wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

spectral statistics for unitary transfer matrices of binary graphs quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits it is proposed here to generalize this approach by considering arbitrary directed graphs with unitary transfer matrices an exponentially increasing contribution to the form factor is identified when performing a diagonal summation over periodic orbit degeneracy classes a special class of graphs so called binary graphs is studied in more detail for these the conditions for periodic orbit pairs to be correlated including correlations due to the unitarity of the transfer matrix can be given explicitly using combinatorial techniques it is possible to perform the summation over correlated periodic orbit pair contributions to the form factor for some low dimensional cases gradual convergence towards random matrix results is observed when increasing the number of vertices of the binary graphs

some results in the theory of crosstalk free transmultiplexers the crosstalk free transmultiplexer cf tmux focuses on crosstalk cancellation cc rather than on suppressing it the authors present an analysis of the cf tmux based on the polyphase component matrices of the filter banks used in tdm to fdm and fdm to tdm conversions respectively thus a necessary and sufficient condition for complete cc is obtained it is shown that the filters for a cf tmux are the same as the filters for a 1 skewed alias free qmf bank in addition if the qmf bank satisfies the perfect reconstruction pr property then the tmux also satisfies pr the relation between cf tmux filters and alias free qmf banks is used to obtain a direct design procedure for cf tmux filters both fir and iir it is also shown that approximately crosstalk free tmux filters can be obtained from any approximately alias free qmc bank design examples and comparison tables are included

quantum graphs a simple model for chaotic scattering we connect quantum graphs with infinite leads and turn them into scattering systems we show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics typical poles delay time and conductance distributions ericson fluctuations and when considered statistically the ensemble of scattering matrices reproduces quite well the predictions of the appropriately defined random matrix ensembles the underlying classical dynamics can be defined and it provides important parameters which are needed for the quantum theory in particular we derive exact expressions for the scattering matrix and an exact trace formula for the density of resonances in terms of classical orbits analogous to the semiclassical theory of chaotic scattering we use this in order to investigate the origin of the connection between random matrix theory and the underlying classical chaotic dynamics being an exact theory and due to its relative simplicity it offers new insights into this problem which is at the forefront of the research in chaotic scattering and related fields

analysis synthesis techniques for subband image coding analysis synthesis systems designed for low bit rate image coding their impact on overall system quality and their computational complexity are discussed the investigation focuses on the design of analysis synthesis systems for image coding and the perceptual impact of these systems at low bit rates two objectives are emphasized in developing these systems confining the total size of the subband images to be equal to the original image size and designing the filters so that perceptual distortion is not introduced by the analysis synthesis system methods based on circular convolution and symmetric extensions are developed and discussed in detail the theory design and implementation of both recursive and nonrecursive filtering systems are discussed methods are introduced which display advantages over conventional quadrature mirror filter based approaches

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

general analysis of two band qmf banks the two channel perfect reconstruction quadrature mirror filter banks pr qmf banks are analyzed in detail by assuming arbitrary analysis and synthesis filters solutions where the filters are fir or iir correspond to the fact that a certain function is monomial or nonmonomial respectively for the monomial case the design problem is formulated as a nonlinear constrained optimization problem the formulation is quite robust and is able to design various two channel filter banks such as orthogonal and biorthogonal arbitrary delay linear phase filter banks to name a few same formulation is used for causal and stable pr iir filter bank solutions

non weyl microwave graphs one of the most important characteristics of a quantum graph is the average density of resonances l where l denotes the length of the graph this is a very robust measure it does not depend on the number of vertices in a graph and holds also for most of the boundary conditions at the vertices graphs obeying this characteristic are called weyl graphs using microwave networks that simulate quantum graphs we show that there exist graphs that do not adhere to this characteristic such graphs are called non weyl graphs for standard coupling conditions we demonstrate that the transition from a weyl graph to a non weyl graph occurs if we introduce a balanced vertex a vertex of a graph is called balanced if the numbers of infinite leads and internal edges meeting at a vertex are the same our experimental results confirm the theoretical predictions of e b davies and a pushnitski analysis and pde 4 729 2011 and are in excellent agreement with the numerical calculations yielding the resonances of the networks

on the level spacing distribution in quantum graphs we derive a formula for the level spacing probability distribution in quantum graphs we apply it to simple examples and we discuss its relation with previous work and its possible application in more general cases moreover we derive an exact and explicit formula for the level spacing distribution of integrable quantum graphs

classical wave experiments on chaotic scattering we review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems scattering theory has to be applied for a quantitative interpretation of the measurements most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation in all studied examples a quantitative agreement between experiment and theory is achieved to this end it is necessary however to take absorption and imperfect coupling into account concepts that were ignored in most previous theoretical investigations classical phase space signatures of scattering are being examined in a small number of experiments

experimental investigation of wigner s reaction matrix for irregular graphs with absorption we use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by t joints to make an experimental study of wigner s reaction k matrix for irregular graphs in the presence of absorption from measurements of the scattering matrix s for each realization of the microwave network we obtain distributions of the imaginary and real parts of k our experimental results are in good agreement with theoretical predictions

experimental and numerical investigation of the reflection coefficient and the distributions of wigner s reaction matrix for irregular graphs with absorption we present the results of an experimental and numerical study of the distribution of the reflection coefficient p r and the distributions of the imaginary p v and the real p u parts of the wigner reaction k matrix for irregular fully connected hexagon networks graphs in the presence of strong absorption in the experiment we used microwave networks which were built of coaxial cables and attenuators connected by joints in the numerical calculations experimental networks were described by quantum fully connected hexagon graphs the presence of absorption introduced by attenuators was modeled by optical potentials the distribution of the reflection coefficient p r and the distributions of the reaction k matrix were obtained from measurements and numerical calculations of the scattering matrix s of the networks and graphs respectively we show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory

perfect reconstruction filter banks having linear phase fir filters with equiripple response the design of equiripple linear phase analysis and synthesis fir filters of two channel perfect reconstruction pr filter banks is formulated as the minimization of a weighted peak error under both linear inequality arising from the desired responses of the analysis filters and nonlinear equality pr constraints the effectiveness of a proposed method to solve the design problem a modified dual affine scaling variant of karmarkar s 1989 algorithm and an approximation scheme is illustrated through several design examples

universal and nonuniversal properties of wave chaotic scattering systems prediction of the statistics of scattering in typical wave chaotic systems requires combining system specific information with universal aspects of chaotic scattering as described by random matrix theory this rapid communication shows that the average impedance matrix which characterizes such system specific properties can be semiclassically calculated in terms of ray trajectories between ports theoretical predictions are compared with experimental results for a microwave billiard demonstrating that the theory successfully uncovered universal statistics of wave chaotic scattering systems

an efficient algorithm to design weighted minimax perfect reconstruction quadrature mirror filter banks an efficient algorithm is presented to design lattice structure two channel perfect reconstruction quadrature mirror filter pr qmf banks we formulate the filter bank design problem as an unconstrained weighted least squares problem with respect to the coefficients of the lattice structure the proposed iterative algorithm optimizes the lattice coefficients and provides flexible control of the filters stopband ripple profiles typically only a few iterations of the algorithm are needed to obtain an optimal solution in the weighted minimax sense we include a set of practical design rules for use with our algorithm these rules allow very good estimation of important filter bank characteristics such as the filter length and the number of signed digits for quantization of the lattice coefficients into canonic signed digit representation to meet a given set of pr qmf bank specifications

association of scattering matrices in quantum networks algorithms based on operations that associate scattering matrices in series or in parallel analogous to impedance association in a classical circuit are developed here we exemplify their application by calculating the total scattering matrix of several types of quantum networks such as star graphs and a chain of chaotic quantum dots obtaining results with good agreement with the literature through a computational time analysis we compare the efficiency of two algorithms for the simulation of a chain of chaotic quantum dots based on series association operations of i two by two centers and ii three by three ones empirical results point out that the algorithm ii is more efficient than i for small number of open scattering channels a direct counting of floating point operations justifies quantitatively the superiority of the algorithm i for large number of open scattering channels

flat phenomena of 2 variable weighted shifts abstract we study the class of mono weakly 2 hyponormal 2 variable weighted shifts t t 1 t 2 resp hyponormal with quadratically hyponormal t 1 and t 2 with two consecutive equal weights in the weight sequence of each of the coordinate operators we show that under natural assumptions on the coordinate operators the presence of consecutive equal weights in t 1 and t 2 leads to the flatness in a way that resembles the situation for 1 variable weighted shifts

explicitly solvable cases of one dimensional quantum chaos we identify a set of quantum graphs with unique and precisely defined spectral properties called regular quantum graphs although chaotic in their classical limit with positive topological entropy regular quantum graphs are explicitly solvable the proof is constructive we present exact convergent periodic orbit expansions for individual energy levels thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete explicit and exact

hyponormal operators with rank two self commutators abstract in this paper it is shown that if t l h satisfies i t is a pure hyponormal operator ii t t is of rank two and iii ker t t is invariant for t then t is either a subnormal operator or the putinar s matricial model of rank two more precisely if t ker t t has a rank one self commutator then t is subnormal and if instead t ker t t has a rank two self commutator then t is either a subnormal operator or the kth minimal partially normal extension t k k of a k 1 hyponormal operator t k which has a rank two self commutator for any k z hence in particular every weakly subnormal or 2 hyponormal operator with a rank two self commutator is either a subnormal operator or a finite rank perturbation of a k hyponormal operator for any k z

reducing nonideal to ideal coupling in random matrix description of chaotic scattering application to the time delay problem we write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with m statistically equivalent channels at nonideal coupling to that for ideal coupling unfolding the phases by their local density leads to universality of their local fluctuations for large m a relation between the partial time delays and diagonal matrix elements of the wigner smith matrix is revealed for ideal coupling this helped us in deriving the joint probability distribution of partial time delays and the distribution of the wigner time delay

operator theory and algebraic geometry on presente des resultats en theorie des operateurs multivariable dont les demonstrations se relient a des techniques issues de la geometrie algebrique

experimental simulation of quantum graphs by microwave networks we present the results of experimental and theoretical study of irregular tetrahedral microwave networks consisting of coaxial cables annular waveguides connected by t joints the spectra of the networks were measured in the frequency range 0 0001 16 ghz in order to obtain their statistical properties such as the integrated nearest neighbor spacing distribution and the spectral rigidity d3sld the comparison of our experimental and theoretical results shows that microwave networks can simulate quantum graphs with time reversal symmetry in particular we use the spectra of the microwave networks to study the periodic orbits of the simulated quantum graphs we also present experimental study of directional microwave networks consisting of coaxial cables and faraday isolators for which the time reversal symmetry is broken in this case our experimental results indicate that spectral statistics of directional microwave networks deviate from predictions of gaussian orthogonal ensembles in random matrix theory approaching especially for small eigenfrequency spacing s results for gaussian unitary ensembles experimental results are supported by the theoretical analysis of directional graphs

parameter dependent spectral statistics of chaotic quantum graphs neumann versus circular orthogonal ensemble boundary conditions the parameter dependent spectral statistics of totally connected quantum graphs with n 4 30 vertices such as the parametric velocities correlation functions and the distribution of curvatures are studied the inverse participation ratio ipr an important measure of localization effects was also numerically investigated in the calculations we successfully used two different theoretical approaches the first approach was based on the graphs eigenenergies and wave functions calculations while the second one used the eigenphases and the eigenvectors of the bond scattering matrix s k we considered graphs with neumann and circular orthogonal ensemble coe boundary conditions we show that in contrast to large neumann graphs for which the departure of many parameter dependent spectral statistics from the random matrix theory rmt predictions is observed for large coe graphs the spectral statistics and ipr are in good agreement with the rmt predictions

universal statistics of the scattering coefficient of chaotic microwave cavities we consider the statistics of the scattering coefficient s of a chaotic microwave cavity coupled to a single port we remove the nonuniversal effects of the coupling from the experimental s data using the radiation impedance obtained directly from the experiments we thus obtain the normalized scattering coefficient whose probability density function pdf is predicted to be universal in that it depends only on the loss quality factor of the cavity we compare experimental pdfs of the normalized scattering coefficients with those obtained from random matrix theory rmt and find excellent agreement the results apply to scattering measurements on any wave chaotic system

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

families of line graphs and their quantization any directed graph g with n vertices and j edges has an associated line graph l g where the j edges form the vertices of l g we show that the non zero eigenvalues of the adjacency matrices are the same for all graphs of such a family ln g we give necessary and sufficient conditions for a line graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions line graphs may therefore serve as models to study the semiclassical limit of large matrix size of a quantum dynamics on graphs with fixed classical behaviour

classical 1d maps quantum graphs and ensembles of unitary matrices we study a certain class of classical one dimensional piecewise linear maps for these systems we introduce an infinite family of markov partitions in equal cells the symbolic dynamics generated by these systems is described by bi stochastic doubly stochastic matrices we analyse the structure of graphs generated from the corresponding symbolic dynamics we demonstrate that the spectra of quantized graphs corresponding to the regular classical systems have locally poissonian statistics while quantized graphs derived from classically chaotic systems display statistical properties characteristic of the circular unitary ensemble even though the corresponding unitary matrices are sparse

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

discrete wavelet transform based on cyclic convolutions a filterbank in which cyclic convolutions are used in place of linear convolutions will be referred to as a cyclic convolution filterbank ccfb a dyadic tree structured ccfb can be used to perform a discrete wavelet transform suitable for coding based on symmetric extension methods this paper derives two types of efficient implementation techniques for the tree structured ccfb one using complex arithmetic and one using only real arithmetic in addition the present paper analyzes in detail the perfect reconstruction pr condition for the two channel ccfb and shows that this condition is much less restrictive than that of usual two channel filterbanks when each of the two channel ccfbs constituting a tree structured ccfb is designed to be pr the whole system is pr a quadrature mirror filter qmf ccfb having the pr property is demonstrated to be easily designed using a standard filter design subroutine in contrast designing a linear phase pr fir qmf bank that has good frequency response is not possible when filters are realized by linear convolutions

quartically hyponormal weighted shifts need not be 3 hyponormal we give the first example of a quartically hyponormal unilateral weighted shift which is not 3 hyponormal

k hyponormality of finite rank perturbations of unilateral weighted shifts in this paper we explore finite rank perturbations of unilateral weighted shifts w first we prove that the subnormality of w is never stable under nonzero finite rank perturbations unless the perturbation occurs at the zeroth weight second we establish that 2 hyponormality implies positive quadratic hyponormality in the sense that the maclaurin coefficients of d n s det p n w sw 2 w sw 2 p n are nonnegative for every n 0 where p n denotes the orthogonal projection onto the basis vectors e 0 e n finally for strictly increasing and w 2 hyponormal we show that for a small finite rank perturbation a of a the shift w remains quadratically hyponormal

global optimum design of uniform fir filter bank with magnitude constraints the optimum design of a uniform finite impulse response filter bank can be formulated as a nonlinear semi infinite optimization problem however this optimization problem is nonconvex with infinitely many inequality constraints in this paper we propose a new hybrid approach for solving this highly challenging nonlinear nonconvex semi infinite optimization problem in this approach a gradient based method is used in conjunction with a filled function method to determine a global minimum of the problem this new hybrid approach finds an optimal result independent of the initial guess of the solution the method is applied to some existing examples the results obtained are superior to those obtained by other existing methods