iterative time limited signal restoration the purpose of this paper is to show that time limited restoration of shift invariant blurred signals can be done by means of fixed point solutions of contraction mappings under rather general conditions for the distortion operator all our results are valid for multidimensional signals an application of these results to the iterative extrapolation of band limited discrete images is shown

tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

chebyshev series method for computing weighted quadrature formulas abstract in this paper we study convergence and computation of interpolatory quadrature formulas with respect to a wide variety of weight functions the main goal is to evaluate accurately a definite integral whose mass is highly concentrated near some points the numerical implementation of this approach is based on the calculation of chebyshev series and some integration formulas which are exact for polynomials in terms of accuracy the proposed method can be compared with rational gauss quadrature formula

error analysis of a class of constrained iterative restoration algorithms in this paper we investigate the problem of noise stability in a class of iterative image restoration algorithms the algorithm is a gerchberg papoulis type algorithm that utilizes incomplete information and partial constraints to specify constraint operators for the iteration the iteration in the absence of noise converges to a unique solution in the presence of noise the restoration is considered as an ill posed problem in this study noise stability of the algorithm is investigated a general error analysis method is derived to predict the optimum number of iterations that minimizes the mean square error between the ideal and the restored image the tradeoff between signal reconstruction and noise amplification has been investigated and it has been shown that by using prior knowledge of the signal and noise statistics it is possible to achieve optimal restoration simulations have been performed to verify the theoretical results

hypersingular integral equations past present future abstract in this address attention is paid to solving hypersingular integral equations and also to its extension supersingular integral equations firstly a short discussion is given of the historical development of these mathematical tools secondly the author s own experience in solving such problems is discussed lastly a glimpse of the future is offered by looking at some of the present techniques for solving hypersingular integral equations

regularized iterative image restoration with ringing reduction linear space invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions it is shown that these artifacts are attributable to the regularization of the ill posed image restoration problem two possible methods to reduce the ringing effects in restored images are proposed the first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm the second method locally regulates the severity of the noise magnification and the ringing phenomenon depending on the edge information in the image a regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted hilbert space both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction

image representation by one bit fourier phase theory sampling and coherent image model the problem of recovering an image from its fourier transform phase quantized to one bit or equivalently finding the locations of the zero crossings of the real part of the fourier transform is addressed theoretical results are presented that set an algebraic condition under which real zero crossings uniquely specify a band limited image it is then shown that sampling in the frequency domain presents a major obstacle to obtaining good reconstruction results the one bit fourier phase reconstruction problem is then considered when the original image is coherent i e the image phase is random and highly uncorrelated examples are given which demonstrate that the information loss produced by frequency sampling is not as severe as that in the nonclassical problem motivated by digital phase only holograms a known random diffuser is used as the image phase and a well known iterative reconstruction procedure is extended to incorporate the knowledge of the image phase at each stage of the iteration this reconstruction method produces good image quality by using a few iterations unlike its noncoherent counterpart

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

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

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

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

fast reconstruction of linearly distorted signals a product expansion of the inverse operator is used to derive a class of iterative algorithms that have a pth order rate of convergence compared to the linear algorithm the number of iterations required to obtain a given reconstruction is reduced from p sup n to n the primary difference between these algorithms and the linear algorithm is that they update both the estimate of x and the operator d rather than the estimate alone several methods that may be used to incorporate linear and nonlinear constraints are also proposed finally some examples of linear inverse problems are presented and the differences in rates of convergence for the linear and the pth order algorithms are compared

the numerical evaluation of hadamard finite part integrals a quadrature rule is described for the numerical evaluation of hadamard finite part integrals with a double pole singularity within the range of integration the rule is based upon the observation that such an integral is the derivative of a cauchy principal value integral

some aspects of band limited signal extrapolation models discrete approximations and noise we present some theoretical results on the band limited signal extrapolation problem in section i we describe four basic models for the extrapolation problem these models are useful in understanding the relationship between the continuous extrapolation problem and some discrete algorithms given in 1 and 2 one of these models was shown to approximate the continuous band limited extrapolation problem 3 another model is obtained when the discrete fourier transform dft is used to implement the well known iterative algorithm given in 4 and 5 which was designed for solving the continuous extrapolation problem in section ii this model is related to the continuous model by means of an interesting approximation theorem also an important conjecture is presented section iii shows some approximation results specifically we prove that some discrete discrete and discrete continuous extrapolations of noisy signals converge to solutions of a certain continuous continuous noisy extrapolation problem when the noise is bounded by a known number max eta x leq epsilon this convergence is obtained by using normal families of entire functions in nand some other complex analysis tools we also show that the extrapolation problem is very sensitive to noise even in cases where only small amounts of extrapolation are desired this result indicates that in the presence of noise extrapolation techniques should be used judiciously in order to obtain reasonable results

an algorithm to find two dimensional signals with specified zero crossings we present an iterative method for finding two dimensional band limited functions with predetermined zero crossings this problem arises when we want to generate a prescribed binary image at the output of a diffraction limited imaging system with high contract recording an important application of this image generation problem is in the design of masks for microlithography after describing the algorithm a proof of its convergence based on the properties of nonexpansive mappings is given the relevance of this algorithm to the image construction problem is then discussed and we conclude by illustrating two patterns generated by our proposed method

a new extrapolation algorithm for band limited signals using the regularization method the ill posedness of the extrapolation problem in the presence of noise is considered a stable algorithm is constructed by solving a fredholm equation based on a regularization method the algorithm appears relatively robust since the noise eta sub delta t is taken as a function in l sup 2 t t t 0 such that the error energy integral mod eta sub delta t mod sup 2 dt

hypersingular integrals how smooth must the density be hypersingular integrals are guaranteed to exist at a point x only if the density function f in the integrand satises certain conditions in a neighbourhood of x it is well known that a su cient condition is that f has a holder continuous rst derivative this is a stringent condition especially when it is incorporated into boundary element methods for solving hypersingular in tegral equations this paper is concerned with nding weaker conditions for the existence of one dimensional hadamard nite part integrals it is shown that it is sucien t for the even part of f with respect to x to have a holder continuous rst derivative the odd part is al lowed to be discontinuous a similar condition is obtained for cauchy principal value integrals these simple results have non trivial consequences they are applied to the calculation of the tangential derivative of a single layer potential and to the normal derivative of a double layer potential particular attention is paid to discontinuous densities and to discontinuous boundary conditions also despite the weaker sucien t conditions it is rearmed that for hypersingular integral equations collocation at a point x at the junction between two standard conforming boundary elements is not permissible theoretically various modications to the denition of nite part integral are explored

convergence and computation of simultaneous rational quadrature formulas we discuss the convergence and numerical evaluation of simultaneous quadrature formulas which are exact for rational functions the problem consists in integrating a single function with respect to different measures using a common set of quadrature nodes given a multi index n the nodes of the integration rule are the zeros of the multi orthogonal hermite pade polynomial with respect to s n where s is a collection of measures and is a polynomial which modifies the measures in s the theory is based on the connection between gauss type simultaneous quadrature formulas of rational type and multipoint hermite pade approximation the numerical treatment relies on the technique of modifying the integrand by means of a change of variable when it has real poles close to the integration interval the output of some tests show the power of this approach in comparison with other ones in use

a note on iterative fourier transform phase reconstruction from magnitude in this correspondence a well known iterative procedure for fourier transform phase reconstruction from magnitude usually referred to as the gerchberg saxton fienup procedure is revisited the convergence of this algorithm has raised some controversy in the recent literature in this correspondence we first point out a potential source of error in the numerical implementation of the algorithm then we present a conjecture which would explain why this algorithm sometimes fails

tensor algebras of c correspondences and their c envelopes abstract we show that the c envelope of the tensor algebra of an arbitrary c correspondence x coincides with the cuntz pimsner algebra o x as defined by katsura t katsura on c algebras associated with c correspondences j funct anal 217 2004 366 401 this improves earlier results of muhly and solel p s muhly b solel tensor algebras over c correspondences representations dilations and c envelopes j funct anal 158 1998 389 457 and fowler muhly and raeburn n fowler p muhly i raeburn representations of cuntz pimsner algebras indiana univ math j 52 2003 569 605 who came to the same conclusion under the additional hypothesis that x is strict and faithful

numerical evaluation of hypersingular integrals abstract boundary integral equations which employ integrals which exist only if defined in the cauchy principal value sense or as the hadamard finite part are currently used with success to solve many two and three dimensional problems of applied mechanics we will recall definitions and main properties of these integrals examine some numerical approaches for their evaluation and present several new results

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

signal reconstruction from noisy partial information of its transform the usual assumption that the available partial information is noiseless is replaced by a more realistic statistical model which compensates for the presence of noise the signal reconstruction is thus viewed as a parameter estimation problem for which the em iterative algorithm of a p dempster n m laird and d b rubin j roy stat soc b vol 39 p 1 37 1977 is especially suitable the posterior probability of the signal increases from iteration to iteration till the signal converges to a stationary point of the posterior distribution each iteration involves one transformation followed by an inverse transformation usually discrete fourier transformation dft and inverse dft algorithms for reconstruction of both one and two dimensional signals from their spectral magnitude spectral phase or modified short time fourier transform are typical examples of the proposed scheme

iterative least squares estimators in nonlinear image restoration the concept of iterative least squares estimation as applied to nonlinear image restoration is considered regarding the convergence analysis of nonlinear iterative algorithms the potential of the global convergence theorem gct is explored the theoretical analysis is performed on a general class of nonlinear algorithms which defines a signal dependent linear mapping of the residual the descent properties of two normed functions are considered furthermore a procedure for the selection of the iteration parameter is introduced the steepest descent sd iterative approach for the solution of the least squares optimization problem is introduced the convergence properties of the particular algorithm are readily derived on the basis of the generalized analysis and the gct the factors that affect the convergence rate of the sd algorithm are thoroughly studied in the case of the sd algorithm structural modifications are proposed and two hybrid sd algorithms attain convergence in a more uniform fashion with respect to their entries in general the algorithms achieve larger convergence rates than the conventional sd technique

an effective method for numerical evaluation of general 2d and 3d high order singular boundary integrals in this paper a robust method is presented for numerical evaluation of weakly strongly hyper and super singular boundary integrals which exist in the cauchy principal value sense in two and three dimensional problems in this method the singularities involved in integration kernels are analytically removed by expressing the non singular parts of the integration kernels as power series in the local distance of the intrinsic coordinate system for three dimensional boundary integrals the radial integration method 1 is applied to transform the surface integral into a line integral over the contour of the surface and to remove various orders of singularities within the radial integrals some examples are provided to verify the correctness and robustness of the presented method

quadrature formulas based on rational interpolation we consider quadrature formulas based on interpolation using the ba sis functions 1 1 tkx k 1 2 3 on 1 1 where tk are parameters on the interval 1 1 we investigate two types of quadratures quadrature formulas of maximum accuracy which correctly integrate as many basis functions as possible gaussian quadrature and quadrature formulas whose nodes are the zeros of the orthogonal functions obtained by orthogonalizing the system of basis functions or thogonal quadrature we show that both approaches involve orthogonal polynomials with modified or varying weights which depend on the number of quadrature nodes the asymptotic distribution of the nodes is obtained as well as various interlacing properties and monotonicity results for the nodes

multitone signals with low crest factor after an introductory discussion of real valued and complex signals it is shown that minimizing the crest factor cf of multitone signals is closely related to the construction of complex sequences with low sidelobes in their aperiodic autocorrelation function inspired by this observation a lower bound on the achievable cf is derived four differing algorithms for the reduction of the cf of complex multitone signals are compared with each other by computer simulation the preferred algorithm is presented in detail and its convergence is proven examples of multitone signals with up to 15 tones and lower cf than previously reported in the literature are given

crossed products of operator algebras applications of takai duality abstract let g be a partially ordered abelian group with haar measure let a g be a dynamical system and let a be the associated semicrossed product using takai duality we establish a stable isomorphism a s a k g ad g where k g denotes the compact operators in the csl algebra alg l g and denotes the right regular representation of g we also show that there exists a complete lattice isomorphism between the invariant ideals of a and the ad invariant ideals of a k g using takai duality we also continue our study of the radical for the crossed product of an operator algebra and we solve open problems stemming from the earlier work of the authors among others we show that the crossed product of a radical operator algebra by a compact abelian group is a radical operator algebra we also show that the permanence of semisimplicity fails for crossed products by r a final section of the paper is devoted to the study of radically tight dynamical systems i e dynamical systems a g for which the identity rad a g rad a g persists a broad class of such dynamical systems is identified

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

evaluation of finite part integrals using a regularization technique that decreases instability a hypersingular integral can be regularized by replacing the whole integrand by a forward difference quotient of 2nd order if the density function is nearly singular then gauss quadrature formulas associated with a suitable modification of the chebyshev weight function allow to obtain great precision with few nodes however in most cases the own nature of this procedure makes unpredictable the location of quadrature nodes this paper presents a simple but effective technique whose aim is to mitigate instability when some node lies too close to the pole some numerical examples are shown to evaluate the performance of the proposed method

a class of c algebras generalizing both graph algebras and homeomorphism c algebras i fundamental results we introduce a new class of c algebras which is a generalization of both graph algebras and homeomorphism c algebras this class is very large and also very tractable we prove the so called gauge invariant unique ness theorem and the cuntz krieger uniqueness theorem and compute the k groups of our algebras

interpolation and the discrete papoulis gerchberg algorithm analyze the performance of an iterative algorithm similar to the discrete papoulis gerchberg algorithm and which can be used to recover missing samples in finite length records of band limited data no assumptions are made regarding the distribution of the missing samples in contrast with the often studied extrapolation problem in which the known samples are grouped together indeed it is possible to regard the observed signal as a sampled version of the original one and to interpret the reconstruction result studied as a sampling result the authors show that the iterative algorithm converges if the density of the sampling set exceeds a certain minimum value which naturally increases with the bandwidth of the data they give upper and lower bounds for the error as a function of the number of iterations together with the signals for which the bounds are attained also they analyze the effect of a relaxation constant present in the algorithm on the spectral radius of the iteration matrix from this analysis they infer the optimum value of the relaxation constant they also point out among all sampling sets with the same density those for which the convergence rate of the recovery algorithm is maximum or minimum for low pass signals it turns out that the best convergence rates result when the distances among the missing samples are a multiple of a certain integer the worst convergence rates generally occur when the missing samples are contiguous

on a conjecture of j l c sanz and t s huang in 1 j l c sanz and t s huang conjectured that the dft implementation of the papoulis gerchberg algorithm for the extrapolation of band limited signals does approach the continuous extrapolation in this respect we prove a result on the approximation of band limited functions by trigonometric polynomials simultaneously increasing its degree and the period length this will imply that the above conjecture is indeed true

the hyperrigidity of tensor algebras of c correspondences abstract given a c correspondence x we give necessary and sufficient conditions for the tensor algebra t x to be hyperrigid in the case where x is coming from a topological graph we obtain a complete characterization

a general algorithm for evaluating nearly singular integrals in anisotropic three dimensional boundary element analysis abstract this paper presents a new general method for the evaluation of nearly singular boundary element integrals arising in anisotropic three dimensional 3d boundary element analysis it is shown that the original nearly singular integrals can be transformed into using a sinh function an element by element sum of regular integrals each one expressed in terms of intrinsic local coordinates as a consequence the actual computation can be performed by using standard n n gaussian quadrature and the procedure can be easily included in any existing computer code this new method has full generality and therefore can be applied to a wide class of integrals the numerical results demonstrate the accuracy and efficiency of the method along with its insensitivity to the location of the nearly singular points it is shown that several orders of magnitude improvement in relative errors can be obtained using this transformation when compared to a straightforward implementation of gaussian quadrature

quadrature rules for weakly singular strongly singular and hypersingular integrals in boundary integral equation methods we present n point gauss gegenbauer quadrature rules for weakly singular strongly singular and hypersingular integrals that arise in integral equation formulations of potential problems in domains with edges and corners the rules are tailored to weight functions with algebraic endpoint singularities related to the geometrical singularities of the domain each rule has two different expressions involving legendre functions and hypergeometric functions respectively numerical examples amply demonstrate the accuracy and stability of the proposed algorithms application to the solution of a singular integral equation is exemplified

certain free products of graph operator algebras abstract we develop a notion of a generalized cuntz krieger family of projections and partial isometries where the range of the partial isometries need not have trivial intersection we associate to these generalized cuntz krieger families a directed graph with a coloring function on the edge set we call such a directed graph an edge colored directed graph we then study the c algebras and the non selfadjoint operator algebras associated to edge colored directed graphs these algebras arise as free products of directed graph algebras with amalgamation we then determine the c envelopes for a large class of the non selfadjoint algebras finally we relate properties of the edge colored directed graphs to properties of the associated c algebra including simplicity and nuclearity using the free product description of these algebras we investigate the k theory of these algebras

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

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

reconstruction of signals from phase efficient algorithms segmentation and generalizations in this paper we develop several new formulations of the phase only reconstruction problem which lead to new efficient algorithms for signal reconstruction we describe a procedure for approximately reconstructing a long duration signal from short segments phase only blind deconvolution for linear phase filters relies on mirror image symmetry in the filter transfer function h z we generalize this deconvolution result to include several other types of symmetries for h z

the use of rational functions in numerical quadrature quadrature problems involving functions that have poles outside the interval of integration can profitably be solved by methods that are exact not only for polynomials of appropriate degree but also for rational functions having the same or the most important poles as the function to be integrated constructive and computational tools for accomplishing this are described and illustrated in a number of quadrature contexts the superiority of such rational polynomial methods is shown by an analysis of the remainder term and documented by numerical examples

implementation of 2 d digital filters by iterative methods a two dimensional 2 d rational filter can be implemented by an iterative computation involving only finite extent impulse response fir filtering operations provided a certain convergence criterion is met in this paper we generalize this procedure so that the convergence criterion is satisfied for any stable 2 d rational transfer function one formulation which guarantees convergence invokes a relaxed form of the iterative computation along with prefiltering the numerator and denominator polynomials of the rational transfer function this implementation may be applied with a frequency varying relaxation parameter for increasing the rate of convergence an alternative generalization uses several previously computed iterates unlike our first modification which utilizes only the most recently computed iterate this formulation can potentially guarantee convergence and also increase the convergence rate without the requirement of prefiltering another extension of the iterative computation incorporates constraints e g positivity or finite extent on the output of each iteration proof of convergence of such constrained iterations relies on the concept of a nonexpansive operator in particular the error introduced within the converging solution resulting from a finite extent constraint is shown to satisfy a homogeneous partial difference equation finally this error computation leads to an important link between our iterative implementation with constraints and an iterative solution to partial difference equations e g laplace s equation with known boundary conditions

af embeddability of crossed products of cuntz algebras abstract we investigate crossed products of cuntz algebras by quasi free actions of abelian groups we prove that our algebras are af embeddable when actions satisfy a certain condition we also give a necessary and sufficient condition that our algebras become simple and purely infinite and consequently our algebras are either purely infinite or af embeddable when they are simple

noncausal nonminimum phase arma modeling of non gaussian processes a method is presented for the estimation of the parameters of a noncausal nonminimum phase arma model for non gaussian random processes using certain higher order cepstra slices the fourier phases of two intermediate sequences h sub min n and h sub max n can be computed where h sub min n is composed of the minimum phase parts of the ar and ma models and h sub max n of the corresponding maximum phase parts under the condition that there are no zero pole cancellations in the arma model these two sequences can be estimated from their phases only and lead to the reconstruction of the ar and ma parameters within a scalar and a time shift the ar and ma orders do not have to be estimated separately but they are by product of the parameter estimation procedure through simulations it is shown that unlike existing methods the estimation procedure is fairly robust if a small order mismatch occurs since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h sub min n and h sub max n the phase errors due to finite length data are studied and their statistics are derived

gaussian rational quadrature formulas for ill scaled integrands a flexible treatment of gaussian quadrature formulas based on rational functions is given to evaluate the integral if x w x dx when f is meromorphic in a neighborhood v of the interval i and w x is an ill scaled weight function some numerical tests illustrate the power of this approach in comparison with gautschi s method