an infinity norm bound for the inverse of dashnic zusmanovich type matrices with applications abstract an upper bound for the infinity norm for the inverse of dashnic zusmanovich type matrices is given it is proved that the upper bound is sharper than the well known varah s bound for strictly diagonally dominant matrices by introducing a new subclass of p matrices dashnic zusmanovich type b matrices dz type b matrices and using the proposed infinity norm bound an error bound is given for the linear complementarity problems of dz type b matrices we also give a new pseudospectra localization to measure the distance to instability

theory and lattice structure of complex paraunitary filterbanks with filters of hermitian symmetry antisymmetry properties the theory of the real coefficient linear phase filterbank lpfb is extended to the complex case in two ways leading to two generalized classes of m channel filterbanks one is the symmetric antisymmetric filterbank safb where all filters are symmetric or antisymmetric the other is the complex linear phase filterbank clpfb where all filters are hermitian symmetric or hermitian antisymmetric and hence have the linear phase property necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated complete and minimal lattice structures are developed for the paraunitary safb and paraunitary clpfb where the channel number m is arbitrary even or odd and the subband filters could have different lengths with the elementary unitary matrices in the structure of the paraunitary safb constrained to be real and orthogonal the structure covers the most general real coefficient paraunitary lpfbs compared with the existing results the number of parameters is reduced significantly

lapped transforms for efficient transform subband coding two lapped transforms for subband transform coding of signals are introduced a version of the lapped orthogonal transform lot which can be efficiently computed for any transform length and the modulated lapped transform mlt which is based on a modulated quadrature mirror qmf bank the mlt can also be efficiently computed by means of a type iv discrete sine transform dst iv the lot and the mlt are both asymptotically optimal lapped transforms for coding an ar 1 signal with a high intersample correlation coefficient the coding gains of the lot and mlt of length m are higher than that of the discrete cosine transform dct of the same length they are actually close to the coding gains obtained with a dct of length 2m an mlt based adaptive transform coder act for speech signals is simulated the code is essentially free from frame rate noise and has a better spectral resolution that dct based atc systems

computation of error bounds for p matrix linear complementarity problems we give new error bounds for the linear complementarity problem where the involved matrix is a p matrix computation of rigorous error bounds can be turned into a p matrix linear interval system moreover for the involved matrix being an h matrix with positive diagonals an error bound can be found by solving a linear system of equations which is sharper than the mathias pang error bound preliminary numerical results show that the proposed error bound is efficient for verifying accuracy of approximate solutions

error bounds for linear complementarity problems of db matrices doubly b matrices db matrices which properly contain b matrices are introduced by pena 2003 2 in this paper we present error bounds for the linear complementarity problem when the matrix involved is a db matrix and a new bound for linear complementarity problem of a b matrix the numerical examples show that the bounds are sharp

frame theory based analysis and design of oversampled filter banks direct computational method this paper studies the frames corresponding to oversampled filter banks fbs for this class of fb frames we present a state space parameterization of perfect reconstruction fb frames and explicit and numerically efficient formulas to compute the tightest frame bounds to obtain the dual fb frame and to construct a tight paraunitary fb frame from a given untight nonparaunitary fb frame the derivation uses well developed techniques from modern control theory which results in the unified formulas for generic infinite impulse response iir and finite impulse response fir fbs these formulas involve only algebraic manipulations of real matrices and can be computed efficiently reliably and exactly without the approximation required in the existing methods for generic fbs the results provide a unified framework for frame theory based analysis and systematic design of oversampled filter banks

improved error bounds based on α m for the linear complementarity problem abstract in this paper the error bounds of the approximate solution and the bounds of the true solution to the linear complementarity problem lcp m q are presented based on the function m which is introduced by mathias and pang in 23 in order to show the accuracy and the effectiveness of our results we perform some numerical experiments to reveal our results are better than other results in the literature

design of linear phase m channel perfect reconstruction fir filter banks we propose two approaches to design m channel nonparaunitary filter banks that satisfy perfect reconstruction pr and linear phase lp properties in the first approach the pr condition is imposed on only a high pass filter although this method does not require nonlinear optimization it has a demerit in that the order of a high pass filter becomes high in the second approach two filters are optimized simultaneously using a lagrange newton method we can design pr filter banks that have the same length the pr constraint is also formulated as a linear and nonlinear equation of the analysis filter coefficients finally some design examples are included

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

error bounds for the linear complementarity problem with a p matrix abstract we introduce a fundamental quantity associated with a p matrix and show how this quantity is useful in deriving error bounds for the linear complementarity problem of the p type we also obtain upper and lower bounds for the quantity introduced

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

lapped unimodular transform and its factorization two types of lapped transforms have been studied in detail in the literature namely the lapped orthogonal transform lot and its extension the biorthogonal lapped transform bolt in this paper we will study the lapped unimodular transform lut all three transforms are first order matrices with finite impulse response fir inverses we will show that like lot and bolt all luts can be factorized into degree one unimodular matrices the factorization is both minimal and complete we will also show that all first order systems with fir inverses can be minimally factorized as a cascade of degree one lot bolt and lut building blocks two examples will be given to demonstrate that despite having a very small system delay the luts have a satisfactory performance in comparison with lot and bolt

filters for distortion free two band multirate filter banks in this paper conditions are given for a two band multi rate filter bank to be alias free and to have a unity frequency response it is shown that the class of quadrature mirror filters qmf s that satisfies these conditions is quite limited a class of filters which does satisfy these conditions is given and a simple procedure for designing filters from this class is presented with an example

a new approach to the design of critically sampled m channel uniform band perfect reconstruction linear phase fir filter banks a new approach is presented for the design of uniform band m channel perfect reconstruction pr fir filter banks employing linear phase analysis and synthesis filters the technique designs on the impulse responses of the analysis filters directly the design problem is formulated as an optimization program the filter bank s pr feature can either be implicitly enforced through a set of mathematical relationships among the analysis filters coefficients or through a set of constraints in the optimization program the former approach results in a filter bank whose pr feature s dependency on hardware and software is eliminated or at least minimized the synthesis filters are then obtained by a set of relationships that describe each synthesis filter as a function of the analysis filters the criterion for optimality is least squares where the square of the difference between the ideal and actual frequency responses is integrated over the appropriate frequency bands for all m analysis filters and minimized

infinity norm bounds for the inverse of nekrasov matrices using scaling matrices abstract for many applications it is convenient to have good upper bounds for the norm of the inverse of a given matrix in this paper we obtain such bounds when a is a nekrasov matrix by means of a scaling matrix transforming a into a strictly diagonally dominant matrix numerical examples and comparisons with other bounds are included the scaling matrices are also used to derive new error bounds for the linear complementarity problems when the involved matrix is a nekrasov matrix these error bounds can improve considerably other previous bounds

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

generalized unequal length lapped orthogonal transform for subband image coding generalized linear phase lapped orthogonal transforms with unequal length basis functions gullots are considered the length of each basis of the proposed gullot can be different from each other whereas all the bases of the conventional genlot are of equal length in general for image coding application the long basis for a low frequency band and the short basis for a high frequency one are desirable to reduce the blocking and the ringing artifact simultaneously therefore the gullot is suitable especially for a subband image coding in order to apply the gullot to a subband image coding we also investigate the size limited structure to process the finite length signal which is important in practice finally some design and image coding examples are shown to confirm the validity of the proposed gullot

an iterative criterion for h matrices we provide an algorithmic characterization of h matrices when a is an h matrix this algorithm determines a positive diagonal matrix d such that ad is strictly row diagonally dominant in effect d is produced iteratively by quantifying and

entrywise perturbation theory for diagonally dominant m matrices with applications this paper introduces a new perspective on the study of computational problems related to diagonally dominant m matrices by establishing some new entrywise perturbation results if a diagonally dominant m matrix is perturbed in a way that each off diagonal entry and its row sums i e the quantities of diagonal dominance have small relative errors we show that its determinant cofactors each entry of the inverse and the smallest eigenvalue all have small relative errors the error bounds are given and they do not depend on any condition number applying this result to the studies of electrical circuits and tail probabilities of a queue whose embedded markov chains is of gi m 1 type we discuss the relative sensitivity of the operating speed of circuits and of the percentile of the queue length respectively

efficient large scale filter filterbank design via lmi characterization of trigonometric curves many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semi infinite constraints recent advances in design methodology are based on various linear matrix inequality lmi characterizations of the semi infinite constraints and semidefinite programming sdp solutions despite these advances the design of filters of several hundredth order which typically arise in multicarrier communication and signal compression cannot be accommodated this hurdle is due mainly to the large number of additional variables incurred in the lmi characterizations this paper proposes a novel lmi characterization of the semi infinite constraints that involves additional variables of miminal dimensions consequently the design of high order filters required in practical applications can be achieved examples of designs of up to 1200 tap filters are presented to verify the viability of the proposed approach

design of linear phase recombination nonuniform filter banks this correspondence proposes a novel method for designing a class of recombination nonuniform filter banks rnfbs with the linear phase lp property in the structure of the proposed nonuniform filter bank fb certain channels of an m channel uniform fb are merged by synthesis filters of transmultiplexers tmuxs yielding nonuniform subbands by a detailed analysis of the frequency characteristics of the rnfbs we derive the existence and matching conditions that are necessary for constructing the proposed rnfbs having good frequency responses with those conditions being satisfied the design problem becomes that of a set of lp uniform fbs by using the parks mcclellan algorithm we are able to design the near perfect reconstruction lp rnfbs in a very simple and efficient way as demonstrated by two examples

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

the polyphase with advance representation and linear phase lifting factorizations a matrix theory is developed for the noncausal polyphase representation that underlies the theory of lifted filter banks and wavelet transforms the theory presented here develops an extensive matrix algebra framework for analyzing and implementing linear phase two channel filter banks via lifting cascade schemes whole sample symmetric and half sample symmetric linear phase filter banks are characterized completely in terms of the polyphase with advance representation and new proofs are given of linear phase lifting factorization theorems for these two principal classes of linear phase filter banks the theory benefits significantly from a number of group theoretic structures arising in the polyphase with advance representation and in the lifting factorization of linear phase filter banks these results form the foundations of the lifting methodology employed in part 2 of the iso iec jpeg 2000 still image coding standard

infimum of error bounds for linear complementarity problems of σ sdd and σ1 ssd matrices abstract in 2013 18 garcia esnaola and pena presented error bounds for the linear complementarity problems of sdd and 1 ssd matrices respectively these bounds all involve a parameter on an open interval it is shown in this paper that the infimum of these error bounds as a function of the parameter exists and then is determined numerical examples are given to verify the theoretical results

dynamical behavior in coupled systems of j j type abstract in this paper we analyze the structure of the global attractor of the coupled josephson junction system system and prove that there exists a unique invariant restricted horizontal curve when the damping is not small and the coupling is not very weak this invariant curve plays a very important role in analyzing the dynamical behavior of the system when the damping is large enough the unique invariant curve is globally attracting so that the system behaves exactly as a onedimensional system

lattice structure for regular paraunitary linear phase filterbanks and m band orthogonal symmetric wavelets parauninary linear phase pulp m channel uniform filterbanks which are also known as the generalized lapped orthogonal transforms genlots can be designed and implemented using lattice structures this paper discusses how to impose regularity constraints onto the lattice structure of pulp filterbanks these conditions are expressed in term of the rotation angles of the lattice components by which the resulting filterbanks are guaranteed to have one or two degrees of regularity iterating these new regular filterbanks on the lowpass subband generates a large family of symmetric m band orthonormal wavelets design procedures with many design examples are presented smooth interpolation using regular pulp filterbanks is illustrated through image coding experiments where the novel m band wavelets consistently yield smoother reconstructed images and better perceptual quality

m band compactly supported orthogonal symmetric interpolating scaling functions in many applications wavelets are usually expected to have the following properties compact support orthogonality linear phase regularity and interpolation to construct such wavelets it is crucial designing scaling functions with the above properties in two and three band cases except for the haar functions there exists no scaling function with the above five properties in m band case m spl ges 4 more free degrees available in design enable us to construct such scaling functions a novel approach to designing such scaling functions is proposed first we extend the two band dubuc 1986 filters to the m band case next the m band fir regular symmetric interpolating scaling filters are parameterized and then m band fir regular orthogonal symmetric interpolating scaling filters osisfs are designed via optimal selection of parameters finally two family of four band and five band osisfs and scaling functions are developed and their smoothness are estimated

maximally decimated perfect reconstruction fir filter banks with pairwise mirror image analysis and synthesis frequency responses structures are presented for the perfect reconstruction quadrature mirror filter bank that are based on lossless building blocks these structures ensure that the frequency responses of the analysis and synthesis filters have pairwise symmetry with respect to pi 2 and require fewer parameters than recently reported structures also based on lossless building blocks the design time for the proposed structures is correspondingly much less than for the earlier methods which did not incorporate such symmetry

the genlot generalized linear phase lapped orthogonal transform the general factorization of a linear phase paraunitary filter bank lppufb is revisited from this new perspective a class of lapped orthogonal transforms with extended overlap generalized linear phase lapped orthogonal transforms genlots is developed as a subclass of the general class of lppufb in this formulation the discrete cosine transform dct is the order 1 genlot the lapped orthogonal transform is the order 2 genlot and so on for any filter length that is an integer multiple of the block size the genlots are based on the dct and have fast implementation algorithms the implementation of genlots is explained including the method to process finite length signals the degrees of freedom in the design of genlots are described and design examples are presented along with image compression tests

error bounds for the linear complementarity problem with a σ sdd matrix abstract we give new error bounds for the linear complementarity problem when the involved matrix is a sdd matrix with positive diagonals the new bounds can improve considerably other previous bounds we also find a subclass of sdd matrices for which the new bound is very simple

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

a new criterion for the h matrix property for many applications it is very useful to know whether a matrix is an h matrix or not recently some iterative tests have been proposed for distinguishing h matrix in this paper we propose a new method for being able to distinguish only a scalar times column vector numerical evidence for the effectiveness of the proposed algorithm is presented

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

a class of nonlinear sturm liouville problems with infinitely many solutions on etudie l existence des solutions des problemes de sturm liouville non lineaires dont la partie lineaire est a la resonance on montre que de tels problemes peuvent avoir une infinite de solutions si les perturbations non lineaires sont periodiques

periodic solutions for systems of forced coupled pendulum like equations abstract the existence of periodic solutions for systems of forced pendulum like equations was studied in the papers by j a marlin internat j nonlinear mech 3 1968 439 447 and j mawhin internat j nonlinear mech 5 1970 335 339 in both works some symmetry hypotheses on the forcing terms were considered this paper discusses the existence and multiplicity of periodic solutions of systems under consideration without any requirement on the symmetry of the forcing terms note that as a model example it is possible to consider the motion of n coupled pendulums see the already mentioned paper by j a marlin or the oscillations of an n coupled point josephson junction with external time dependent disturbances studied in the autonomous case by m levi f c hoppensteadt and w l miranker quart appl math 36 1978 167 198

error bounds for linear complementarity problems of s nekrasov matrices and b s nekrasov matrices abstract an error bound involving a parameter which does not always work for the linear complementarity problem lcp when the involved matrices are s nekrasov matrices is provided by m garcia esnaola and j m pena 2014 in this paper a new error bound for the lcp of s nekrasov matrices is presented which depends only on the entries of the involved s nekrasov matrices based on the obtained results we also give an error bound for the lcp of b s nekrasov matrices

parameterizations of masks for 3 band tight wavelet frames by symmetric extension of polyphase matrix this paper deals with the construction of 3 band tight wavelet frames with symmetric properties using symmetric extension and parameterizations of the paraunitary matrix firstly we construct a paraunitary matrix which is a symmetric extension of polyphase matrix corresponding to compactly supported wavelet frames with the least number generators further we present symmetric characters and uniformity of wavelet frames with different filter lengths in terms of paraunitary matrix then we focus on investigating the parameterizations of masks for 3 band tight wavelet frames with 3n filter length finally examples of 3 band wavelet frames with good smoothness are constructed based on the parameterizations of masks

coding gain in paraunitary analysis synthesis systems a formal proof that bit allocation results hold for the entire class of paraunitary subband coders is presented the problem of finding an optimal paraunitary subband coder so as to maximize the coding gain of the system is discussed the bit allocation problem is analyzed for the case of the paraunitary tree structured filter banks such as those used for generating orthonormal wavelets the even more general case of nonuniform filter banks is also considered in all cases it is shown that under optimal bit allocation the variances of the errors introduced by each of the quantizers have to be equal expressions for coding gains for these systems are derived

problems at resonance for equations with periodic nonlinearities we study differential equations with periodic nonlinearities in particular we prove that for a small the equation u u g u h t a sin t phi where g is a c 1 periodic function with zero mean value and h is orthogonal to cos t and sin t has 2pi periodic solutions the proof relies on an abstract result based on variational arguments its application makes use of integral estimates by the stationary phase method we also study the existence of multiple solutions c 2003 elsevier ltd all rights reserved

robust image watermarking based on multiband wavelets and empirical mode decomposition in this paper we propose a blind image watermarking algorithm based on the multiband wavelet transformation and the empirical mode decomposition unlike the watermark algorithms based on the traditional two band wavelet transform where the watermark bits are embedded directly on the wavelet coefficients in the proposed scheme we embed the watermark bits in the mean trend of some middle frequency subimages in the wavelet domain we further select appropriate dilation factor and filters in the multiband wavelet transform to achieve better performance in terms of perceptually invisibility and the robustness of the watermark the experimental results show that the proposed blind watermarking scheme is robust against jpeg compression gaussian noise salt and pepper noise median filtering and con vfilter attacks the comparison analysis demonstrate that our scheme has better performance than the watermarking schemes reported recently

m channel nonlinear phase filter banks in image compression structure design and signal extension this paper describes a transform coding technique based on m channel perfect reconstruction filter banks with a nonlinear phase in contrast with linear phase filter banks the nonlinearity provides an extra degree of freedom that can be used to design a more efficient transform we present new lattice structures of paraunitary and perfect reconstruction biorthogonal filter banks which can be implemented with a lower computational complexity and or represented by a few free parameters through the decomposition of the lattice blocks and the displacement across the delay block we further discuss a smooth extension method for nonlinear phase filter banks to obtain a nonexpansive transform the promise of our proposed approaches is demonstrated through several design examples extended signals and compression results

m band scaling function with filter having vanishing moments two and minimal length abstract in this paper we consider the holder continuity local linearity linear independence and interpolation problem of the m band scaling function with a filter having vanishing moments two and minimal length in particular we find some new properties that are not true when m 2 such as local linearity local linear dependence differentiability at adjoint m adic points and interpolation problem at integer knots

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

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a group theoretic approach to multidimensional filter banks theory and applications in this paper we provide a new method for analyzing multidimensional filter banks this method enables us to solve various open problems in multidimensional filter bank characterization and design the essential element in this new approach is the redefinition of polyphase components it will be shown that a rich set of mathematical tools in particular algebraic group theory will become available for use in the analysis of filter banks we demonstrate the elegance and power of the tool set by employing it for the characterization of multidimensional filter banks and applying it to two open problems the first problem is concerned with the development of a general method to design multichannel spl ges 2 multidimensional filter banks using transformations while the second problem is concerned with the derivation of general restrictions on group delays in linear phase filter banks the treatment of these problems is only an illustration of the power of the tool set of algebraic group theory employed for the first time in the context of multidimensional filter banks

dct based general structure for linear phase paraunitary filterbanks in this paper we present a general structure for linear phase paraunitary filterbanks lppufb via both time domain pre processing and frequency domain post processing of the discrete cosine transform dct the proposed structure not only covers existing frameworks with either pre processing or post processing of the dct but enables the design of dct based lppufb with both partial block overlapping and variable length filters as well some high performance and low complexity transforms can be obtained by fine tuning the structure parameters furthermore a dct oriented initialization method is developed to improve the convergence and to simplify the parameterization in the filterbank optimization process the application in image compression is demonstrated

a boundary value problem with a periodic nonlinearity soit g r r une fonction continue et periodique de periode t 0 et soit h l 1 0 on considere le probleme d existence pour le probleme aux limites de picard u u g u h u 0 0 u

on minimal lattice factorizations of symmetric antisymmetric multifilterbanks this paper introduces two minimal lattice structures for symmetric antisymmetric multiwavelets samwts and symmetric antisymmetric multifilterbanks samfbs first by exploring the relation of the symmetric antisymmetric property in multifilterbanks and the linear phase property in traditional scalar filterbanks we show that the implementation and design of an samfb can be converted into that of a four channel scalar linear phase perfect reconstruction filterbank lpprfb then based on the lattice factorization for lpprfbs we propose two fast modular minimal structures for samfbs to demonstrate the effectiveness of the proposed lattice structures several rational or dyadic coefficient samwt design examples are presented along with their application in image coding

tight frames of compactly supported affine wavelets this paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by daubechies commun pure appl math 41 909 1988 for each integer n 1 a family of wavelet functions having support 0 2n 1 is constructed such that jk x 2j 2 2jx k kj k z is a tight frame of l2 r i e for every f l2 r f c jk jk f jk for some c 0 this family is parametrized by an algebraic subset vn of r4n furthermore for n 2 a proper algebraic subset wn of vn is specified such that all points in vn outside of wn yield orthonormal bases the relationship between these tight frames and the theory of group representations and coherent states is discussed

asymptotic analysis of oscillating parametric integrals and ordinary boundary value problems at resonance abstract this paper deals with boundary value problems whose nonlinear part involves periodic functions and such that the linear part has a one dimensional solution space we shall study the existence and multiplicity of solutions using various methods of nonlinear analysis such as the lyapunov schmidt reduction and methods of critical point theory the proofs are based on some general results on the oscillation and asymptotic behavior of certain parametric integrals

nonseparable two and three dimensional wavelets we present two and three dimensional nonseparable wavelets they are obtained from discrete time bases by iterating filter banks we consider three sampling lattices quincunx separable by two in two dimensions and fco the design methods are based either on cascade structures or on the mcclellan transformation in the quincunx case we give a few design examples in particular the first example of an orthonormal 2 d wavelet basis with symmetries is constructed

digital filter bank design quadratic constrained formulation formulate the filter bank design problem as an quadratic constrained least squares minimization problem the solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters the formulations of the perfect reconstruction cosine modulated filter bank of the near perfect reconstruction pseudo qmf bank and of the two channel biorthogonal linear phase filter bank are derived using the proposed approach compared with other design methods the proposed technique yields pr filter banks with much higher stopband attenuation the proposed technique can also be extended to design multidimensional filter banks

a comparison of error bounds for linear complementarity problems of h matrices we give new error bounds for the linear complementarity problem when the involved matrix is an h matrix with positive diagonals we find classes of h matrices for which the new bounds improve considerably other previous bounds we also show advantages of these new bounds with respect the computational cost a new perturbation bound of h matrices linear complementarity problems is also presented

complete factorization for poly phase matrix with linear phase based on semi rank orthogonal projection matrix abstract this paper puts forward a new factorization named the semi rank factorization for para unitary poly phase matrix with linear phase and reveals the equivalent relationship between the orthogonal projection matrix and the linear phase and characterizes the orthogonal projection matrix the semi rank factorization has the completeness property no matter for even or odd number of channels in addition a decomposition technique for the starting block matrix is developed using the reflection matrix the semi rank factorization provides an efficient and compact representation for multi band filter banks with linear phase in particular the complete representation for multi band symmetry filter banks with odd number of channels is brand new as a result the programmable algorithms are obtained for designs of optimal filter banks based on the complete representation the optimal examples are presented to illustrate the excellent performance on image compression

accurate computation of the smallest eigenvalue of a diagonally dominant m matrix if each off diagonal entry and the sum of each row of a diagonally dominant m matrix are known to certain relative accuracy then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers in this paper we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms

symmetric nearly shift invariant tight frame wavelets k regular two band orthogonal filterbanks have been applied to image processing such filters can be extended into a case of downsampling by two and more than two filters provided that they satisfy a set of conditions such a setup allows for more degrees of freedom but also at the cost of higher redundancy the latter depends directly on the number of the wavelet filters involved tight frame filters allow the design of smooth scaling functions and wavelets with a limited number of coefficients moreover such filters are nearly shift invariant a desirable feature in many applications we explore a family of symmetric tight frame finite impulse response fir filters characterized by the relations h sub 3 z h sub 0 z and h sub 2 z h sub 1 z they are simple to design and exhibit a degree of near orthogonality in addition to near shift invariance both properties are desirable for noise removal purposes