algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws abstract in this work we modify a continuous galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures discrete entropy conditions are used to determine the minimal amount of entropy stabilization and constrain antidiffusive corrections of a property preserving low order scheme the addition of a second order entropy dissipative component to the antidiffusive part of a nearly entropy conservative numerical flux is generally insufficient to prevent violations of local bounds in shock regions our monolithic convex limiting technique adjusts a given target flux in a manner which guarantees preservation of invariant domains validity of local maximum principles and entropy stability the new methodology combines the advantages of modern entropy stable entropy conservative schemes and their local extremum diminishing counterparts the process of algebraic flux correction is based on inequality constraints which provably provide the desired properties no free parameters are involved the proposed algebraic fixes are readily applicable to unstructured meshes finite element methods general time discretizations and steady state residuals numerical studies of explicit entropy constrained schemes are performed for linear and nonlinear test problems

eigenvectors and functions of the discrete fourier transform a method is presented for computing an orthonormal set of eigenvectors for the discrete fourier transform dft the technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the dft it is also shown how fractional powers of the dft can be efficiently computed and possible applications to multiplexing and transform coding are suggested

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

discrete fractional fourier transform based on new nearly tridiagonal commuting matrices based on discrete hermite gaussian like functions a discrete fractional fourier transform dfrft which provides sample approximations of the continuous fractional fourier transform was defined and investigated recently in this paper we propose a new nearly tridiagonal matrix which commutes with the discrete fourier transform dft matrix the eigenvectors of the new nearly tridiagonal matrix are shown to be dft eigenvectors which are more similar to the continuous hermite gaussian functions than those developed before rigorous discussions on the relations between the eigendecomposition of the newly proposed nearly tridiagonal matrix and the dft matrix are described furthermore by appropriately combining two linearly independent matrices that both commute with the dft matrix we develop a method to obtain dft eigenvectors even more similar to the continuous hermite gaussian functions hgfs then new versions of dfrft produce their transform outputs closer to the samples of the continuous fractional fourier transform and their applications are described related computer experiments are performed to illustrate the validity of the works in this paper

one dimensional hadamard naturalness preserving transform reconstruction of signals degraded by nonstationary noise processes the problem of reconstructing a time varying one dimensional signal from segments of its hadamard naturalness preserving transform npt is considered closed form reconstruction formulas are derived for specific formats of available hadamard npt segments two fast reconstruction schemes which in a single iteration provide the same solution as the general iterative reconstruction algorithm are introduced for these formats simulation results of the algorithms when applied to first order gauss markov and image signals are good however the reconstruction of speech signals is poor due to the poor estimates derived from the available segments of the transformed signal the reconstruction algorithm is proposed for interframe two layer packet transmission of image signals over an orwell ring based network good pictorial results are obtained at up to 50 packet loss rate

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

discrete fourier invariant signals design and application in this paper two methods for the design of discrete fourier invariant signals are proposed the direct design method provides splitting between independent and dependent signal parts and calculation of the dependent part for any given independent part the iterative design method generates a family of discrete fourier invariant signals by a successive approach further we show how the proposed direct design method can be combined with the gabor uncertainty principle to generate discrete fourier invariant signals with the minimum product of their bandwidth b and their time width t we show that these signals as well as signal families generated with the iterative design method achieve the theoretical lower bt bound also it is shown that the bt product of discrete hermite gauss signals converges to the theoretical lower bound finally possible applications are illustrated in the case of time frequency spectral analysis using the obtained discrete fourier invariant signals as the window that provides isoresolution

generating and counting binary bent sequences two general classes of binary bent sequences bent based and linear based are introduced algorithms that allow easy generation of bent sequences from either class are given based on some simple computation and a computer search the authors conjecture a lower bound on the total number of binary bent sequences of a given order this lower bound is exact for bent sequences of order 16 a list is included from which all such sequences can be derived

stabilized galerkin approximation of convection diffusion reaction equations discrete maximum principle and convergence we analyze a nonlinear shock capturing scheme for h1 conforming piecewise affine finite element approximations of linear elliptic problems the meshes are assumed to satisfy two standard conditions a local quasi uniformity property and the xu zikatanov condition ensuring that the stiffness matrix associated with the poisson equation is an m matrix a discrete maximum principle is rigorously established in any space dimension for convection diffusion reaction problems we prove that the shock capturing finite element solution converges to that without shock capturing if the cell peclet numbers are sufficiently small moreover in the diffusion dominated regime the difference between the two finite element solutions super converges with respect to the actual approximation error numerical experiments on test problems with stiff layers confirm the sharpness of the a priori error estimates

the eigenstructure of finite field trigonometric transforms in this paper we discuss the eigenstructure of finite field trigonometric transforms fftt this transform family includes different types of cosine and sine transforms that correspond in the finite field case to the well known discrete cosine and sine transforms defined over the real numbers more specifically we determine the eigenvalues of the fftt matrices and study their multiplicities we propose procedures for constructing the associated eigenvectors applications of the developed theory to multiuser communication systems and error correcting codes are also suggested

a maximum principle preserving finite element method for scalar conservation equations this paper introduces a first order viscosity method for the explicit approximation of scalar conservation equations with lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension provided the lumped mass matrix is positive definite the method is shown to satisfy the local maximum principle under a usual cfl condition the method is independent of the cell type for instance the mesh can be a combination of tetrahedra hexahedra and prisms in three space dimensions

eigenvalues and eigenvectors of generalized dft generalized dht dct iv and dst iv matrices in this paper the eigenvalues and eigenvectors of the generalized discrete fourier transform gdft the generalized discrete hartley transform gdht the type iv discrete cosine transform dct iv and the type iv discrete sine transform dst iv matrices are investigated in a unified framework first the eigenvalues and their multiplicities of the gdft matrix are determined and the theory of commuting matrices is applied to find the real symmetric orthogonal eigenvectors set that constitutes the discrete counterpart of hermite gaussian function then the results of the gdft matrix and the relationships among these four unitary transforms are used to find the eigenproperties of the gdht dct iv and dst iv matrices finally the fractional versions of these four transforms are defined and an image watermarking scheme is proposed to demonstrate the effectiveness of fractional transforms

eigenvectors of ordinary generalized centered and offset discrete fourier transforms based on lookup table methods efficiency and approximation uses in this paper we first propose a methodology to construct an eigenvector of the n n discrete fourier transform dft matrix from any eigenvector of the k 2 n k 2 n dft matrix where k is a positive integer specifically using the procedure to down sample by k any k 2 n point dft eigenvector with zero as the initial index and then fold modulus n and add the resultant down sampled kn point vector we obtain an n point dft eigenvector computing an n point dft eigenvector using the proposed method is very efficient which requires only n k 1 additions and no multiplications with a pre stored lookup table of k 2 n point dft eigenvectors similar efficient methods are also developed to compute n point eigenvectors of other dft related transforms including the generalized dft gdft centered dft cdft and the offset dft odft from k 2 n point eigenvectors of their corresponding transforms or the dft as application examples we apply the proposed methods to compute n point dft gdft cdft and odft eigenvectors which are closer to samples of the continuous hermite gaussian function hgf than existing n point eigenvectors from their corresponding k 2 n point eigenvectors these improved n point hermite gaussian like eigenvectors can be used to define fractional versions of the various n n dft transforms whose outputs are closer to samples of the continuous fractional fourier transform than outputs of the corresponding existing fractional transforms finally we perform computer experiments to verify the effectiveness and demonstrate applications of our proposed methods

monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws abstract using the theoretical framework of algebraic flux correction and invariant domain preserving schemes we introduce a monolithic approach to convex limiting in continuous finite element schemes for linear advection equations nonlinear scalar conservation laws and hyperbolic systems in contrast to flux corrected transport fct algorithms that apply limited antidiffusive corrections to bound preserving low order solutions our new limiting strategy exploits the fact that these solutions can be expressed as convex combinations of bar states belonging to a convex invariant set of physically admissible solutions each antidiffusive flux is limited in a way which guarantees that the associated bar state remains in the invariant set and preserves appropriate local bounds there is no free parameter and no need for limit fluxes associated with the consistent mass matrix of time derivative term separately moreover the steady state limit of the nonlinear discrete problem is well defined and independent of the pseudo time step in the case study for the euler equations the components of the bar states are constrained sequentially to satisfy local maximum principles for the density velocity and specific total energy in addition to positivity preservation for the density and pressure the results of numerical experiments for standard test problems illustrate the ability of built in convex limiters to resolve steep fronts in a sharp and nonoscillatory manner

invariant domains and second order continuous finite element approximation for scalar conservation equations we propose a technique for approximating nonlinear scalar conservation equations that uses continuous finite elements and is formally at least second order accurate in space and maximum principle preserving the method is explicit in time uses unstructured continuous finite elements in space and works in any space dimension the stability and accuracy of the method are achieved by adapting the artificial viscosity

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

linear summation of fractional order matrices yeh and pei presented a computation method for the discrete fractional fourier transform dfrft that the dfrft of any order can be computed by a linear summation of dfrfts with special orders based on their work we investigate linear summation of fractional order matrices in a general and comprehensive manner in this paper we have found that for any diagonalizable periodic matrices linear summation of fractional order forms with special orders is related to the size and the period of the fractional order matrix moreover some properties and generalized results about linear summation of fractional order matrices are also presented

tridiagonal commuting matrices and fractionalizations of dct and dst matrices of types i iv v and viii in this paper we first establish new relationships in matrix forms among discrete fourier transform dft generalized dft gdft and various types of discrete cosine transform dct and discrete sine transform dst matrices two new independent tridiagonal commuting matrices for each of dct and dst matrices of types i iv v and viii are then derived from the existing commuting matrices of dft and gdft with these new commuting matrices the orthonormal sets of hermite like eigenvectors for dct and dst matrices can be determined and the discrete fractional cosine transform dfrct and the discrete fractional sine transform dfrst are defined the relationships among the discrete fractional fourier transform dfrft fractional gdft and various types of dfrct and dfrst are developed to reduce computations for dfrft and fractional gdft

generalized commuting matrices and their eigenvectors for dfts offset dfts and other periodic operations it is well known that some matrices such as dickinson steiglitz s matrix can commute with the discrete fourier transform dft and that one can use them to derive the complete and orthogonal dft eigenvector set recently candan found the general form of the dft commuting matrix in this paper we further extend the previous work and find the general form of the commuting matrix for any periodic quasi periodic and offset quasi periodic operations using the general commuting matrix we can derive the complete and orthogonal eigenvector sets for offset dfts dcts of types 1 4 5 and 8 dsts of types 1 4 5 and 8 discrete hartley transforms of types 1 and 4 the walsh transform and the projection operation the operation that maps a whole vector space into a subspace successfully moreover several novel ways of finding dft eigenfunctions are also proposed furthermore we also extend our theories to the continuous case i e if a continuous transform is periodic quasi periodic or offset quasi periodic such as the ft and some cyclic operations in optics we can find the general form of the commuting operation and then find the complete and orthogonal eigenfunctions set for the continuous transform

a second order maximum principle preserving lagrange finite element technique for nonlinear scalar conservation equations this paper proposes an explicit at least second order maximum principle sat isfying lagrange finite element method for solving nonlinear scalar conservation equations the technique is based on a new viscous bilinear form introduced in guermond and nazarov com put methods appl mech engrg 272 2014 pp 198 213 a high order entropy viscosity method and the boris book zalesak flux correction technique the algorithm works for arbitrary meshes in any space dimension and for all lipschitz fluxes the formal second order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

bearing estimation in the bispectrum domain a new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data the method is based on the asymptotic distribution of cross bispectrum estimates and uses maximum likelihood theory it is demonstrated that when the noise additive sources are spatially correlated gaussian with unknown cross spectral matrix csm the cross bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known csm analytical studies and simulations are given to document the performance of the new method

invariant domain preserving discretization independent schemes and convex limiting for hyperbolic systems abstract we introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving the method is discretization independent provided elementary symmetry and skew symmetry properties are satisfied by the scheme the method is formally first order accurate in space then we introduce a series of higher order methods when these methods violate the invariant domain properties they are corrected by a limiting technique that we call convex limiting after limiting the resulting methods satisfy all the invariant domain properties that are imposed by the user see theorem 7 24 and is formally high order accurate the two key novelties are that i limiting is done by enforcing bounds on quasiconcave functionals ii the bounds that are enforced on the solution at each time step are necessarily satisfied by the low order approximation

a transform based covariance differencing approach for some classes of parameter estimation problems a method of parameter estimation is presented for a class of problems in which the desired signal is embedded in colored noise with unknown covariance the proposed algorithm does not require multiple estimates of the signal covariance matrix instead it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while the signal component is transformed in some appropriate manner the noise component is then eliminated by forming the difference of the original and transformed covariance differencing methods to be applied to a wider class of problems than was previously possible this is illustrated by applying the algorithm to the problems of bearing estimation resolution of overlapping echos and transient response analysis simulation results demonstrate that the technique affords significant improvement in certain situations over conventional methods

entropy viscosity method for nonlinear conservation laws a new class of high order numerical methods for approximating nonlinear conservation laws is described entropy viscosity method the novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand this new approach does not use any flux or slope limiters applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation various benchmark problems are solved with finite elements spectral elements and fourier series to illustrate the capability of the proposed method

cumulant based approach to harmonic retrieval and related problems a frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored gaussian noise in practice the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density a cumulant based approach to these problems is proposed the cumulants of complex processes are defined and it is shown that specific 1 d slices of the fourth order cumulant of the noisy signal for the direction of arrival doa and retrieval of harmonics in noise rhn problems are identical to the autocorrelation of a related noiseless signal hence correlation based high resolution methods may be used with fourth order cumulants as well the effectiveness of the proposed methods is demonstrated through standard simulation examples

transform domain adaptive filters an analytical approach transform domain adaptive filters refer to lms filters whose inputs are preprocessed with a unitary data independent transformation followed by a power normalization stage the transformation is typically chosen to be the discrete fourier transform dft although other transformations such as the cosine transform dct the hartley transform dht or the walsh hadamard transform have also been proposed in the literature the resulting algorithms are generally called dft lms dct lms etc this preprocessing improves the eigenvalue distribution of the input autocorrelation matrix of the lms filter and as a consequence ameliorates its convergence speed in this paper we start with a brief intuitive explanation of transform domain algorithms we then analyze the effects of the preprocessing performed in dft lms and dct lms for first order markov inputs in particular we show that for markov 1 inputs of correlation parameter spl rho spl isin 0 1 the eigenvalue spread after dft and power normalization tends to 1 spl rho l 1 spl rho as the size of the filter gets large whereas after dct and power normalization it reduces to 1 spl rho for comparison the eigenvalue spread before transformation is asymptotically equal to 1 spl rho sup 2 1 spl rho sup 2 the analytical method used in the paper provides additional insight into how the algorithms work and is expected to extend to other input signal classes and other transformations

symmetric convolution and the discrete sine and cosine transforms this paper discusses the use of symmetric convolution and the discrete sine and cosine transforms dsts and dcts for general digital signal processing the operation of symmetric convolution is a formalized approach to convolving symmetrically extended sequences the result is the same as that obtained by taking an inverse discrete trigonometric transform dtt of the product of the forward dtts of those two sequences there are 16 members in the family of dtts each provides a representation for a corresponding distinct type of symmetric periodic sequence the author defines symmetric convolution relates the dsts and dcts to symmetric periodic sequences and then use these principles to develop simple but powerful convolution multiplication properties for the entire family of dsts and dcts symmetric convolution can be used for discrete linear filtering when the filter is symmetric or antisymmetric the filtering will be efficient because fast algorithms exist for all versions of the dtts conventional linear convolution is possible if one first zero pad the input data symmetric convolution and its fast implementation using dtts are now an alternative to circular convolution and the dft

digital computation of the fractional fourier transform an algorithm for efficient and accurate computation of the fractional fourier transform is given for signals with time bandwidth product n the presented algorithm computes the fractional transform in o nlogn time a definition for the discrete fractional fourier transform that emerges from our analysis is also discussed

generalized discrete hartley transforms the discrete hartley transform is generalized into four classes in the same way as the generalized discrete fourier transform fast algorithms for the resulting transforms are derived the generalized transforms are expected to be useful in applications such as digital filter banks fast computation of the discrete hartley transform for any composite number of data points fast computations of convolution and signal representation the fast computation of skew circular convolution by the generalized transforms for any composite number of data points is discussed in detail

second order invariant domain preserving ale approximation of hyperbolic systems abstract in this paper we introduce an invariant domain preserving arbitrary lagrangian eulerian method for solving hyperbolic systems the time stepping is explicit and the approximation in space is done with continuous finite elements the method is second order in space and made invariant domain preserving by using a newly introduced convex limiting technique

direction finding algorithms based on high order statistics two direction finding algorithms are presented for nongaussian signals which are based on the fourth order cumulants of the data received by the array the first algorithm is similar to music while the second is asymptotically minimum variance in a certain sense the first algorithm requires singular value decomposition of the cumulant matrix while the second is based on nonlinear minimization of a certain cost function the performance of the minimum variance algorithm can be assessed by analytical means at least for the case of discrete probability distributions of the source signals and spatially uncorrelated gaussian noise the numerical experiments performed seem to confirm the insensitivity of these algorithms to the gaussian noise parameters

a partition of unity approach to adaptivity and limiting in continuous finite element methods abstract the partition of unity finite element method pufem proposed in this paper makes it possible to blend space and time approximations of different orders in a continuous manner the lack of abrupt changes in the local mesh size h and polynomial degree p simplifies implementation and eliminates the need for using sophisticated hierarchical data structures in contrast to traditional h p adaptivity for finite elements the proposed approach preserves discrete conservation properties and the continuity of traces at common boundaries of adjacent mesh cells in the context of space discretizations a continuous blending function is used to combine finite element bases corresponding to high order polynomials and piecewise linear approximations based on the same set of nodes in a similar vein spatially partitioned time discretizations can be designed using weights that depend continuously on the space variable the design of blending functions may be based on a priori knowledge e g in applications to problems with singularities or boundary layers local error estimates smoothness indicators and or discrete maximum principles in adaptive methods changes of the finite element approximation exhibit continuous dependence on the data the presented numerical examples illustrate the typical behavior of local h 1 and l 2 errors

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

cumulant based identification of multichannel moving average models given cumulants of a stationary perhaps noisy non gaussian r variate moving average ma q process identifiability conditions are studied under which the ma coefficient matrices the input statistics and the order q can be uniquely determined the selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves fewer restrictions than that corresponding to a given covariance structure two algorithms are derived for estimating the possibly nonminimum phase ma coefficient matrices

a discrete commutator theory for the consistency and phase error analysis of semi discrete c 0 finite element approximations to the linear transport equation a novel method based on a discrete commutator for the analysis of consistency error and phase relations for semi discrete continuous finite element approximation of the one way wave equation is presented the technique generalizes to arbitrary dimension accommodates the use of compatible quadratures does not require the use of complex calculations is applicable on non uniform mesh geometries and is especially useful when conventional taylor series or fourier approaches are intractable following the theory the analysis method is demonstrated for several test cases

subcell flux limiting for high order bernstein finite element discretizations of scalar hyperbolic conservation laws abstract this work extends the concepts of algebraic flux correction and convex limiting to continuous high order bernstein finite element discretizations of scalar hyperbolic problems using an array of adjustable diffusive fluxes the standard galerkin approximation is transformed into a nonlinear high resolution scheme which has the compact sparsity pattern of the piecewise linear or multilinear subcell discretization the representation of this scheme in terms of invariant domain preserving states makes it possible to prove the validity of local discrete maximum principles under cfl like conditions in contrast to predictor corrector approaches based on the flux corrected transport methodology the proposed flux limiting strategy is monolithic i e limited antidiffusive terms are incorporated into the well defined residual of a nonlinear semi discrete problem a stabilized high order galerkin discretization is recovered if no limiting is performed in the limited version the compact stencil property prevents direct mass exchange between nodes that are not nearest neighbors a formal proof of sparsity is provided for simplicial and box elements the involved element contributions can be calculated efficiently making use of matrix free algorithms and precomputed element matrices of the reference element numerical studies for q 2 discretizations of linear and nonlinear two dimensional test problems illustrate the virtues of monolithic convex limiting based on subcell flux decompositions

the discrete fractional fourier transform we propose and consolidate a definition of the discrete fractional fourier transform that generalizes the discrete fourier transform dft in the same sense that the continuous fractional fourier transform generalizes the continuous ordinary fourier transform this definition is based on a particular set of eigenvectors of the dft matrix which constitutes the discrete counterpart of the set of hermite gaussian functions the definition is exactly unitary index additive and reduces to the dft for unit order the fact that this definition satisfies all the desirable properties expected of the discrete fractional fourier transform supports our confidence that it will be accepted as the definitive definition of this transform

discrete fractional fourier transform based on orthogonal projections the continuous fractional fourier transform frft performs a spectrum rotation of signal in the time frequency plane and it becomes an important tool for time varying signal analysis a discrete fractional fourier transform has been developed by santhanam and mcclellan see ibid vol 42 p 994 98 1996 but its results do not match those of the corresponding continuous fractional fourier transforms we propose a new discrete fractional fourier transform dfrft the new dfrft has dft hermite eigenvectors and retains the eigenvalue eigenfunction relation as a continous frft to obtain dft hermite eigenvectors two orthogonal projection methods are introduced thus the new dfrft will provide similar transform and rotational properties as those of continuous fractional fourier transforms moreover the relationship between frft and the proposed dfrft has been established in the same way as the conventional dft to continuous fourier transform

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

a cumulant based hankel approach to direction of arrival estimation a new cumulant based approach to doa estimation for independent nongaussian sources and a uniform linear array is presented the doas are obtained by finding the eigenvalues of a matrix made up from cumulants of the data as with other cumulant based methods the present method does not need the characteristics of the noise when the noise is gaussian this algorithm is developed using an approach that leads to a general relation between the cumulant functions and the parameters to be estimated this general relation gives a common framework for developing other algorithms for doa estimation computer simulation results show the effectiveness of this new method

a naturalness preserving transform for image coding and reconstruction we have developed a new image transform that possesses some unusual properties that may be useful for some special applications especially for those instances in which the communications must pass through channels whose quality and characteristics are unpredictable due to nonstationary noise processes or jamming we present an example of a use for the new transform that can be characterized as a man in the loop error correction procedure a stable and an efficient algorithm has been developed for the proposed correction scheme and the algorithm is amenable for an array processor the algorithm is shown to be superior to the conventional least squares type algorithms and can operate in near real time

a note on the eigenvectors of hadamard matrices of order 2n abstract a set of 2n mutually orthogonal eigenvectors of hadamard matrices of order 2n are explicitly derived and their properties are developed an instance of pell s equation driven by the thue morse sequence is noted

invariant regions for systems of conservation laws on decrit des conditions necessaires et suffisantes pour qu une region dans r n soit invariante pour des solutions du systeme de n lois de conservations u t f u x o

generalized eigenvectors and fractionalization of offset dfts and dcts the offset discrete fourier transform dft is a discrete transform with kernel exp j2 spl pi m a n b n it is more generalized and flexible than the original dft and has very close relations with the discrete cosine transform dct of type 4 dct iv dct viii discrete sine transform dst iv dst viii and discrete hartley transform dht iv in this paper we derive the eigenvectors eigenvalues of the offset dft especially for the case where a b is an integer by convolution theorem we can derive the close form eigenvector sets of the offset dft when a b is an integer we also show the general form of the eigenvectors in this case then we use the eigenvectors eigenvalues of the offset dft to derive the eigenvectors eigenvalues of the dct iv dct viii dst iv dst viii and dht iv after the eigenvectors eigenvalues are derived we can use the eigenvectors decomposition method to derive the fractional operations of the offset dft dct iv dct viii dst iv dst viii and dht iv these fractional operations are more flexible than the original ones and can be used for filter design data compression encryption and watermarking etc