linear phase cosine modulated maximally decimated filter banks with perfect reconstruction we propose a novel way to design maximally decimated fir cosine modulated filter banks in which each analysis and synthesis filter has a linear phase the system can be designed to have either the approximate reconstruction property pseudo qmf system or perfect reconstruction property pr system in the pr case the system is a paraunitary filter bank as in earlier work on cosine modulated systems all the analysis filters come from an fir prototype filter however unlike in any of the previous designs all but two of the analysis filters have a total bandwidth of 2 spl pi m rather than spl pi m where 2m is the number of channels in our notation a simple interpretation is possible in terms of the complex hypothetical analytic signal corresponding to each bandpass subband the coding gain of the new system is comparable with that of a traditional m channel system rather than a 2m channel system this is primarily because there are typically two bandpass filters with the same passband support correspondingly the cost of the system in terms of complexity of implementation is also comparable with that of an m channel system we also demonstrate that very good attenuation characteristics can be obtained with the new system

general synthesis procedures for fir lossless transfer matrices for perfect reconstruction multirate filter bank applications a recently reported procedure see ibid vol assp 35 p 476 492 apr 1987 and proc ieee int conf acoust speech sig processing apr 1987 p 2169 2172 for the design of m channel perfect reconstruction quadrature mirror filter qmf bands uses the concept of lossless alias component matrices the synthesis of such qmf banks centers around the generation of a lossless m m finite impulse response fir transfer matrix e z recent results for such generation have been somewhat ad hoc i e not sufficiently general a general procedure is outlined for the generation of such transfer matrices the procedure is based on a cascaded lattice structure derived from a state space viewpoint the structure is such that it generates only m m lossless fir transfer matrices regardless of parameter values and conversely any m m lossless fir transfer matrix can be obtained by a suitable choice of parameters these parameters turn out to be angles theta sub k and the structure is such that the number of angles is minimal a design example is presented to demonstrate the main results

global stability of volterra models with time delay abstract easily verifiable conditions are obtained for the global stability of the positive steady state in volterra models with discrete and distributed time delays

perfect reconstruction fir filter banks some properties and factorizations perfect reconstruction finite impulse response fir filter banks are analyzed both in the z transform and time domains showing the alternatives between designs in the two domains various classes of perfect reconstruction schemes are indicated and relations between previously known systems are given windowed modulated filter banks with low computational complexity and perfect reconstruction are shown new factorizations of polyphase filter matrices leading in particular to linear phase filters are given the computational complexity and the architecture of the new structures are indicated

stability criteria for a system involving two time delays a system of two autonomous ordinary differential equations with two discrete time delays is considered with a view to determining the stability of equilibria using the nyquist criterion on the characteristic equation estimates on the length of delays are given for which a system which is stable in the absence of delays remains stable conditions are also derived for there to be no change in stability even for unbounded delays the above mentioned criteria are applied to a system modeling competitive interacting populations and to a predator prey system

on m channel linear phase fir filter banks and application in image compression this paper investigates the theory and structure of a large subclass of m channel linear phase perfect reconstruction fir filter banks systems with analysis and synthesis filters of length l sub i k sub i m spl beta where spl beta is an arbitrary integer 0 spl les spl beta m and k sub i is any positive integer for this subclass of systems we first investigate the necessary conditions for the existence of linear phase perfect reconstruction filter banks lpprfbs next we develop a complete and minimal factorization for all even channel linear phase paraunitary systems the most general lapped orthogonal transforms to date finally several design examples as well as comparisons with previous generalized lapped orthogonal transforms genlots in image compression are presented to confirm the validity of the theory

the lot transform coding without blocking effects an exact derivation of an optimal lapped orthogonal transform lot is presented the optimal lot is related to the discrete cosine transform dct in such a way that a fast algorithm for a nearly optimal lot is derived compared to the dct the fast lot requires about 20 30 more computations mostly additions an image coding example demonstrates the effectiveness of the lot in reducing blocking effects the lot actually leads to slightly smaller signal reconstruction errors than does the dct

parallel auxiliary space amg solver for h div problems in this paper we present a family of scalable preconditioners for matrices arising in the discretization of h div problems using the lowest order raviart thomas finite elements our approach belongs to the class of auxiliary space based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities we provide a detailed algebraic description of the theory parallel implementation and different variants of this parallel auxiliary space divergence solver ads and discuss its relations to the hiptmair xu hx auxiliary space decomposition of h div siam j numer anal 45 2007 pp 2483 2509 and to the auxiliary space maxwell solver ams j comput math 27 2009 pp 604 623 an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large scale h div problems with large jumps in the material coefficients

linear phase paraunitary filter banks theory factorizations and designs m channel maximally decimated filter banks have been used in the past to decompose signals into subbands the theory of perfect reconstruction filter banks has also been studied extensively nonparaunitary systems with linear phase filters have also been designed the authors study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase specific instances of this problem have been addressed by other authors and linear phase paraunitary systems have been shown to exist this property is often desirable for several applications particularly in image processing they begin by answering several theoretical questions pertaining to linear phase paraunitary systems next they develop a minimal factorization for a large class of such systems this factorization will be proved to be complete for even m further they structurally impose the additional condition that the filters satisfy pairwise mirror image symmetry in the frequency domain this significantly reduces the number of parameters to be optimized in the design process they then demonstrate the use of these filter banks in the generation of m band orthonormal wavelets several design examples are also given to validate the theory

a development of symmetric extension method for subband image coding describes the development of a technique for subband image coding called the symmetric extension method which utilizes the nature of a symmetrically extended image to achieve high quality coding there are however some restrictions on the usable subband coding system the development is done based on the property of a symmetrically extended signal in the analysis process to remove the restriction the behavior of the sequence after two processes filtering and decimation is examined and formulated the development extends the application area of the technique

linear multifrequency grey acceleration recast for preconditioned krylov iterations the linear multifrequency grey acceleration lmfga technique is used to accelerate the iterative convergence of multigroup thermal radiation diffusion calculations in high energy density simulations although it is effective and efficient in one dimensional calculations the lmfga method has recently been observed to significantly degrade under certain conditions in multidimensional calculations with large discontinuities in material properties to address this deficiency we recast the lmfga method in terms of a preconditioned system that is solved with a krylov method lmfgk results are presented demonstrating that the new lmfgk method always requires fewer iterations than the original lmfga method the reduction in iteration count increases with both the size of the time step and the inhomogeneity of the problem however for reasons later explained the lmfgk method can cost more per iteration than the lmfga method resulting in lower but comparable efficiency in problems with small time steps and weak inhomogeneities in problems with large time steps and strong inhomogeneities the lmfgk method is significantly more efficient than the lmfga method

hopf bifurcation and global stability for a delayed predator prey system with stage structure for predator abstract in this paper a delayed predator prey system with stage structure for predator is proposed and studied it is found that the time delay is harmless for permanence of the stage structured system if 1 we show that the unique positive equilibrium is locally asymptotically stable when time delay is sufficiently small while loss of stability by a hopf bifurcation can occur as the delay increases

global stability for large systems of volterra lotka type integrodifferential population delay equations on considere l equation integrodifferentielle non lineaire x i t x i t e i j 1 n p ij x j t j 1 n o r s ij k ij x j t d i 1 n ou 1 i j n e i p ij s ij sont des constantes on etudie la stabilite globale de la solution q 1 q n par rapport aux solutions positives

theory and design of m channel maximally decimated quadrature mirror filters with arbitrary m having the perfect reconstruction property based on the concept of losslessness in digital filter structures this paper derives a general class of maximally decimated m channel quadrature mirror filter banks that lead to perfect reconstruction the perfect reconstruction property guarantees that the reconstructed signal hat x n is a delayed version of the input signal x n i e hat x n x n n 0 it is shown that such a property can be satisfied if the alias component matrix ac matrix for short is unitary on the unit circle of the z plane the number of channels m is arbitrary and when m is two the results reduce to certain recently reported 2 channel perfect reconstruction qmf structures a procedure based on recently reported fir cascaded lattice structures is presented for optimal design of such fir m channel filter banks design examples are included

robust interval stability persistence and partial stability on lotka volterra systems with time delay abstract lotka volterra ecological systems with discrete time delays are studied where the information about the biological vital parameters such as the rates of birth death and interaction between species is incomplete but their upper and lower bounds are known by using stability theory of the interval dynamical systems and constructing suitable liapunov functionals robust stability partial robust stability and robust persistence of those lotka volterra systems are investigated and sufficient conditions are obtained respectively

multilevel quasidiffusion method with mixed order time discretization for multigroup thermal radiative transfer problems abstract in this paper we present a numerical method for solving multigroup thermal radiative transfer trt problems in 2d cartesian geometry it is based on the quasidiffusion aka variable eddington factor method and defined by the multilevel system of multigroup high order radiative transfer rt equations and multigroup and grey low order equations for moments of the intensity with the exact closures we apply time integration schemes of different orders of accuracy to approximate the high order and low order equations the first order scheme is used for the high order rt equations the second order scheme is applied to the low order equations this improves the accuracy of the trt solution while using robust and relatively inexpensive scheme for the high order rt equations the solution of the low order equations is non monotonic because the hyperbolic low order quasidiffusion qd equations are discretized by the second order scheme to reduce non monotonicity of the low order solution we apply a monotonization procedure to the discretized time dependent low order equations based on the limited trapezoidal method numerical results of the fleck cummings test are presented to demonstrate performance of the developed mixed order time integration scheme for the multilevel system of high order and low order qd equations we use this trt test problem to analyze the convergence in time of the mixed order scheme

symmetric extension methods for m channel linear phase perfect reconstruction filter banks the symmetric extension method has been shown to he an efficient way for subband processing of finite length sequences this paper presents an extension of this method to general linear phase perfect reconstruction filter banks we derive constraints on the length and symmetry polarity of the permissible filter banks and propose a new design algorithm in the algorithm different symmetric sequences are formulated in a unified form based on the circular symmetry framework the length constraints in symmetrically extending the input sequence and windowing the subband sequences are investigated the effect of shifting the input sequence is included when the algorithm is applied to equal length filter banks we explicitly show that symmetric extension methods can always be constructed to replace the circular convolution approach

design and factorization of fir paraunitary filter banks given several analysis filters this correspondence discusses the design and factorization of fir paraunitary filter banks where several analysis filters are given a lattice factorization based algorithm is presented that provides complete and minimal characterization for nonlinear phase and balanced linear phase systems as a result the design problem can be formulated as an unconstrained optimization of the lattice coefficients whereas paraunitariness and linear phase properties are structurally guaranteed the second presented algorithm formulates the design problem in quadratic form that provides better control on the frequency responses of the embedding solution an unitary scaling filter design algorithm is also presented that can be paired with the paraunitary embedding solution to design an orthonormal wavelet basis with high regularity a design example is presented

a linear discontinuous spatial differencing scheme forsnradiative transfer calculations various types of linear discontinuous spatial differencing schemes have been developed for thesn discrete ordinates equations approximating the linear boltzmann transport equation it has been shown through an asymptotic analysis that the 1d slab geometry lumped linear discontinuous scheme not only goes over to a convergent and robust differencing of the diffusion equation in the monoenergetic thick diffusion limit but it also yields the correct interior solution even when boundary layers are left unresolved by the spatial mesh in the present work we generalize this scheme to obtain a 1d slab geometry lumped linear discontinuous scheme for the nonlinear radiative transfer equation and the associated material temperature equation we present a full nonlinear energy dependent asymptotic analysis of the behavior of this scheme in the thick equilibrium diffusion limit we find that this scheme goes over to a convergent and robust differencing of the equilibrium diffusion equation on the interior of the mesh but it does not yield the exact interior solution when boundary layers are left unresolved by the spatial mesh nevertheless the interior solution obtained with spatially unresolved boundary layers is always well behaved and fairly accurate computational results are presented which test the predictions of our asymptotic analysis and demonstrate the efficiency of our solution technique

structures for m channel perfect reconstruction fir qmf banks which yield linear phase analysis filters the authors develop structures for fir finite impulse response perfect reconstruction qmf quadrature mirror filter banks which cover a subclass of systems that yield linear phase analysis filters for arbitrary m the parameters of these structures can be optimized to design analysis filters with minimum stopband energy which at the same time have linear phase and satisfy the perfect reconstruction property if there are m subbands then depending on whether the coefficients h sub k n of each analysis filter are symmetric or antisymmetric several combinations of filter banks are possible some of these permit perfect reconstruction and some do not for a given m the authors develop a formula for the number of combinations for a subclass of linear phase perfect reconstruction structures as an example they elaborate on a perfect reconstruction linear phase lattice structure for three channels the lattice structure is such that regardless of the parameter values the qmf bank enjoys the perfect reconstruction property while at the same time the analysis filters have linear phase a design example is presented along with tables of impulse response coefficients

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

stability analysis of a multilevel quasidiffusion method for thermal radiative transfer problems abstract in this paper we analyze a multilevel quasidiffusion qd method for solving time dependent multigroup nonlinear radiative transfer problems which describe interaction of photons with matter the multilevel method is formulated by means of the high order radiative transfer equation and a set of low order moment equations the fully implicit scheme is used to discretize equations in time the stability analysis is applied to the method in semi continuous and discretized forms to perform fourier analysis the system of equations of the multilevel method is linearized about an equilibrium solution the effects of discretization with respect to different independent variables are studied the multilevel method is shown to be stable and fast converging we also consider a version of the method in which time evolution in the radiative transfer equation is treated by means of the approximation the fleck cummings test problem is used to demonstrate performance of the multilevel qd method and study its iterative stability

the necessary and sufficient condition for global stability of a lotka volterra cooperative or competition system with delays abstract this paper presents the necessary and sufficient condition for the global stability of the following lotka volterra cooperative or competition system with time delays x t x t r 1 ax t x t 11 y t 12 y t y t r 2 ay t x t 21 y t 22 it is showed that the positive equilibrium of the system is globally asymptotically stable for all delays ij 0 i j 1 2 if and only if

stability analysis of nonlinear two grid method for multigroup neutron diffusion problems abstract we present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems this method is formulated with two energy grids that are defined by i fine energy groups structure and ii coarse grid with just a single energy group the coarse grid equations are derived by averaging of the multigroup diffusion equations over energy the method uses a nonlinear prolongation operator we perform stability analysis of iteration algorithms for inhomogeneous fixed source and eigenvalue neutron diffusion problems to apply fourier analysis the equations of the method are linearized about solutions of infinite medium problems the developed analysis enables us to predict convergence properties of this two grid method in different types of problems numerical results of problems in 2d cartesian geometry are presented to confirm theoretical predictions