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

phase diagram for turbulent transport sampling drift eddy diffusivity and variational principles we study the long time large scale transport in a three parameter family of isotropic incompressible velocity fields with power law spectra scaling law for transport is characterized by the scaling exponent q and the hurst exponent h as functions of the parameters the parameter space is divided into regimes of scaling laws of different em functional forms of the scaling exponent and the hurst exponent we present the full three dimensional phase diagram the limiting process is one of three kinds brownian motion h 1 2 persistent fractional brownian motions 1 2

on the condition numbers of large semidefinite toeplitz matrices abstract this paper is devoted to asymptotic estimates for the spectral or euclidean condition numbers t n a t n a t 1 n a of large n n toeplitz matrices t n a in the case where the symbol a is an l function and re a 0 almost everywhere we describe several classes of symbols a for which t n a increases like log n x n x or even e xn

to what class of fractals does the alexander orbach conjecture apply discussion de la decouverte numerique recente d alexander et orbach selon laquelle pour un agregat infini naissant en percolation le rapport d f d w dimension fractale de l agregat dimension fractale d une marche aleatoire dans l agregat est approximativement independant de d pour d 1

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

optimal block diagonal l_2 scaling of matrices this paper is concerned with optimal one sided and two sided scaling of a matrix with respect to the class of block diagonal matrices optimality conditions are presented a series of lower bounds for the symmetric scaling problems is introduced then for some special cases the solutions are given in a closed form finally differentiability of the best condition number as a function of a symmetric matrix is discussed

closure approximations for passive scalar turbulence a comparative study on an exactly solvable model with complex features some standard closure approximations used in turbulence theory are analyzed by examining systematically the predictions these approximations produce for a passive scalar advection model consisting of a shear flow with a fluctuating cross sweep this model has a general geometric structure of a jet flow with transverse disturbances which occur in a number of contexts and it encompasses a wide variety of possible spatio temporal statistical structures for the velocity field including strong long range correlations even though the eulerian and lagrangian velocity statistics are not equal and the passive scalar statistics exhibit broader than gaussian intermittency this model is nevertheless simple enough so that many passive scalar statistics can be computed exactly and compared systematically with the predictions of the closure approximations our comparative study illustrates the strength and weaknesses of the closure approximations and points out the physical phenomena that these approximations are able or not able to describe properly in particular it is shown that the direct interaction approximation dia one of the most sophisticated closure approximations available fails to reproduce adequately the statistical features of the scalar and may even lead to absdurd predictions even though the equations it produces are rather complicated and difficult to analyze two alternative closure approximations the modified dia mdia and the renormalized lagrangian approximation rla with different levels of sophistication both are simpler to use than the dia and perform better in particular it is shown that both closure approximations always reproduce exactly the second order statistics for the scalar and that the mdia is even able to capture intermittency effects

time scales in homogenization of periodic flows with vanishing molecular diffusion abstract we study the long time transport property of conservative systems perturbed by a small white noise we introduce the dissipation and martingale times and show how they are related to the diffusion time on which a limit theorem is valid the limit theorem is a probabilistic version of homogenization with vanishing molecular diffusion examples of nontrivial time scales are given

optimal bounds on the effective bulk modulus of polycrystals the classical problem of bounding the effective bulk modulus of isotropic polycrystalline aggregates built from a single anisotropic phase is studied for three dimensional composites we find that the voigt and reuss bounds are each attained by multi layered laminate geometries and hence are optimal for two dimensional composites the reuss lower bound is proved to be optimal while a new optimal upper bound is derived

stochastic mode reduction for the immersed boundary method we apply the formulation of a stochastic mode reduction method developed in a recent paper of majda timofeyev and vanden eijnden comm pure appl math 54 2001 pp 891 974 mtv to obtain simplified equations for the dynamics of structures immersed in a thermally fluctuating fluid at low reynolds or kubo number as simulated by a recent extension of the immersed boundary ib method by kramer and peskin proceedings of the second mit conference on computational fluid and solid mechanics elsevier science oxford uk 2003 pp 1755 1758 the effective dynamics of the immersed structures are not obvious in the primitive equations which involve both fluid and structure dynamics but the procedure of mtv allows the rigorous derivation of a reduced stochastic system for the immersed structures alone we find in the limit of small reynolds or kubo number that the lagrangian particle constituents of the immersed structures undergo a drift diffusive motion with several physically correct featur

a multiscale relaxation algorithm for snr maximization in nonorthogonal subband coding develops a technique for improving the applicability of complete nonorthogonal multiresolution transforms to image coding as is well known the l sup 2 norm of the quantization errors is not preserved by nonorthogonal transforms so the l sup 2 reconstruction error may be unacceptably large however given the quantizers and synthesis filters the authors show that this artifact can be eliminated by formulating the coding problem as that of minimizing the l sup 2 reconstruction error over the set of possible encoded images with this new formulation the coding problem becomes a high dimensional discrete optimization problem and features a coupling between the redundancy removing and quantization operations a practical solution to the optimization problem is presented in the form of a multiscale relaxation algorithm using inter and intrascale quantization noise feedback filters bounds on the coding gain over the standard coding technique are derived a simple extension of the algorithm allows for the use of a weighted l sup 2 error criterion and deadband non mmse quantizers experiments using biorthogonal spline filter banks demonstrate appreciable snr gains over the standard coding technique and comparable visual improvements

on singular singularly perturbed initial value problems singularly perturbed systems of ordinary differential equations are considered for which the reduced problem has an infinite family of solutions recent approaches to such problems are compared an

mathematical models with exact renormalization for turbulent transport ii fractal interfaces non gaussian statistics and the sweeping effect this paper continues the study of a model for turbulent transport with an exact renormalization theory which has recently been proposed and developed by the authors three important topics are analyzed with complete mathematical rigor for this model 1 renormalized higher order statistics of a passively advected scalar such as the pair distance distribution and the fractal dimension of interfaces 2 the effect of non gaussian turbulent velocity statistics on renormalization theory 3 the sweeping effect of additional large scale mean velocities a special emphasis is placed on renormalization theory in the vicinity of the value of the analogue of the kolmogorov spectrum in the model in the authors earlier paper it was established that the kolmogorov value is at a phase transition boundary in the exact renormalization theory it is found here that the qualitative model despite its simplicity contains in the vicinity of the kolmogorov value a remarkable amount of the qualitative behavior of turbulent transport which has been uncovered in recent experiments and proposed in phenomenological theories in particular the richardson 4 3 law for pair dispersion and interfaces with fractal dimension defect of 2 3 occur in the model rigorously as limits when the kolmogorov spectrum is approached as a limit from one side of the phase transition boundary alternative corrections to the richardson law with the same form as those proposed heuristically in the recent literature and interfaces with fractal dimension defect 1 3 occur in the model when the kolmogorov spectrum is approached from the other side of the phase transition it is very interesting that fractal dimension defects of roughly the value either 1 3 or 2 3 for level sets and interfaces of passive scalars have been ubiquitous in recent turbulence experiments as regards non gaussian the asymptotic normality of normalized integrals b 56 corresponding to compactly supported blobs with mean zero the proof of this latter fact is done in the same way as step 2 proposition b 3 using the fact that the corresponding random processes tilde v delta s have finite domain of dependence this concludes the proof of proposition b 4

probabilistic bounds on error amplification of randomly generated frames hilbert space frames have recently attracted attention in the signal processing community in this paper we consider the problem of describing the statistical distribution of the error amplification and lower bound of a frame obtained by randomly picking vectors from a larger frame the frame pool the key result of this paper is an analytic bound to the probability of having an error amplification larger than a given value we also consider the possibility of content reconstruction using an approximate but efficient algorithm the theoretical results are completed by means of numerical experiments

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 spatial feature extraction and regularization model for the head related transfer function a functional representation is proposed for complex valued amplitude and phase head related transfer functions hrtfs including both frequency and spatial dependence the frequency variation is spanned by a set of eigentransfer functions efs that are generated using the karhunen loeve expansion any hrtf is represented as a weighted combination of the efs where the weights are functions of the hrtfs spatial location and are termed spatial characteristic functions scfs samples of the scfs are obtained by projecting the measured hrtfs onto the efs a regularization framework is employed to obtain a functional representation for the scfs by fitting each set of scf samples with a two dimensional spline acoustic validation of the model s fidelity and predictive capability is provided using 2188 measured hrtfs from a kemar manikin and 1816 measured hrtfs from an anesthetized live cat errors between measured and modeled hrtfs are generally less than one percent larger errors occur in the contralateral regions for kemar and lower back regions for the cat as a consequence of the relatively small hrtf amplitudes resulting from head shadowing methods for reducing these errors are discussed

percolation of level sets for two dimensional random fields with lattice symmetry let x x 2 be a random field which may be viewed as the potential of an incompressible flow for which the trajectories follow the level lines of percolation methods are used to analyze the sizes of the connected components of level sets x x h and sets x x h in several classes of random fields with lattice symmetry in typical cases there is a sharp transition at a critical value ofh from exponential boundedness for such components to the existence of an unbounded component in some examples however there is a nondegenerate interval of values ofh where components are bounded but not exponentially so and in other cases each level set may be a single infinite line which visits every region of the lattice

heat equilibrium distribution in a turbulent flow we consider a shear flow of a scale invariant gaussian random velocity field that does not depend on the coordinates in the direction of the flow we investigate a heat advection coming from a gaussian random homogeneous source we discuss a relaxation at large time of a temperature distribution determined by the forced advection diffusion equation we represent the temperature correlation functions by means of the feynman kac formula jensen inequalities are applied for lower and upper bounds on the correlation functions we show that at finite time there is no velocity dependence of long range temperature correlations low momentum asymptotics in the direction of the flow but the equilibrium heat distribution has large distance correlations low momentum behavior with an index depending on the scaling index of the random flow and of the index of the random forcing if the velocity has correlations growing with the distance a turbulent flow then the large distance correlations depend in a crucial wa

on the superdiffusive behavior of passive tracer with a gaussian drift in the present article we consider a motion of a passive tracer particle whose trajectory satisfies the ito stochastic differential equation d x t v t x t dt sqrt 2 kappa d w t where w is a brownian motion v is a stationary gaussian random field with incompressible realizations independent of w and 0 we prove the superdiffusive character of the motion under certain conditions on the energy spectrum of the velocity field the result is shown both for steady time independent and time dependent and markovian velocity fields in addition we provide explicit upper and lower bounds for the hurst exponent of the trajectory all previous rigorous results concerned explicitely solvable shear flows cases

on strong anomalous diffusion superdiffusive behavior i e x2 t t2 with 1 2 is in general not completely characterized by a unique exponent we study some systems exhibiting strong anomalous diffusion i e x t q tq q where 2 1 2 and q q is not a linear function of q this feature is different from the weak superdiffusive regime i e q const 1 2 occurring in random shear flows strong anomalous diffusion can be generated by nontrivial chaotic dynamics e g lagrangian motion in 2d time dependent incompressible velocity fields 2d symplectic maps and 1d intermittent maps typically the function q q is piecewise linear this is due to two mechanisms a weak anomalous diffusion for the typical events and a ballistic transport for the rare excursions in order to have strong anomalous diffusion one needs a violation of the hypothesis of the central limit theorem this happens only in a very narrow region of the control parameters space in the presence of strong anomalous diffusion one does not have a unique exponent and therefore one has the failure of the usual scaling p x t t f x t of the probability density this implies that the effective equation at large scale and long time for p x t obeys neither the usual fick equation nor other linear equations involving temporal and or spatial fractional derivatives

frame analysis for biorthogonal cosine modulated filterbanks this paper addresses the efficient computation of frame bounds for cosine modulated filterbanks we derive explicit expressions for the eigenvalues of the frame operator that can be easily computed from the prototype s polyphase components the number of channels and the downsampling factor may be even or odd and the oversampling factor is supposed to be an integer the analysis of low delay biorthogonal filterbanks shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and thus to an undesirable numerical behavior because the computational cost of determining the frame bounds with the proposed method is very low we can directly use the bounds during prototype optimization and obtain prototypes with minimum stopband energy under the condition of fixed frame bounds various design examples are presented

stieltjes integral representation of effective diffusivities in time dependent flows a stieltjes integral representation for the effective diffusivity of a passive scalar in time dependent incompressible flows is developed the representation provides a summability formula for the perturbative expansion of the diffusivity in powers of the p eclet number in particular upper and lower bounds on the effective diffusivity are obtained from pad e approximants of the series

generating 3d audio using a regularized hrtf hrir filter 3d sound is generated using an improved hrtf modeling technique for synthesizing hrtfs with varying degrees of smoothness and generalization a plurality n of spatial characteristic function sets are regularized or smoothed before combination with corresponding eigen filter functions and summed to provide an hrtf or hrir filter having improved smoothness in a continuous auditory space a trade off is allowed between accuracy in localization and smoothness by controlling the smoothness level of the regularizing models with a lambda factor improved smoothness in the hrtf filter allows the perception by the listener of a smoothly moving sound rendering free of annoying discontinuities creating clicks in the 3d sound

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

biorthogonal filterbanks and energy preservation property in image compression the energy preservation property is among the most widely used properties of orthogonal transforms in image compression because the reconstruction error can be computed as the sum of the subband distortions thus this is a key point in the use of efficient bit allocation techniques such as rate distortion algorithms therefore we study the nonorthogonality of biorthogonal filterbanks with reference to energy preservation from both theoretical and applicative points of view we calculate the riesz bounds as energy preservation bounds for filterbanks and discrete wavelet transforms and then connect these results with the riesz bounds of the related continuous wavelet transform the simultaneous use of biorthogonal filterbanks and rate distortion algorithms is then discussed as the issue of estimating the reconstruction error as an additive function of the subband distortion we propose a weighted sum of the subband distortions as an estimate whose accuracy is calculated by a wide range of experiments this accuracy is shown to be correlated to the riesz bounds of the filterbanks we conclude that from this point of view most of the usual biorthogonal filterbanks may be considered as nearly orthogonal

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

maximal effective diffusivity for time periodic incompressible fluid flows in this paper we establish conditions for the maximal pe 2 behavior of the effective diffusivity in time periodic incompressible velocity fields for both the pe to infty and pe to 0 limits using ergodic theory these conditions can be interpreted in terms of the lagrangian time averages of the velocity we reinterpret the maximal effective diffusivity conditions in terms of a poincare map of the velocity field the connection between the pe 2 asymptotic behavior of the effective diffusivity and t 2 asymptotic dispersion of a nondiffusive tracer is established several examples are analyzed we relate the existence of accelerator modes in a flow with pe 2 effective diffusivity and show how maximal effective diffusivity can appear as a result of a time dependent perturbation of a steady cellular velocity field also three dimensional symmetric time dependent duct velocity fields are analyzed and the mechanism for an effective diffusivity with peclet number dependence other than p

variational principles for complex conductivity viscoelasticity and similar problems in media with complex moduli linear processes in media with dissipation arising in conductivity optics viscoelasticity etc are considered time periodic fields in such media are described by linear differential equations for complex valued potentials the properties of the media are characterized by complex valued tensors for example by complex conductivity or complex elasticity tensors variational formulations are suggested for such problems the functionals whose euler equations coincide with the original ones are constructed four equivalent variational principles are obtained two minimax and two minimal ones the functionals of the obtained minimal variational principles are proportional to the energy dissipation averaged over the period of oscillation the last principles can be used in the homogenization theory to obtain the bounds on the effective properties of composite materials with complex valued properties tensors

improved rigorous upper bounds for transport due to passive advection described by simple models of bounded systems the work of j a krommes and r a smith on rigorous upper bounds for the turbulent transport of a passively advected scalar is extended in two directions 1 for their reference model improved upper bounds are obtained by utilizing more sophisticated two time constraints which include the effects of cross correlations up to fourth order numerical solutions of the model stochastic differential equation are also obtained they show that the new bounds compare quite favorably with the exact results even at large reynolds and kubo numbers 2 the theory is extended to take account of afinite spatial autocorrelation lengthlc as a reasonably generic example the problem of particle transport due to statistically specified stochastic magnetic fields in a collisionless turbulent plasma is revisited a bound is obtained which reduces for smalllc to the quasilinear limit and for largelc to the strong turbulence limit and which provides a reasonable and rigorous interpolation for intermediate values oflc

large deviations for brownian motion in a random scenery we prove large deviations principles in large time for the brownian occupation time in random scenery frac 1 t int 0 t xi b s ds the random field is constant on the elements of a partition of d into unit cubes these random constants say left lbrace xi j j in mathbb z d right rbrace consist of i i d bounded variables independent of the brownian motion bs s 0 this model is a time continuous version of kesten and spitzer s random walk in random scenery we prove large deviations principles in quenched and annealed settings

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

diffusion in turbulence we prove long time diffusive behavior homogenization for convection diffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix simple shear flow examples show that this result is sharp for flows that have stationary stream matrices

on superdiffusive behavior of a passive tracer in a random flow abstract in this note we consider a passive tracer model describing particle dispersion in a turbulent flow the trajectory of the particle is given by the solution of an ordinary differential equation x t f x t x 0 x 0 where f x is a divergence free random vector field that is spatially homogeneous and isotropic we show that trajectories of the tracer display superdiffusive behavior when the random velocity f x decorrelates at large distances but does it not rapidly but rather at some moderate rate the main tools used in the proofs are variational principles and tauberian type theorems

tight weyl heisenberg frames in l sup 2 z tight weyl heisenberg frames in l sup 2 z are the tool for short time fourier analysis in discrete time they are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory good resolution of short time fourier analysis in the joint time frequency plane is not attainable unless some redundancy is introduced that is the reason for considering overcomplete weyl heisenberg expansions the main result of this correspondence is a complete parameterization of finite length tight weyl heisenberg frames in l sup 2 z with arbitrary rational oversampling ratios this parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks which is introduced first

stieltjes integral representation and effective diffusivity bounds for turbulent transport a stieltjes integral representation for the effective diffusivity in turbulent transport is developed this formula is valid for all peclet numbers and yields a rigorous resummation of the divergent perturbation series in peclet number provided that all diagrams are computed exactly another consequence of the integral representation is convergent upper and lower bounds on effective diffusivity for all peclet numbers utilizing a prescribed finite number of terms in their perturbation series

boundary layers for cellular flows at high peclet numbers we analyze the behavior of solutions of steady advection diffusion problems in bounded domains with prescribed dirichlet data when the peclet number pe 1 is large we show that the solution converges to a constant in each flow cell outside a boundary layer of width o 1 2 pe 1 around the flow separatrices we construct an dependent approximate water pipe problem purely inside the boundary layer that provides a good approximation of the solution of the full problem but has independent computational cost we also define an asymptotic problem on the graph of streamline separatrices and show that solution of the water pipe problem itself may be approximated by an asymptotic independent problem on this graph finally we show that the dirichlet to neumann map of the water pipe problem approximates the dirichlet to neumann map of the separatrix problem with an error independent of the flow outside the boundary layers 2004 wiley periodicals inc

time domain oversampled lapped transforms theory structure and application in image coding this paper generalizes time domain lapped transforms tdlts proposed by tran et al to oversampled systems thus leading to time domain oversampled lapped transforms tdolts these new transforms correspond to a subclass of oversampled linear phase perfect reconstruction filterbanks olpprfbs which can be implemented by adding a prefilter before the discrete cosine transform dct and a post filter after the inverse discrete cosine transform idct structures of the pre and post filters are developed and the frame theoretic properties of tdolts are analyzed a new parameterization of lattice matrices through the givens qr factorization is proposed for unconstrained optimization comparisons with other parameterization methods are also included several design examples along with some image coding results are presented to demonstrate the validity of the theory and the potential of tdolts in image coding especially in error resilient coding

percolation transport in random flows with drift and time dependence effects abstract this paper considers the influence of drift flow and time dependence effects on the passive scalar behavior in the framework of the percolation approach it is suggested to modify the renormalization condition of the small parameter of the percolation model in accordance with the additional external influences superimposed on the system this approach makes it possible to consider simultaneously both parameters the characteristic drift velocity ud and the characteristic perturbation frequency the effective diffusion coefficient d eff 1 7 satisfactory describes the low frequency region in which the long range correlation effects play a significant role

precoder design and blind identification of mimo channels in this paper blind identification problem based on second order statistics sos of received signals is investigated for multiple input multiple output mimo channels it is shown that precoders introduced in transmitters can provide certain extra information for blind identification problem and commonly used identifiability conditions on mimo channels can be relaxed a design criterion for the precoders in frequency domain is proposed two blind identification algorithms based on the knowledge of the precoders and sos of the received signals are then developed in these algorithms due to particular structure of the precoders the blind identification problem for a mimo channel is decomposed into several independent single input multiple output simo channel identification problems the presented algorithms are robust to an overestimated channel order and not sensitive to signal to noise ratio snr compared with the existing results a larger class of mimo finite impulse response fir channels can be identified by the new methods

on discrete short time fourier analysis weyl heisenberg frames are a principal tool of short time fourier analysis we present a comprehensive study of weyl heisenberg frames in l sup 2 z with a focus on frames that are tight a number of properties of these frames are derived a complete parameterization of finite length windows for tight weyl heisenberg frames in l sup 2 z is described design of windows for tight weyl heisenberg frames requires optimization of their frequency characteristics under nonlinear constraints we propose an efficient design method based on expansions with respect to prolate spheroidal sequences the advantages of the proposed method over standard optimization procedures include a reduction in computational complexity and the ability to provide long windows that can be specified concisely using only a few parameters these advantages become increasingly pronounced as the frame redundancy increases the resilience of overcomplete weyl heisenberg expansions to additive noise and quantization is also studied we show that manifestations of degradation due to uncorrelated zero mean additive noise are inversely proportional to the expansion redundancy whereas the quantization error is for a given quantization step inversely proportional to the square of the expansion redundancy

diffusion advection in cellular flows with large peclet numbers for periodic two dimensional cellular flows in incompressible fluids we provide explicit upper and lower estimates of the effective diffusivity which have the correct scaling behavior for large peclet numbers we demonstrate that all allowed scaling laws can occur the bounds prove that there is no residual diffusion in the infinite peclet number limit for holder continuous flows answering a problem posed by kozlov

homogenization of a diffusion process in a divergence free random field on etudie le probleme d homogeneisation pour un processus de diffusion dans un champ de derive aleatoire independant de la divergence dans le cas particulier d un petit champ gaussien on derive un developpement asymptotique de la matrice de diffusion efficace en termes de sa densite spectrale

minimizing the euclidean condition number this paper considers the problem of determining the row and or column scaling of a matrix a that minimizes the condition number of the scaled matrix this problem has been studied by many authors for the cases of the infty norm and the 1 norm the scaling problem was completely solved in the 1960s it is the euclidean norm case that has widespread application in robust control analyses for example it is used for integral controllability tests based on steady state information for the selection of sensors and actuators based on dynamic information and for studying the sensitivity of stability to uncertainty in control systems minimizing the scaled euclidean condition number has been an open question researchers proposed approaches to solving the problem numerically but none of the proposed numerical approaches guaranteed convergence to the true minimum this paper provides a convex optimization procedure to determine the scalings that minimize the euclidean condition number this optimization can be solved in polynomial time with off the shelf software

numerical study of strong anomalous diffusion the superdiffusion behavior i e x2 t t2 with 1 2 in general is not completely characterized by a unique exponent we study some systems exhibiting strong anomalous diffusion i e x t q tq q where 2 1 2 and q q is not a linear function of q this feature is different from the weak superdiffusion regime i e q const 1 2 as in random shear flows the strong anomalous diffusion can be generated by nontrivial chaotic dynamics e g lagrangian motion in 2d time dependent incompressible velocity fields 2d symplectic maps and 1d intermittent maps typically the function q q is piecewise linear this corresponds to two mechanisms a weak anomalous diffusion for the typical events and a ballistic transport for the rare excursions in order to have strong anomalous diffusion one needs a violation of the hypothesis of the central limit theorem this happens only in a very narrow region of the control parameters space in the presence of strong anomalous diffusion one does not have a unique exponent and therefore one has the failure of the usual scaling of the probability distribution i e p x t t f x t this implies that the effective equation at large scale and long time for p x t can obey neither the usual fick equation nor other linear equations involving temporal and or spatial fractional derivatives

blind identification with periodic modulation a time domain approach we propose a method for blind identification of finite impulse response fir channels with periodic modulation the time domain formulation in terms of block signals is simple compared with existing frequency domain formulations it is shown that the linear equations relating the products of channel coefficients and the autocorrelation matrix of the received signal can be further arranged into decoupled groups the arrangement reduces computations and improves accuracy of the solution it also leads to very simple identifiability conditions and a very natural formulation of the optimal modulating sequence selection problem the proposed optimal selection minimizes the effects of channel noise and error in autocorrelation matrix estimation it results in a consistent channel estimate when the channel noise is white simulation results show that the method yields good performance it compares favorably with an existing subspace modulation induced cyclostationarity method and it is robust with respect to channel order overestimation the effect of modulation period and threshold of the modulating sequence are also discussed

convection enhanced diffusion for random flows we analyze the effective diffusivity of a passive scalar in a two dimensional steady incompressible random flow that has mean zero and a stationary stream function we show that in the limit of small diffusivity or large peclet number with convection dominating there is substantial enhancement of the effective diffusivity our analysis is based on some new variational principles for convection diffusion problems and on some facts from continuum percolation theory some of which are widely believed to be correct but have not been proved yet we show in detail how the variational principles convert information about the geometry of the level lines of the random stream function into properties of the effective diffusivity and substantiate the result of isichenko and kalda that the effective diffusivity behaves like 3 13 when the molecular diffusivity is small assuming some percolation theoretic facts we also analyze the effective diffusivity for a special class of convective flows random cellular flows where the facts from percolation theory are well established and their use in the variational principles is more direct than for general random flows

condition numbers and their condition numbers abstract various normwise relative condition numbers that measure the sensitivity of matrix inversion and the solution of linear systems are characterized new results are derived for the cases where two common noninduced matrix norms are used and where different vector norms are used for the domain and range of the matrix condition numbers that respect the structure of symmetric problems are also analyzed the sensitivity of the condition number itself is then investigated and we obtain sharp examples of demmel s general result that for certain problems in numerical analysis the condition number of the condition number is the condition number finally upper bounds are derived for the sensitivity of componentwise condition numbers

voice activity detection method and apparatus using the same free field to eardrum transfer functions fetf s are developed by comparing auditory data for points in three dimensional space for a model ear and auditory data collected for the same listening location with a microphone each fetf is represented as a weighted sum of frequency dependent functions obtained from an expansion of the measured fetf s covariance matrix spatial transformation characteristic functions stcf s are applied to transform the weighted frequency dependent factors to functions of spatial variables for azimuth and elevation a generalized spline model is fit to each stcf to filter out noise and permit interpolation of the stcf between measured points sound is reproduced for a selected direction by synthesizing the weighted frequency dependent factors with the smoothed and interpolated stcf s

spectral analysis and computation for homogenization of advection diffusion processes in steady flows advective diffusion plays a key role in the transport of salt heat buoys and markers in geophysical flows in the dispersion of pollutants and trace gases in the atmosphere and even in the dynamics of sea ice floes influenced by winds and ocean currents the long time large scale behavior of such systems is equivalent to an enhanced diffusion process with an effective diffusivity matrix d three decades ago a stieltjes integral representation for the homogenized matrix involving a spectral measure of a self adjoint operator was developed however analytical calculations of d have been obtained for only a few simple flows and numerical computations of the effective behavior based on this spectral representation have apparently not been attempted we overcome these limitations by providing a mathematical foundation for the computation of stieltjes integral representations of d we explore two different approaches and for each approach we derive new stieltjes integral representations and rigorous bounds for the symmetric and antisymmetric parts of d involving the molecular diffusivity and a spectral measure of a self adjoint operator that depends on the characteristics of a randomly perturbed periodic flow in discrete formulations of each approach we express explicitly in terms of standard or generalized eigenvalues and eigenvectors of hermitian matrices we develop and implement an efficient numerical algorithm that combines beneficial numerical attributes of each approach we use this method to compute the effective behavior for model flows and relate spectral characteristics to flow geometry and transport properties advective diffusion plays a key role in the transport of salt heat buoys and markers in geophysical flows in the dispersion of pollutants and trace gases in the atmosphere and even in the dynamics of sea ice floes influenced by winds and ocean currents the long time large scale behavior of such systems is equivalent to an enhanced diffusion process with an effective diffusivity matrix d three decades ago a stieltjes integral representation for the homogenized matrix involving a spectral measure of a self adjoint operator was developed however analytical calculations of d have been obtained for only a few simple flows and numerical computations of the effective behavior based on this spectral representation have apparently not been attempted we overcome these limitations by providing a mathematical foundation for the computation of stieltjes integral representations of d we explore two different approaches and for each approach we derive new stieltjes integral representations and rigorou

front propagation in reactive systems with anomalous diffusion abstract we study front propagation of reactive fields in systems whose diffusive behavior is anomalous both superdiffusive and subdiffusive the features of the front propagation depend not only on the scaling exponent x t 2 t 2 but also on the detailed shape of the probability distribution of the diffusive process from the analysis of different systems we have three possible behavior of front propagation the usual fisher kolmogorov like scenario i e the field has a spatial exponential tail moving with constant speed v f and thickness the field has a spatial exponential tail but v f and change in time as a power law and finally the field has a spatial power law tail and v f increases exponentially in time a linear analysis of the front tail is in quantitative agreement with the numerical simulations it is remarkable the fact that anomalous diffusion is neither necessary nor sufficient condition for the linear front propagation moreover if the probability distribution of the transport process follows the scaling relation given by the flory argument the front propagation is standard fisher kolmogorov like even in presence of super or sub diffusion

macrodispersion in a radially diverging flow field with finite peclet numbers 1 perturbation theory approach we study the transport behavior of a tracer in a radially diverging heterogeneous velocity field making use of homogenization theory we derive effective transport equations these effective transport equations are very similar to those defined on the local scale however the local transport parameters such as local dispersion coefficients are replaced by effective dispersion coefficients for smoothly varying heterogeneous media explicit results for effective radial dispersion coefficients are derived starting with the purely advective transport behavior infinite peclet numbers we extend our calculations to transport with finite peclet numbers we find that the impact of molecular diffusion on the effective dispersivity differs from the impact of local dispersion including local dispersion leads to effective dispersivities which are constant and equivalent to the effective dispersivities found in uniform flow configurations in contrast effective dispersivities including diffusion are not constant but depend on the radial distance we compare the results found by homogenization theory with those derived by neuweiler et al this issue by standard method of moments

boundary value problem with unbounded fast oscillatory random flows abstract we use tartar s weak convergence method in conjunction with a variational principle to prove a sharp homogenization theorem for diffusion in steady random flows the flow has a stationary and square integrable stream matrix the key of our approach is introducing approximate correctors by means of a saddle point variational principle we also obtain the two term asymptotics

diffusion in layered random flows polymers electrons in random potentials and spin depolarization in random fields several related models are studied in a common framework we first reconsider the model of matheron and de marsilly for anomalous tracer dispersion in a stratified porous medium in each horizontal layer the flow velocity is constant parallel to the layer and depends randomly on the vertical coordinate z this model is mapped onto ad 1 localization problem in a random potential and equivalently onto ad 1 polymer at larget theaveraged distribution of horizontal displacementsx takes the scaling form p x t z 0 at 5 4q bxt 3 4 whereq y is independent of the details of the model q y a andb are obtained exactly for a large class of models from the lifschitz tails of the localization problem we find in the regionx t3 4 i e y thatq y y exp c y 4 3 we also obtain exactly ind 1 the scaling functions for the local and total average magnetization of spins diffusing in a random magnetic field by mapping onto a polymer problem as well as the average local concentration for diffusion in the presence of random sources and sinks these mappings are then used to study higher dimensional extensions of these models

method and apparatus for regularizing measured hrtf for smooth 3d digital audio the present invention provides an improved hrtf modeling technique for synthesizing hrtfs with varying degrees of smoothness and generalization a plurality n of spatial characteristic function sets are regularized or smoothed before combination with corresponding eigen filter functions and summed to provide an hrtf or hrir filter having improved smoothness in a continuous auditory space a trade off is allowed between accuracy in localization and smoothness by controlling the smoothness level of the regularizing models with a lambda factor improved smoothness in the hrtf filter allows the perception by the listener of a smoothly moving sound rendering free of annoying discontinuities creating clicks in the 3d sound

design of multirate filter banks by spl hscr sub spl infin optimization a procedure is developed to design iir synthesis filters in a multirate filter bank the filters minimize the l sub 2 induced norm of the error system between the multirate filter bank and a desired pure time delay system this criterion is reduced to one of spl hscr sub spl infin optimization for which there is ready made software

bound ratio minimization of filter bank frames this paper investigates and solves the problem of frame bound ratio minimization for oversampled perfect reconstruction pr filter banks fbs for a given analysis prfb a finite dimensional convex optimization algorithm is derived to redesign the subband gain of each channel the redesign minimizes the frame bound ratio of the fb while maintaining its original properties and performance the obtained solution is precise without involving frequency domain approximation and can be applied to many practical problems in signal processing the optimal solution is applied to subband noise suppression and tree structured fb gain optimization resulting in deeper insights and novel solutions to these two general classes of problems and considerable performance improvement effectiveness of the optimal solution is demonstrated by extensive numerical examples

convection of microstructure and related problems we study how two flows that vary spatially in two widely separated scales evolve under the dynamics of euler s equations we use a multiple scale approach which we motivate by studying some simpler model problems

multiscale numerical methods for passive advection diffusion in incompressible turbulent flow fields we propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection diffusion equations with steady incompressible velocity fields with multi spatial scales the method uses decompositions of the velocity fields in the fourier space which are similar to the decomposition in large eddy simulations it also uses a hierarchy of local domains with different resolutions as in multigrid methods the effective diffusivity from finer scale is used for the next coarser level computation and this process is repeated up to the coarsest scale of interest the grids are only in local domains whose sizes decrease depending on the resolution level so that the overall computational complexity increases linearly as the number of different resolution grids increases the method captures interactions between finer and coarser scales but has to sacrifice some of interactions between different scales the proposed method is numerically tested with 2d examples including a successful approximation to a continuous spectrum flow

an integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows precise necessary and sufficient conditions on the velocity statistics for mean field behavior in advection diffusion by a steady incompressible velocity field are developed here under these conditions a rigorous stieltjes integral representation for effective diffusivity in turbulent transport is derived this representation is valid for all peclet numbers and provides a rigorous resummation of the divergent perturbation expansion in powers of the peclet number one consequence of this representation is that convergent upper and lower bounds on effective diffusivity for all peclet numbers can be obtained utilizing a prescribed finite number of terms in the perturbation series explicit rigorous examples of steady incompressible velocity fields are constructed which have effective diffusivities realizing the simplest upper or lower bounds for all peclet numbers a nonlocal variational principle for effective diffusivity is developed along with applications to advection diffusion by random arrays of vortices a new class of rigorous examples is introduced these examples have an explicit stieltjes measure for the effective diffusivity furthermore the effective diffusivity behaves likek0 pe 1 2 in the limit of large peclet numbers wherek0 is the molecular diffusivity formal analogies with the theory of composite materials are exploited systematically

acceleration of the frame algorithm shows how polynomial acceleration techniques which have been developed for the solution of large linear systems can be employed to improve and accelerate the frame algorithm these methods permit a reduction in the number of necessary iterations by an order of magnitude when the frame algorithm is slow the author gives several examples from the theory of irregular sampling from wavelet theory and from gabor theory where these methods are probably mandatory for efficient reconstruction

multirate periodic systems and constrained analytic function interpolation problems multirate periodic systems and some related constrained analytic function interpolation problems are studied in this paper after showing how to convert a general multirate periodic system to an equivalent linear time invariant lti system with a structural constraint we formulate some analytic function interpolation problems with such a constraint that can find various applications in the study of multirate and periodic systems both the solvability conditions and characterization of all solutions are presented to these constrained interpolation problems

double preconditioning for gabor frames the authors present an application of the general idea of preconditioning in the context of gabor frames while most iterative algorithms aim at a more or less costly exact numerical calculation of the inverse gabor frame matrix we propose here the use of cheap methods to find an approximation for it based on double preconditioning we thereby obtain good approximations of the true dual gabor atom at low computational costs since the gabor frame matrix commutes with certain time frequency shifts it is natural to make use of diagonal and circulant preconditioners sharing this property part of the efficiency of the proposed scheme results from the fact that all the matrices involved share a well known block matrix structure at least for the smooth gabor atoms typically used the combination of these two preconditioners leads consistently to good results these claims are supported by numerical experiments in this paper for numerical evaluations we introduce two new matrix norms which can be calculated efficiently by exploiting the structure of the frame matrix

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

network approximation for transport properties of high contrast materials we show that the effective complex impedance of materials with conductivity and dielectric permittivity that have high contrast can be calculated approximately by solving a suitable resistor capacitor network we use variational principles extensively for the analysis and we assess the accuracy of the network approximation by numerical computations

mathematical models with exact renormalization for turbulent transport the advection diffusion of a passive scalar by incompressible velocity fields which admit a statistical description and involve a continuous range of excited spatial and or temporal scales is very important in applications ranging from fully developed turbulence to the diffusion of tracers in heterogeneous porous media a variety of renormalization theories which typically utilize partial resummation of divergent perturbation series according to various recipes have been applied to this problem in various contexts in this paper a simple model problem for the advection diffusion of a passive scalar is introduced and the complete renormalization theory is developed with full mathematical rigor explicit formulas for the anomalous time scaling in various regimes as well as the green s function for the large scale long time ensemble average are developed here formulas for the renormalized higher order statistics are also developed the simple form of the model problem is deceptive the renormalization theory for this problem exhibits a remarkable range of different renormalization phenomena as parameters in the velocity statistics are varied these phenomena include the existence of several distinct anomalous scaling regimes as the spectral parameter tilde varepsilon is varied as well as explicit regimes in tilde varepsilon where the effective equation for the ensemble average is not a simple diffusion equation but instead involves an explicit random nonlocal eddy diffusivity we use fourier analysis and the feynman kac formula as main tools in the explicit exact renormalization theory developed here

efficient computation of frame bounds using lmi based optimization this correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction pr filter banks fbs it first shows that computation of the optimal frame bounds for complex valued oversampled pr fbs can be formulated as a convex optimization subject to complex valued linear matrix inequality lmi constraints and solved by effective interior point algorithms it then deals with discrete time weyl heisenberg wh frames to compute bounds on the wh frames by real valued lmi optimization the wh frames are closely related to modulated fbs and have complex coefficients four examples are given to illustrate the generality and effectiveness of the proposed method

diffusion coefficients as function of kubo number in random fields particle standard diffusion d k in 2d homogeneous isotropic stationary random velocity fields is studied numerically as a function of the dimensionless kubo number k defined as the ratio between the correlation time of the velocity field and its sweeping time the three cases corresponding to the energy spectra proportional in the inertial range respectively to k 3 k 5 3 and k 2 are considered and two different power law regimes are found for large but finite k

optimal two sided diagonal scaling for filter bank frames two sided diagonal scaling for transfer matrices is formulated an efficient algorithm is proposed to compute globally optimal solutions using the iterated bi section and linear matrix inequality lmi solver it is shown that the two sided scaling of filter bank fb frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal and that the frame bound ratio of fb frames can be effectively improved by such scaling explicit formulas are established for both uniform and nonuniform fb frames including detail formulas for discrete weyl heisenberg frames and tree structured fbs discrete wavelets different examples show the effectiveness of the obtained results

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

a martingale approach to homogenization of unbounded random flows we study the asymptotic behavior of brownian motion in steady unbounded incompressible random flows we prove an invariance principle for almost all realizations of random flows the key compactness result is obtained by moser s iterative scheme in pde theory

asymptotic analysis of quasi static transport in high constrast conductive media we show that transport in high contrast conductive media has a discrete behavior in the asymptotic limit of infinitely high contrast the effective impedance and the magnetic field in such media are given by discrete min max variational principles furthermore we show that the transport problem has an asymptotic resistor inductor capacitor network approximation we use new variational formulations of the effective impedance of the media and we assess the accuracy of the asymptotic approximation by numerical computations

bounds for effective parameters of heterogeneous media by analytic continuation we give a mathematical formulation of a method for obtaining bounds on effective parameters developed by d bergman and g w milton this method in contrast to others used before does not rely on a variational principle but exploits the properties of the effective parameter as an analytic function of the component parameters the method is at present restricted to two component media