent images from the fourier transform ft magnitude as well as from the phase through their respective group delay functions we compare these images to those obtained through iterative reconstruction from the ft magnitude and phase respectively

optimal reconstruction of images from localized phase the importance of localized phase in signal representation is investigated the convergence rate of the pocs algorithm projection onto convex sets used for image reconstruction from spectral phase is defined and analyzed and the characteristics of images optimally reconstructed from phase only information are presented it is concluded that images of geometric form are most efficiently reconstructed from their spectral phase whereas images of symmetric form have the poorest convergence characteristics the transition between the two extremes is shown to be continuous the results provide a new approach and analysis of the previously reported advantages of the localized phase representation over the global approach and suggest possible compression schemes

eigenfilter design of 1 d and 2 d iir digital all pass filters the eigenfilter approach is extended to design 1d and 2d iir digital all pass filters instead of the integration of the filter magnitude error the integration of phase error is minimized such that the design problem can be characterized by an eigenformulation the stability is obtained by constraining the phase specification

the reconstruction of a multidimensional sequence from the phase or magnitude of its fourier transform this paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its fourier transform the first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude although phase or magnitude information alone is not sufficient in general to uniquely specify a sequence a large class of sequences are shown to be recoverable from their phase or magnitude the second issue which is addressed in this paper concerns the actual reconstruction of a multidimensional sequence from its phase or magnitude for those sequences which are uniquely specified by their phase several practical algorithms are described which may be used to reconstruct a sequence from its phase several examples of phase only reconstruction are also presented unfortunately however even for those sequences which are uniquely defined by their magnitude it appears that a practical algorithm is yet to be developed for reconstructing a sequence from only its magnitude nevertheless an iterative procedure which has been proposed is briefly discussed and evaluated

blind ofdm channel estimation using fir constraints reduced complexity and identifiability in this correspondence blind channel estimators exploiting finite alphabet constraints are discussed for orthogonal frequency division multiplexing ofdm systems considering the channel and data jointly a joint maximum likelihood jml algorithm is described along with identifiability conditions in the noise free case this approach enables development of general identifiability conditions for the minimum distance md finite alphabet blind algorithm of zhou and giannakis both the jml and md algorithms suffer from high numerical complexity as they rely on exhaustive search methods to resolve a large number of ambiguities we present a substantially more efficient blind algorithm the reduced complexity minimum distance rmd algorithm by exploiting properties of the assumed finite length impulse response fir channel the rmd algorithm exploits constraints on the unwrapped phase of fir systems and results in significant reductions in numerical complexity over existing methods in many cases the rmd approach is able to completely eliminate the exhaustive search of the jml and md approaches while providing channel estimates of the same quality

signal representation in the combined phase spatial space reconstruction and criteria for uniqueness motivated by the major roles of the spectral phase in signal structure and by previous results on the importance of localized representation in images we develop conditions for unique representation of a signal by a combination of its spectral fourier phase and spatial samples methods for signal reconstruction from various combinations of spatial and phase information are introduced it is concluded that most of the previous results in the area of phase only representation and reconstruction are special cases of the general approach presented here

signal reconstruction from the phase of the bispectrum the authors present a simple procedure the bispectrum signal reconstruction bsr algorithm to recover the fourier phase of a signal from the phase of its bispectrum by simple analogy a procedure that recovers the fourier magnitude of a signal from the magnitude of its bispectrum is also presented in addition the authors propose an iterative scheme the bicepstrum iterative reconstruction algorithm bira for the reconstruction of a finite impulse response fir sequence from only the phase of its bispectrum and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the fourier phase of the signal whereas their sums contain the fourier magnitude information

buckling analysis of shear deformable plates by boundary element method in this paper the derivation and numerical implementation of boundary integral equations for the buckling analysis of shear deformable plates are presented plate buckling equations are derived as a standard eigenvalue problem the formulation is formed by coupling boundary element formulations of shear deformable plate and two dimensional plane stress elasticity the eigenvalue problem of plate buckling yields the critical load factor and buckling modes the domain integrals which appear in this formulation are treated in two different ways initially the integrals are evaluated using constant cells and next they are transformed into equivalent boundary integrals using the dual reciprocity method drm several examples with different geometry loading and boundary conditions are presented to demonstrate the accuracy of the formulation

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

differential quadrature element method for buckling analysis of rectangular mindlin plates having discontinuities in this paper a new solution approach the differential quadrature element method is applied to the buckling analysis of discontinuous rectangular plates based on the mindlin plate theory the domain decomposition method is used to divide the solution domain into smaller elements according to the discontinuities contained in the plate then differential quadrature procedures are applied to each element to formulate the discretized element governing equations these discrete equations are then assembled into an overall equation system using the compatibility conditions and solved by a standard eigensolver detailed formulations for modeling of the plate and the compatibility conditions are derived convergence and comparison studies are carried out to examine the reliability and accuracy of the numerical solutions four rectangular mindlin plates with different discontinuities mixed boundary conditions and cracks are analyzed to show the applicability and flexibility of the present methodology for solving a class of buckling problems due to the lack of published solutions for buckling of thick discontinuous plates and the high accuracy of the present approach the solutions obtained may serve as benchmark values for further studies

free vibration of plates by the high accuracy quadrature element method in this paper a highly accurate and rapidly converging hybrid approach is presented for the quadrature element method qem solution of plate free vibration problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm for the efficient solution of differential equations with the generality of the finite element formulation this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm a series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges in all cases the results obtained are quite accurate

analytical three dimensional elasticity solutions to some plate problems and some observations on mindlin s plate theory abstract solutions are obtained using the exact three dimensional theory of elasticity to i the eigenvalue problem or buckling under biaxial compression or the free lateral vibration of a simply supported rectangular plate with orthotropic stress strain properties and ii the static response of the same plate to a lateral load that varies sinusoidally in two directions the eigenvalue in problem i and the lateral deflections of both the surface and middle plane of the plate as well as the bending strains in problem ii are obtained in the form of series expansions in even powers of the plate thickness exact algebraic expressions are presented for the first two coefficients in the case of orthotropic plates additional coefficients can be obtained if required and are given for the much simpler case of isotropic plates in all cases the first term agrees with classical plate theory the solutions are compared with those obtained from mindlin s plate theory in neither problem is it found to be possible in general to choose values for mindlin s effective shear moduli to make the mindlin solution agree with the first two terms of the exact solution there are however two exceptions to this namely a restricted class of orthotropic materials embracing all isotropic ones in which the elastic constants satisfy a certain condition and the case of cylindrical bending when the mindlin plate reduces to a timoshenko beam of wide rectangular cross section in both these exceptional cases appropriate values for the effective shear moduli are obtained

significance of group delay functions in signal reconstruction from spectral magnitude or phase in this paper we discuss the problem of signal reconstruction from spectral magnitude or phase using group delay functions we define two separate group delay functions for a signal one is derived from the magnitude and the other from the phase of the fourier transform of the signal the group delay functions offer insight into the problem of signal reconstruction and suggest methods for reconstructing signals from partial information such as spectral magnitude or phase we examine the problem of signal reconstruction from spectral magnitude or phase on the basis of these two group delay functions and derive the conditions for signal reconstruction based on existing iterative and noniterative algorithms for signal reconstruction we propose new algorithms for some special classes of signals the algorithms are illustrated with several examples our study shows that the relative importance of spectral magnitude and phase depends on the nature of signals speech signals are used to illustrate the importance of spectral magnitude and picture signals are used to illustrate the importance of phase in signal reconstruction problems using the group delay functions we explain the convergence behavior of the existing iterative algorithms for signal reconstruction

design of recursive group delay filters by autoregressive modeling a new method of design of recursive group delay filters is presented in this paper the method uses autoregressive modeling to derive parameters of the filter the design is based on the following line of argument the desired group delay characteristics are to be realized through a stable all pass filter the transfer function of an all pass filter is completely determined by the coefficients of either the numerator or the denominator polynomial for a stable all pass filter the denominator polynomial must be a minimum phase polynomial for a minimum phase polynomial the magnitude function and the group delay function are related through cepstral coefficients therefore from the given group delay specification the cepstral coefficients corresponding to the pole part inverse of the denominator polynomial of the desired filter are first determined the magnitude spectrum corresponding to these cepstral coefficients is approximated using autoregressive modeling a wide variety of group delay filters can be realized by the proposed method depending on the nature of approximation used and the accuracy desired the design procedure is illustrated through examples

novel criteria of uniqueness for signal reconstruction from phase an approach for ascertaining whether a signal is uniquely determined by its fourier transform phase is proposed it is shown that uniqueness corresponds to the nonsingularity of a matrix which can be formed from the finite length real sequence the criterion of uniqueness for reconstructing a one dimensional finite length sequence from its phase is discussed the criterion of uniqueness for reconstructing a multidimensional finite length sequence is presented

jordan pair assignment via state feedback this note considers the assignment of the eigenstructure of the closed loop system via state feedback this assignment is achieved by assigning the jordan pair of the denominator matrix polynomial of the controllable mimo system via state feedback it turns out that for proper assignment one must take into account the almost forgotten infinite eigenstructure of the system even though they are invariant under constant state feedback however the infinite eigenstructure affects the selection of the eigenvectors

static analysis of structures by the quadrature element method qem abstract the differential quadrature method dqm is an alternative discrete approach to solving directly the governing equations of engineering and mathematical physics since the dqm does not require the derivation of the weak forms of the governing equations like the fem it can greatly reduce formulation efforts in higher order approximation the dqm has been applied in the past to the analyses of various single structural components such as bars beams membranes and plates all of the component analyses yielded good to excellent results however previous studies were limited to simple geometries and simple boundary conditions due to the limitation of using global basis functions in the present study a domain decomposition technique for the dqm is proposed to analyse truss and frame structures where the whole structural domain is represented by a collection of simple element subdomains connected together at specific nodal points this method is named the quadrature element method qem

on two dimensional hilbert integral equations generalized minimum phase signals and phase retrieval one dimensional 1 d causal signals admit hilbert integral relations between the real and imaginary parts of their fourier spectra for 1 d minimum phase signals the log magnitude and phase spectra also admit such hilbert relations in this paper we extend these results to 2 d signals we first establish the hilbert integral equations for 2 d first quadrant signals for continuous domain 2 d signals we present the partial hilbert transform relations between the real and imaginary parts of the spectrum for the discrete domain counterpart we show that the partial hilbert transform does not suffice which motivates us to introduce the composite hilbert transform considering the problem of phase retrieval we show that in both 1 d 2 d and continuous discrete domains there exists a generalized class of signals which subsumes the well known class of 1 d minimum phase signals with a rational transfer function for which hilbert integral relations exist between the log magnitude and phase spectra we introduce them under the nomenclature of generalized minimum phase signals for this class of signals phase retrieval is possible by using the hilbert transform without the requirement of a rational transfer function furthermore we show that a generalized minimum phase signal admits a stable convolutional inverse which also belongs to the same class simulation results demonstrating accurate reconstruction of 1 d and 2 d generalized minimum phase signals from their magnitude spectra are presented to support the theoretical developments

significance of group delay functions in spectrum estimation a method of spectrum estimation using group delay functions is proposed this method exploits the additive property of the fourier transform ft phase to extract spectral information of the signal in the presence of noise the phase is generally featureless due to random polarity and wrappings but the group delay function can be processed to derive significant information such as peaks in the spectral envelope in the resulting spectral estimates obtained the resolution properties of the periodogram estimate are preserved while the variance is reduced variance caused by the sidelobe leakage due to windows and additive noise are significantly reduced even in the spectral estimate obtained using a single realization of the observation peak resolution is primarily dictated by the size of the data window the method works even for high noise levels the results of this procedure are demonstrated through two illustrative examples estimation of sinusoids in noise and estimation of the narrowband autoregressive process in noise

iterative techniques for minimum phase signal reconstruction from phase or magnitude in this paper we develop iterative algorithms for reconstructing a minimum phase sequence from the phase or magnitude of its fourier transform these iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain this approach is the basis of a new means of computing the hilbert transform of the log magnitude or phase of the fourier transform of a minimum phase sequence which does not require phase unwrapping finally we discuss the potential use of this iterative computation in determining samples of the unwrapped phase of a mixed phase sequence

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

blind mimo system estimation based on parafac decomposition of higher order output tensors we present a novel framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs samples of the system frequency response are obtained based on parallel factorization parafac of three or four way tensors constructed based on respectively third or fourth order cross spectra of the system outputs the main difficulties in frequency domain methods are frequency dependent permutation and filtering ambiguities we show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity important features of the proposed approach are that it does not require channel length information needs no phase unwrapping and unlike the majority of existing methods needs no prewhitening of the system outputs

design of arma digital filters by pole zero decomposition a new technique for design of digital filters is presented in this paper the technique exploits the spectral approximation property of autoregressive modeling to reduce ripple at the edges of the transition band in the filter response an autoregressive model approximates a given spectrum better at the peaks than at the valleys spectral information around the transition band is transformed into peaks by splitting the given squared magnitude frequency response into two component spectra this splitting is accomplished using a pole zero decomposition technique which in turn uses the properties of the derivative of phase spectrum of minimum phase filters one of the component spectra corresponds nearly to the response of an all pole filter and the other component spectrum corresponds nearly to the response of an all zero filter each of these corresponends spectra can be represented by a small number of coefficients using autoregressive modeling the resulting two sets of autoregressive coefficients determine poles and zeros of the autoregressive moving average arma digital filter ripple characteristics in the response of the arma filter can be controlled by appropriately choosing the number of poles and zeros it is shown that a wide variety of magnitude frequency response characteristics can be approximated by an arma filter of low order using this technique the technique does not work well in cases where spectral approximation by autoregressive modeling is poor such cases arise when the component spectra have very large dynamic range

exact phase retrieval for a class of 2 d parametric signals we address the problem of two dimensional 2 d phase retrieval from magnitude of the fourier spectrum we consider 2 d signals that are characterized by first order difference equations which have a parametric representation in the fourier domain we show that under appropriate stability conditions such signals can be reconstructed uniquely from the fourier transform magnitude we formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal we show that the problem can be solved by employing the annihilating filter method particularly for the case when the parameters are distinct for the more general case of the repeating parameters the annihilating filter method is not applicable we circumvent the problem by employing the algebraically coupled matrix pencil acmp method in the noiseless measurement setup exact phase retrieval is possible we also establish a link between the proposed analysis and 2 d cepstrum in the noisy case we derive cramer rao lower bounds crlbs on the estimates of the parameters and present monte carlo performance analysis as a function of the noise level comparisons with state of the art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the fienup and relaxed averaged alternating reflections raar algorithms in the presence of noise

exact phase retrieval in principal shift invariant spaces we address the problem of phase retrieval from fourier transform magnitude spectrum for continuous time signals that lie in a shift invariant space spanned by integer shifts of a generator kernel the phase retrieval problem for such signals is formulated as one of reconstructing the combining coefficients in the shift invariant basis expansion we develop sufficient conditions on the coefficients and the bases to guarantee exact phase retrieval by which we mean reconstruction up to a global phase factor we present a new class of discrete domain signals that are not necessarily minimum phase but allow for exact phase retrieval from their fourier magnitude spectra we also establish hilbert transform relations between log magnitude and phase spectra for this class of discrete signals it turns out that the corresponding continuous domain counterparts need not satisfy a hilbert transform relation notwithstanding the continuous domain signals can be reconstructed from their fourier magnitude spectra we validate the reconstruction guarantees through simulations for some important classes of signals such as bandlimited signals and piecewise smooth signals we also present an application of the proposed phase retrieval technique for artifact free signal reconstruction in frequency domain optical coherence tomography fdoct

bayesian image reconstruction from partial image and aliased spectral intensity data an image reconstruction problem motivated by x ray fiber diffraction analysis is considered the experimental data are sums of the squares of the amplitudes of particular sets of fourier coefficients of the electron density and a part of the electron density is known the image reconstruction problem is to estimate the unknown part of the electron density the image a bayesian approach is taken in which a prior model for the image is based on the fact that it consists of atoms i e the unknown electron density consists of separated sharp peaks currently used heuristic methods are shown to correspond to certain maximum a posteriori estimates of the fourier coefficients an analytical solution for the bayesian minimum mean square error estimate is derived simulations show that the minimum mean square error estimate gives good results even when there is considerable data loss and out performs the maximum a posteriori estimates

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

rectangular thick plates on winkler foundation differential quadrature element solution abstract this paper deals with the static analysis of homogenous isotropic rectangular plates on winkler foundation on the basis of first order shear deformation theory an improved differential quadrature dq method called the differential quadrature element method dqem has been developed for this analysis the plates considered are subjected to a patch load or a concentrated line load which are not solvable by the global dq method the convergence and comparison studies are carried out to establish the reliability of the dqem results then the numerical results for different boundary conditions i e ssss cccc s s s s and sfsf are presented showing the parametric effects of dimensions of loading area line relative thickness ratio and elastic foundation modulus on the deflection bending and twisting moments and shear forces at selected locations most of these data are new and due to the high accuracy of the dq solution they can be useful for benchmarking future work

differential quadrature element method a new approach for free vibration analysis of polar mindlin plates having discontinuities this paper presents the numerical development of the differential quadrature element method dqem for free vibration analysis of the shear deformable plates in polar coordinates this is an improvement on the global differential quadrature method dqm the formulations of the dqem for polar plate vibration element are derived in detail the convergence characteristics of the dqem for solving the free vibration of polar plates are carefully examined the reliability and flexibility of the dqem are illustrated by solving several selected example polar plates having discontinuities which are not solvable directly by the dqm the accuracy of the dqem is evaluated and verified by comparing the present numerical results with the existing exact or approximate solutions or the fem solutions computed using the software package ansys version 5 3

three dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method this paper presents accurate three dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces two opposite sides simply supported and two other sides having combinations of simply supported clamped and free boundary conditions the solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides the eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method the numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios these results are supported by appropriate convergence studies and comparisons with the results of other authors

differential quadrature element method for static analysis of reissner mindlin polar plates abstract in this paper a new numerical technique the differential quadrature element method dqem has been developed for static analysis of the two dimensional polar reissner mindlin plate in the polar coordinate system by integrating the domain decomposition method ddm with the differential quadrature method dqm the detailed formulations for the sectorial dqem plate bending element and the compatibility conditions between each element are presented the convergence properties and the accuracy of the dqem for bending of thick polar plates are investigated through a number of numerical computations consequently the dqem has been successfully applied to analyze several annular sector plates with discontinuous loading and boundary conditions and cutouts to illustrate the simplicity and flexibility of this method for solving reissner mindlin plates in polar coordinate system which are not solvable directly using the differential quadrature method the numerical results are verified by the existing exact solutions or the fem solutions obtained using the software package ansys version 5 3

phase unwrapping of digital signals in order to unwrap the phase of a digital signal the signal s z plane zeros which lie close to the unit circle are located by repeatedly expanding the z plane in small steps and detecting a zero s crossing of the unit circle this detection is accomplished by determining the step which gives rise to a maximum change in the phase at any frequency sampling point and across any segment of the unit circle this method and its associated computer program have been rigorously tested and the phase was successfully unwrapped in most cases with the few exceptions involving sequences generated from high density clusters of zeros

on the duality of time and frequency domain signal reconstruction from partial information certain results on one dimensional signal representation and reconstruction from partial information in the frequency domain are related to and derived using relevant results obtained in the time or positional information domain in particular we adopt logan s approach and apply his results concerning zero crossing representation of certain bandpass signals we also apply voelcker s results on demodulation of analytic ssb signals by an am detector exploiting the duality of the fourier stieltjes transform and its inverse we rederive and extend to continuous one dimensional signals some results concerning the representation of fourier transformed discrete time finite sequences by partial information such as one bit or complete fourier phase fourier magnitude or signed magnitude the duality and interrelationship of characteristics and constraints attributed to time and frequency signal representation create further possibilities of drawing results and interpretations from one to its counter domain in particular we indicate possible extensions of certain results to problems of n dimensional signals and to issues of stochastic signals we also highlight basic issues concerning the structure of signals and their reconstruction from partial information

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

invariant image classification using triple correlation based neural networks triple correlation based neural networks are introduced and used in this paper for invariant classification of 2d gray scale images third order correlations of an image are appropriately clustered in spatial or spectral domain to generate an equivalent image representation that is invariant with respect to translation rotation and dilation an efficient implementation scheme is also proposed which is robust to distortions insensitive to additive noise and classifies the original image using adequate neural network architectures applied directly to 2d image representations third order neural networks are shown to be a specific category of triple correlation based networks applied either to binary or gray scale images a simulation study is given which illustrates the theoretical developments using synthetic and real image data

an algorithm for pole assignment of time invariant linear systems an algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed loop system has specified eigenvalues the algorithm is more efficient than many comparable techniques and has some desirable numerical properties it is closely related to the qr algorithm for the eigenproblem and extends to descriptor systems

analytical formulae for reconstruction of certain discrete signals from phase level and line crossings we provide simple and explicit formulae for reconstructing any member of a class of discrete time signals from the frequencies at which its fourier phase crosses any specific level of constant phase or a linear phase line with integer slope provided that the number of crossings equals the length of the signal support unlike previous closed form solutions solution of an ill conditioned system of linear equations is not required the associated uniqueness results reduce in special cases to previous results for reconstruction from fourier transform real and imaginary part zero crossings

the bezoutian the hankel matrix output feedback and system eigenstructure abstract given a minimal linear time invariant system for which the transfer matrix has a right rp 1 and a left d 1 n coprime matrix fraction description an inverse relation is established between the block hankel matrix formed from the markov parameters of the eigenstructure of p and d and the generalized bezoutian matrix formed from the polynomial matrices r p n and d furthermore it is shown that all eigenstructures that are assignable by output feedback form the same markov parameters and this suggests a new approach to eigenstructure assignment

synthesis of accurate fractional gaussian noise by filtering this paper describes a method for generating long sample paths of accurate fractional gaussian noise fgn the increment process of fractional brownian motion fbm the method is based on a wold decomposition in which fgn is expressed as the output of a finite impulse response filter with discrete white gaussian noise as input the form of the ideal filter is derived analytically in the continuous time case for the finite length discrete time case an iterative projection algorithm incorporating a newton raphson step is described for computing the coefficients of a length n filter in a time approximately proportional to n fast convolution of discrete white gaussian noise with the computed filter impulse response yields arbitrarily long sequences which exactly match the correlation structure of fgn over a finite range of lags for values of the hurst parameter h smaller than a critical value hcritap0 85 and large n the finite length autocorrelation sequence of fgn is positive definite and this range of lags can be as large as the filter autocorrelation length when h h crit the finite length autocorrelation sequence of fgn is no longer positive definite and a modification is made to allow a wold decomposition the generated sequences then exactly match the autocorrelation structure of fgn over a more restricted range of lags which becomes smaller as h approaches unity

convergence of iterative nonexpansive signal reconstruction algorithms iterative algorithms for signal reconstruction from partial time and frequency domain knowledge have proven useful in a number of application areas in this paper a general convergence proof applicable to a general class of such iterative reconstruction algorithms is presented the proof relies on the concept of a nonexpansive mapping in both the time and frequency domains two examples studied in detail are time limited extrapolation equivalently band limited extrapolation and phase only signal reconstruction the proof of convergence for the phase only iteration is a new result obtained by this method of proof the generality of the approach allows the incorporation of nonlinear constraints such as time or space domain positivity or minimum and maximum value constraints finally the underrelaxed form of these iterations is also shown to converge even when the solution is not guaranteed to be unique

optical wavefront reconstruction theory and numerical methods optical wavefront reconstruction algorithms played a central role in the effort to identify gross manufacturing errors in nasa s hubble space telescope hst nasa s success with reconstruction algorithms on the hst has led to an effort to develop software that can aid and in some cases replace complicated expensive and error prone hardware among the many applications is hst s replacement the next generation space telescope ngst indent this work details the theory of optical wavefront reconstruction reviews some numerical methods for this problem and presents a novel numerical technique that we call extended least squares we compare the performance of these numerical methods for potential inclusion in prototype ngst optical wavefront reconstruction software we begin with a tutorial on rayleigh sommerfeld diffraction theory