analytical bounds for block approximate factorization methods abstract we derive simple analytical upper bounds on the spectral condition number associated with the preconditioning of large sparse linear systems by the so called modified block incomplete factorizations the results prove to handle a large class of discrete second order elliptic partial differential equations and support the conclusion that sparse approximate block matrix factorizations provide powerful preconditioners

a non gaussian kalman filter with application to the estimation of vehicular speed single inductive loop detectors ilds which provide online measurements of traffic volume and occupancy are widely used devices in road systems because of the nature of traffic flow fast estimation and forecasting of vehicular speed using the data collected by an ild are crucial to online road traffic management here we formulate statistical inference for vehicular speed as a dynamic generalized linear model with a reciprocal inverse gaussian observational distribution the formulation motivates us to extend the gaussian kalman filter to this non gaussian scenario this results in a set of simple recursive formulas in which the current estimate of the parameter of interest is updated as a weighted harmonic average of the previous estimate and the current observation by applying the developed non gaussian kalman filter to analyze traffic data collected by an ild we provide a competitive alternative for estimating vehicular speed at a minimum computational cost

network tomography estimating source destination traffic intensities from link data abstract the problem of estimating the node to node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under poisson assumptions and two types of traffic routing regimens deterministic a fixed known path between each directed pair of nodes and markovian a random path between each directed pair of nodes determined according to a known markov chain fixed for that pair maximum likelihood estimation and related approximations are discussed and computational difficulties are pointed out a detailed methodology is presented for estimates based on the method of moments the estimates are derived algorithmically taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an em algorithm resulting in a particularly simple solution to a hard problem a small simulation study is carried out

computation of the para pseudoinverse for oversampled filter banks forward and backward greville formulas frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience in frame expansions the least square signal reconstruction operator is called the dual frame which can be obtained by choosing the synthesis filter bank as the para pseudoinverse of the analysis bank in this paper we study the computation of the dual frame by exploiting the greville formula which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended here we first develop the backward greville formula to handle the case of row deletion based on the forward greville formula we then study the computation of para pseudoinverse for extended filter banks and laplacian pyramids through the backward greville formula we investigate the frame based error resilient transmission over erasure channels the necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived a postfiltering structure is also presented to implement the para pseudoinverse when the transform coefficients in one subband are completely lost

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

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

efficient reconstruction of band limited sequences from nonuniformly decimated versions by use of polyphase filter banks an efficient polyphase structure for the reconstruction of a band limited sequence from a nonuniformly decimated version is developed theoretically the reconstruction involves the implementation of a bank of multilevel filters and it is shown that how all these reconstruction filters can be obtained at the cost of one mth band low pass filter and a constant matrix multiplier the resulting structure is therefore more general than previous schemes in addition the method offers a direct means of controlling the overall reconstruction distortion t z by appropriate design of a low pass prototype filter p z extension of these results to multiband band limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized along with generalizations to the multidimensional case design examples are included to demonstrate the theory and the complexity of the new method is seen to be much lower than earlier ones

orthonormal and biorthonormal filter banks as convolvers and convolutional coding gain convolution theorems for filter bank transformers are introduced both uniform and nonuniform decimation ratios are considered and orthonormal as well as biorthonormal cases are addressed all the theorems are such that the original convolution reduces to a sum of shorter decoupled convolutions in the subbands that is there is no need to have cross convolution between subbands for the orthonormal case expressions for optimal bit allocation and the optimized coding gain are derived the contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum with one of the convolved sequences taken to be the unit pulse function e coding gain expressions reduce to those for traditional subband and transform coding the filter bank convolver has about the same computational complexity as a traditional convolver if the analysis bank has small complexity compared to the convolution itself

nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for r sup n new results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented among the topics discussed are sampling in multiple dimensions multidimensional perfect reconstruction filter banks the two channel case in multiple dimensions the synthesis of multidimensional filter banks and the design of compactly supported wavelets

a general incomplete block matrix factorization method abstract a general method for incomplete factorization of m matrices in block matrix form is presented the method generalizes previous methods for pointwise incomplete factorization methods of varga 1960 of wo nicki 1973 and of meijerink and van der vorst 1977 as well as a method for tridiagonal block matrices also we present a new and more general result on the existence of so called modified incomplete factorizations which satisfy a generalized rowsum criterion

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

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

families of biorthogonal wavelets several families of biorthogonal wavelet bases are constructed with various properties in particular for a given filter fn of finite length 2n 1 a parametric family of dual filters fvn of length 2n 1 is constructed the parametric nature of the dual filters makes it possible to design the optimum dual filter fv0n corresponding to a fixed filter fn

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

linc a common theory of transform and subband coding a common theory of lapped orthogonal transforms lots and critically sampled filter banks called l into n coding linc is presented the theory includes a unified analysis of both coding methods and identity relations between the transform inverse transform analysis filter bank and synthesis filter bank a design procedure for linc analysis synthesis systems which satisfy the conditions for perfect reconstruction is developed the common linc theory is used to define an ideal linc system which is used together with the power spectral density of the input signal to calculate theoretical bounds for the coding gain a generalized overlapping block transform obt with time domain aliasing cancellation tdac is used to approximate the ideal linc a generalization of the obt includes multiple block overlap and additional windowing a recursive design procedure for windows of arbitrary lengths is presented the coding gain of the generalized obt is higher than that of the karhunen loeve transform klt and close to the theoretical bounds for linc in the case of image coding the generalized obt reduces the blocking effects when compared with the dct

subband coding of images using asymmetrical filter banks we address the problem of the choice of subband filters in the context of image coding the ringing effects that occur in subband based compression schemes are the major unpleasant distortions a new set of two band filter banks suitable for image coding applications is presented the basic properties of these filters are linear phase perfect reconstruction asymmetric length and maximum regularity the better overall performances compared to the classical qmf subband filters are explained the asymmetry of the filter lengths results in a better compaction of the energy especially in the highpass subbands moreover the quantization error is reduced due to the short lowpass synthesis filter the undesirable ringing effect is considerably reduced due to the good step response of the synthesis lowpass filter the proposed design takes into account the statistics of natural images and the effect of quantization errors in the reconstructed images which explains the better coding performance

on some versions of incomplete block matrix factorization iterative methods abstract various forms of preconditioning matrices for iterative acceleration methods are discussed the preconditioning is based on two versions of incomplete block matrix factorization

ordering strategies for modified block incomplete factorizations in this study the aim is to first investigate how the rate of convergence of unperturbed modified block incomplete factorization methods depends on the discrete partial differential equation pde to solve and next on this basis to provide simple practical rules for easily selecting orderings that result in rapid convergence it emerges from the analysis here that for discrete pdes ordering schemes that optimize the rate of convergence strongly depend on the variation of both the pde coefficients and the mesh sizes the arguments made which bring to light the appreciable potentialities of modified methods also display insight into why block versions are more robust than pointwise ones

subband decomposition of signals with generalized sampling the authors generalize down and up sampling operations by proposing block sampling perfect reconstruction conditions for two band subband coding with block sampling are derived by generalizing the sampling operation new degrees of freedom are introduced and as a result filter banks which were not previously possible become possible generalized down sampler introduces different aliasing components than that of the traditional down sampler this can be used to ease some the requirements of the filter bank design problem a constructive sampling method is proposed so that coprimeness of the transfer functions of the analysis filter banks is not only a necessary but also sufficient condition for perfect reconstruction the results are extended to the case where the filter banks are linear periodically time varying the multichannel case is analyzed and the relation between unimodular matrices and perfect reconstruction filter banks is discussed

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

on coefficient quantization and computational roundoff effects in lossless multirate filter banks it is shown that fir lossless transfer matrices in multirate analysis synthesis systems having the perfect reconstruction property can be implemented such that the lossless property and hence perfect reconstruction can be retained regardless of coefficient quantization such a result was previously shown to be true only for two channel filter banks a noise gain result is presented for lossless systems which finds application in analyzing roundoff noise in multirate filter banks

near perfect reconstruction pseudo qmf banks a novel approach to the design of m channel pseudo quadrature mirror filter qmf banks is presented in this approach the prototype filter is constrained to be a linear phase spectral factor of a 2mth band filter as a result the overall transfer function of the analysis synthesis system is a delay moreover the aliasing cancellation ac constraint is derived such that all the significant aliasing terms are canceled consequently the aliasing level at the output is comparable to the stopband attenuation of the prototype filter in other words the only error at the output of the analysis synthesis system is the aliasing error which is at the level of stopband attenuation using this approach it is possible to design a pseudo qmf bank where the stopband attenuation of the analysis and thus synthesis filters is on the order of spl minus 100 db moreover the resulting reconstruction error is also on the order of spl minus 100 db several examples are included

reconstruction of signals after filtering and sampling rate reduction a wave digital filter wdf two port has two input and two output terminals by using these to appropriately connect a wdf to its transpose the filtering effect is fully compensated except for an all pass phase and this independently of any selectivity requirement this remains true if at the points of interconnection every second sample is reduced to zero provided that a certain condition easily to be satisfied exactly is fulfilled very efficient solutions are then possible the method is of interest e g for subband coding

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

constructive solutions to spectral and inner outer factorizations with respect to the disk we use state space realizations to solve the spectral and inner outer factorization problems with respect to the unit disk formulated for a completely general rational matrix the algorithm is based on orthogonal transformations and standard reliable procedures for solving stein and riccati equations the formulas apply in particular to general descriptor systems or polynomial matrices the main novelty is that we allow for arbitrary rank poles and zeros on the unit circle or at infinity

optimal design of oversampled synthesis fbs with lattice structure constraints oversampled filter banks fbs with lattice structure allow fast implementation and guarantee the linear phase and perfect reconstruction property for such fbs the synthesis fb is not unique this nonuniqueness provides extra design freedom for optimal reduction of subband noise required in many applications however the existing design methods of synthesis fb for optimal reduction of subband noise cannot guarantee the linear phase and lattice structure property this paper studies the design of oversampled synthesis fbs with guaranteed lattice structure for optimal reduction of subband noise based on a state space parameterization of all synthesis fbs with lattice structure the explicit formulae are derived to find the optimal solution for noise reduction numerical examples are presented to demonstrate the effectiveness of the new design methods obtained

on the conditioning analysis of block approximate factorization methods abstract the paper is devoted to the conditioning analysis of modified block incomplete factorizations of a given stieltjes matrix we obtain new results improve other theories and compare all existing upper bounds through numerical experiments applied to discrete elliptic pdes our results show that an o h 1 spectral bound can be achieved for a large class of problems

bezout space time precoders and equalizers for mimo channels the transmitter receiver diversities in p input q output multiple input multiple output mimo channels will play a key role in future high rate wireless communication the major challenge in mimo signal recovery is the mitigation of the inevitable intersymbol interference isi and interchannel interference ici in multipath mimo channels the bezout system theory provides a simple solution for isi ici cancellation and thus can serve as a powerful mathematical foundation for mimo systems if p q and the mimo system h d is left coprime the system is perfectly recoverable via a bezout precoder assuming the channel information is available at the transmitter for a robust channel design a quantitative analysis of signal to noise ratio snr of the optimal bezout equalizer precoder can be derived from the bezout null space compared with the alamouti see ieee j select areas commun vol 16 p 1451 58 oct 1998 space time coding the bezout precoder is shown to be more appealing in slowly time varying channels where the feedback of the channel information induces minor overhead the bezout system can work well jointly with the space time block coding stbc the stbc can be adopted to artificially construct a larger q spl times p q p virtual transfer function without the channel information a necessary and sufficient condition is provided for perfect recoverability pr for the stbc induced virtual mimo systems based on the virtual transfer function both channel independent and channel dependent precoding strategies are feasible via a singular value decomposition svd analysis the bezout precoder can be shown to outperform the orthogonal frequency division multiplexing ofdm precoder in bit error rate ber transmission rate and receiver implementation the interplay of the two design parameters n and spl rho is analyzed to provide a simple guideline for an optimal configuration the combined stbc and bezout equalization techniques offer a broader spectrum of transceiver system configuration to achieve optimal design tradeoff among ber transmission rate and implementation complexity

role of anticausal inverses in multirate filter banks i system theoretic fundamentals in a maximally decimated filter bank with identical decimation ratios for all channels the perfect reconstructibility property and the nature of reconstruction filters causality stability fir property and so on depend on the properties of the polyphase matrix various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse in this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties i e properties of state space descriptions mcmillan degree degree of determinant and so forth we find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory we study their properties both for the fir and iir cases techniques for implementing anticausal iir inverses based on state space descriptions are outlined it is found that causal fir matrices with anticausal fir inverses cafacafi have a key role in the characterization of fir filter banks

on axelsson s perturbations abstract a nice perturbation technique was introduced by axelsson and further developed by gustafsson to prove that factorization iterative methods are able under appropriate conditions to reach a convergence rate larger by an order of magnitude than that of classical schemes gustafsson observed however that the perturbations introduced to prove this result seemed actually unnecessary to reach it in practice in the present work on the basis of eigenvalue bounds recently obtained by the author we offer an alternative approach which brings a partial confirmation of gustafsson s conjecture

lagrange multiplier approaches to the design of two channel perfect reconstruction linear phase fir filter banks the authors present two approaches to the design of two channel perfect reconstruction linear phase finite impulse response fir filter banks both approaches analyze and design the impulse responses of the analysis filter bank directly the synthesis filter bank is then obtained by simply changing the signs of odd order coefficients in the analysis filter bank the approach deals with unequal length filter banks by designing the lower length filters first one can take advantage of the fact that the number of variables for designing the higher length filters is more than the number of perfect reconstruction constraint equations the second approach generalizes the first and covers the design for all parts of linear phase perfect reconstruction constraint equations

realizable spatio temporal tomlinson harashima precoders theory and fast computation we derive the optimal realizable tomlinson harashima precoder for frequency selective multiple input multiple output mimo channels with respect to a simplified mean square error mse criterion realizability means that in contrast to other works we do not restrict the internal filters of the precoder to have finite impulse responses firs but nevertheless ensure that the precoder can be operated in real time subject to a finite latency time which can be chosen by the system designer in particular this allows us to consider channels with infinite impulse responses iirs as they occur e g in digital subscriber lines the feedforward filter is located at the transmitter in our system model and an additional scalar gain is employed at the receiver the relocation of the feedforward filter allows us to consider decentralized receivers however it also makes it necessary to impose a transmit power constraint the power constraint often has the effect that the input signals at the receiver have to be rescaled we argue that the inclusion of the additional scalar gain allows us to incorporate the effect of the rescaling operation into the optimization special emphasis is put on the fast computation of the realizable tomlinson harashima precoder via displacement structure theory we propose a fast algorithm which includes a successive construction of a close to optimal ordering of the data streams the complexity of this algorithm is only cubic in the number of channel inputs and quadratic in the latency time the algorithm can also be applied in situations where certain fir constraints have to be fulfilled because we find that the optimal realizable tomlinson harashima precoder involves only fir filters as soon as the channel is fir our results are reproducible

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

conditioning analysis of modified block incomplete factorizations abstract we improve the conditioning analysis of modified block incomplete factorizations of stieltjes matrices letting n denote the number of diagonal blocks our results show that the spectral condition number is bounded by n for a large class of two dimensional pdes

new quadrature mirror filter structures this paper introduces new quadrature mirror filter qmf structures for the frequency domain analysis and synthesis of digital signals the conventional qmf technique is first extended to cover complex quadrature mirror filters cqmf in which a digital signal is split into n adjacent complex subbands where the real and imaginary parts are subsampled by 1 2n with respect to the original signal the computational complexity of qmf banks is then analyzed and a new scheme which reduces the computational complexity by about a factor of two over conventional qmf implementations is proposed finally the filter design tradeoffs are discussed and the microprogramed implementation of qmf banks is evaluated

sampled data and discrete time h_2 optimal control this paper deals with the sampled data h 2 optimal control problem given a linear time invariant continuous time system the problem of minimizing the h 2 performance over all sampled data controllers with a fixed sampling period can be reduced to a pure discrete time h 2 optimal control problem this discrete time h 2 problem is always singular motivated by this in this paper we give a treatment of the discrete time h 2 optimal control problem in its full generality the results we obtain are then applied to the singular discrete time h 2 problem arising from the sampled data h 2 problem in particular we give conditions for the existence of optimal sampled data controllers we also show that the h 2 performance of a continuous time controller can always be recovered asymptotically by choosing the sampling period sufficiently small finally we show that the optimal sampled data h 2 performance converges to the continuous time optimal h 2 performance as the sampling period converges to zero

perfect reconstruction iir digital filter banks supporting nonexpansive linear signal extensions in this paper perfect reconstruction polyphase infinite impulse response iir filter banks involving causal and anticausal inverses are examined for finite length signals first a novel and efficient nonexpansive perfect reconstruction algorithm based on the state space implementation is presented then the proposed method is extended to support linear signal extensions at the boundaries in a nonexpansive manner the powerfulness of the proposed algorithm is demonstrated with the image compression results

design of filter banks using transformation of variables new results the design problem of multirate filter banks can be divided into two parts the first part involves the issue of reconstruction errors the second part involves the issue of designing good quality subband filters there is a class of techniques that we refer to as transformation of variables which satisfactorily addresses the two parts of the design problem this class of filter banks is specified by its prototype filters and transformation kernel it is the flexibility and relative ease in designing the kernel that enables the technique to satisfactorily address the second part of the design problem we present two new methods of designing the kernel that will enhance the design techniques flexibility and effectiveness the first is the combination of the mcclellan transformation and rotation operators the second introduces and uses the concept of directional singular value decomposition svd

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

conditioning analysis of block incomplete factorizations and its application to elliptic equations the paper deals with eigenvalue estimates for block incomplete fac torization methods for symmetric matrices first some previous results on upper bounds for the maximum eigenvalue of preconditioned matrices are generalized to each eigenvalue second upper bounds for the maximum eigenvalue of the preconditioned matrix are further estimated which presents a substantial im provement of earlier results finally the results are used to estimate bounds for every eigenvalue of the preconditioned matrices in particular for the maximum eigenvalue when a modified block incomplete factorization is used to solve an elliptic equation with variable coefficients in two dimensions the analysis yields a new upper bound of type h 1 for the condition number of the preconditioned matrix and shows clearly how the coefficients of the differential equation influ ence the positive constant

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

narrowband interference suppression using undecimated wavelet packets in direct sequence spread spectrum receivers a new algorithm for narrowband interference suppression in direct sequence spread spectrum ds ss communications is presented the algorithm combines the undecimated wavelet packet transform uwpt with frequency shifts to confine the interference energy in a subband that is subsequently eliminated computer simulation shows a robust performance that appears to be independent of the interference frequency

existence and conditioning properties of sparse approximate block factorizations a particular class of sparse approximate block lu factorizations is investigated sufficient conditions are determined for the existence of b lp 1 u for a given coefficient matrix a bounds on the spectral condition number of b 1 a are obtained for symmetric b and a when applied to discrete multidimensional elliptic partial differential equations these results lead under reasonable assumptions to o h 1 spectral condition numbers

bayesian inference for origin destination matrices of transport networks using the em algorithm information on the origin destination od matrix of a transport network is a fundamental requirement in much transportation planning a relatively inexpensive method for updating an od matrix is to draw inference about the od matrix based on a single observation of traffic flows on a specific set of network links where the bayesian approach is a natural choice for combining the prior knowledge about the od matrix and the current observation of traffic flows the existing approaches of bayesian modeling of od matrices include using normal approximations to poisson distributions which leads to the posterior being intractable even under some simple special cases and using markov chain monte carlo simulation which incurs extreme demand of computational efforts in this article through the em algorithm bayesian inference is reinvestigated for a transport network for estimating the population means of traffic flows reconstructing traffic flows and predicting future traffic flows it is shown that the r

linear periodic systems and multirate filter design we present a systematic procedure for the design of filters intended for multirate systems this procedure is motivated by viewing the equiripple design of filters in linear time invariant systems as a process of obtaining optimum minimax filters for a class of bounded energy input signals the philosophy of designing optimum minimax filters for classes of input signals is extended to multirate systems which are not time invariant we develop a generalized fourier analysis appropriate for linear periodic systems and use it to derive new error criteria for multirate filter design using such criteria yields optimum minimax multirate filters for the input signal class the utility of our method is demonstrated by using it to analyze several multirate systems we give numerical results on the design of a multirate implementation of a narrowband filter and compare our work to previous work on multirate filter design our numerical analysis is based upon a new formulation of the design as a semi infinite linear programming problem

on the eigenvalue distribution of a class of preconditioning methods a class of preconditioning methods depending on a relaxation parameter is presented for the solution of large linear systems of equationax b wherea is a symmetric positive definite matrix the methods are based on an incomplete factorization of the matrixa and include both pointwise and blockwise factorization we study the dependence of the rate of convergence of the preconditioned conjugate gradient method on the distribution of eigenvalues ofc 1a wherec is the preconditioning matrix we also show graphic representations of the eigenvalues and present numerical tests of the methods

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

novel system inversion algorithm with application to oversampled perfect reconstruction filter banks we derive a novel algorithm for linear discrete time system inversion with decision delay and frequency weighted norm criterion complexity of the algorithm grows only linearly with the decision delay the algorithm also applies to certain singular cases where optimal inverses may be nonunique in that case the set of optimal inverses is parametrized a scilab implementation of the algorithm is provided applications in oversampled perfect reconstruction filter banks are given

kronecker products unitary matrices and signal processing applications discrete unitary transforms are extensively used in many signal processing applications and in the development of fast algorithms kronecker products have proved quite useful in this semitutorial paper we briefly review properties of kronecker products and direct sums of matrices which provide a compact notation in treating patterned matrices a generalized matrix product which inherits some useful algebraic properties from the standard kronecker product and allows a large class of discrete unitary transforms to be generated from a single recursion formula is then introduced the notation is intimately related to sparse matrix factorizations and examples are included illustrating the utility of the new notation in signal processing applications finally some novel characteristics of hadamard transforms and polyadic permutations are derived in the framework of kronecker products

lower eigenvalue bounds for pencils of matrices abstract eigenvalue bounds are obtained for pencils of matrices a vb where a is a stieltjes matrix and b is positive definite under assumptions suitable for the estimation of asymptotic convergence rates of factorization iterative methods where b represents the approximate factorization of a the upper bounds obtained depend on the connectivity structure of the matrices involved which enters through matrix graph considerations in addition a more classical argument is used to obtain a lower bound potential applications of these results include a partial confirmation of gustafsson s conjecture concerning the nonnecessity of axelsson s perturbations

modified block approximate factorization strategies two variants of modified incomplete block matrix factorization with additive correction are proposed for the iterative solution of large linear systems of equations both rigorous theoretical support and numerical evidence are given displaying their efficiency when applied to discrete second order partial differential equations pdes even in the case of quasi singular problems

nonuniform multirate filter banks analysis and design with an spl hscr sub spl infin performance measure a general multirate filter bank system with multiple channels and nonuniform bands is studied with the reconstruction performance measured by the worst case energy gain spl hscr sub spl infin norm of the error system between the multirate system and a pure time delay system using blocking and polyphase decomposition we associate with the multirate system an equivalent linear time invariant lti system whose transfer matrix can be computed by a simple procedure based on this lti system the optimal design problem can be reduced to one of spl hscr sub spl infin optimization which can be solved by ready made software in many cases for illustration optimal synthesis filters are designed for a two channel example and their properties are studied in detail

partial spectrum reconstruction using digital filter banks the problem of reconstructing a part of the spectrum is reduced to designing the filter bank to satisfy a set of conditions for the case considered here these conditions cannot be satisfied simultaneously so perfect reconstruction is not possible the necessary and sufficient conditions on the filters so that the resulting filter bank cancels most alias components are found such filter banks are called partial alias cancellation filter banks the product of the polyphase transfer matrices of these filter banks must be a block pseudocirculant matrix an algorithm design procedure is discussed and examples are given to demonstrate the theory

quadrature mirror filter design in the time domain a new technique for designing quadrature mirror filters is described the formulation carried out in the time domain is shown to result in an optimization problem requiring minimization of a quartic multinomial an iterative solution is suggested which involves computation of the eigenvector of a matrix with a dimensionality equal to one half the number of filter taps our experiments show that convergence to the optimum tap weights is stable and the accuracy of the final solution is limited only by the accuracy of the eigenvalue eigenvector routine as in an earlier technique the user can specify the stop band frequency the relative weights of the passband ripple energy and the stopband residual energy and of course the number of filter taps

on bounds of shift variance in two channel multirate filter banks critically sampled multirate fir filter banks exhibit periodically shift variant behavior caused by nonideal antialiasing filtering in the decimation stage we assess their shift variance quantitatively by analysing changes in the output signal when the filter bank operator and shift operator are interchanged we express these changes by a so called commutator we then derive a sharp upper bound for shift variance via the operator norm of the commutator which is independent of the input signal its core is an eigensystem analysis carried out within a frequency domain formulation of the commutator leading to a matrix norm which depends on frequency this bound can be regarded as a worst case instance holding for all input signals for two channel fir filter banks with perfect reconstruction pr we show that the bound is predominantly determined by the structure of the filter bank rather than by the type of filters used moreover the framework allows to identify the signals for which the upper bound is almost reached as so called near maximizers of the frequency dependent matrix norm for unitary pr filter banks these near maximizers are shown to be narrow band signals to complement this worst case bound we derive an additional bound on shift variance for input signals with given amplitude spectra where we use wide band model spectra instead of narrow band signals like the operator norm this additional bound is based on the above frequency dependent matrix norm we provide results for various critically sampled two channel filter banks such as quadrature mirror filters pr conjugated quadrature filters wavelets and biorthogonal filters banks

subband coder design incorporating recursive quadrature filters and optimum adpcm coders this paper presents the results of an analytical and experimental study of the use of iir quadrature mirror filters and forward adapting adpcm with optimum quantizers for octave band subband coders for speech it is shown that the underlying analysis synthesis systems can be designed such that there is no interband aliasing distortion in the coded speech and such that the analysis synthesis transfer function has no frequency distortion or no phase distortion but not both the experimental study showed that subband coders based on a mixture of infinite impulse response iir and finite duration impulse response fir filters resulted in higher quality coding systems using fewer multiplies than for systems based on fir filters alone it was also found that a signal to noise ratio snr gain of about 4 db could be obtained using optimum quantizers for forward adapting adpcm coders over linear quantizers in backward adapting apcm codes but no perceptual quality gain was observed

a survey of some estimates of eigenvalues and condition numbers for certain preconditioned matrices eigenvalue and condition number estimates for preconditioned iteration matrices provide the information required to estimate the rate of convergence of iterative methods such as preconditioned conjugate gradient methods in recent years various estimates have been derived for perturbed modified block incomplete factorizations we survey and extend some of these and derive new estimates in particular we derive upper and lower estimates of individual eigenvalues and of condition number this includes a discussion that the condition number of preconditioned second order elliptic difference matrices is o h 1 some of the methods are applied to compute certain parameters involved in the computation of the preconditioner

quadrature mirror filter design for an arbitrary number of equal bandwidth channels the two channel quadrature mirror filter structure of croisier and esteban may be extended to an arbitrary number of equal bandwidth channels given certain restrictions on the bandpass filters the most serious restriction is that the stopband attenuation of eacli band pass filter must be high for all frequencies outside twice the nominal 3 db bandwidth of the filter this restriction is not really a limiting factor for speech subband waveform coding since high adjacent channel attenuation is a necessity for the confinement of quantization noise a key feature of our filter structure is that the number of multiplies adds and stored coefficients required for implementation is significantly less than those needed for the conventional qmf structure given the same number of channels fortran code for a 16 channel filter structure is listed as an example of efficient implementation

optimal noise reduction in oversampled pr filter banks this paper studies the optimal noise reduction problem for oversampled filter banks fbs with perfect reconstruction pr constraint both the optimal design and worst case design are considered where the former caters for the noise with known power spectral density psd and the latter for the noise with unknown psd state space based explicit formulae involving only algebraic riccati equation and matrix manipulations are provided for the general iir or fir oversampled pr fbs and the relations between different cases are analyzed and revealed extensive numerical examples are provided to illustrate the proposed design methods and to show their effectiveness

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