direct frequency domain deconvolution when the signals have no spectral inverse a method for frequency domain deconvolution when the kernel has no spectral inverse is presented discrete frequency interpolation is used to avoid zero valued frequency samples the algorithm does not suffer from the spectral singularities of the original kernal and its complexity is proportional to that of the fast fourier transform a comparative noise study showed improved performance relative to the direct frequency domain method

solution of the h sub infinity optimal linear filtering problem for discrete time systems the solution of l sub 2 minimum variance and h sub infinity estimation problems is considered using a polynomial systems approach the results for the l sub 2 filtering problem which corresponds with wiener or kalman filtering prediction are first presented in polynomial matrix form attention then turns to the solution of the h sub infinity estimation problem for scalar systems numerous examples are presented to illustrate the computational procedures the two types of estimator are appropriate to very different estimation problems and the new h sub infinity devices should be valuable in certain application areas

acoustic propagation in non uniform waveguides revisiting webster equation using evanescent boundary modes the scattering of an acoustic wave propagating in a non uniform waveguide is inspected by revisiting improved multimodal methods in which the introduction of additional modes so called boundary mo

the complex cepstrum of higher order cumulants and nonminimum phase system identification a computationally efficient identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase system the method is based on the idea of computing the complex cepstrum of higher order cumulants of the system output in particular the differential cepstrum parameters of the nonminimum phase impulse response are estimated directly from higher order cumulants by least squares solution or two dimensional fft operations the method reconstructs the minimum phase and maximum phase impulse response components separately it is flexible enough to be applied on autoregressive ar moving average ma or arma system without a priori knowledge of the type of the system benchmark simulation examples demonstrate the effectiveness of the method even with short length data records

joint data and channel estimation using blind trellis search techniques a novel method of maximum likelihood sequence estimation is proposed for data that are transmitted over unknown linear channels this procedure does not require a startup sequence for estimating the channel impulse response rather the data and the channel are simultaneously estimated it is implemented without any loss of optimality by a trellis search algorithm which searches for the best data sequence from among a number of hypothesized trellises which are constructed from the observed sequence the number of states in each trellis and the number of trellises grow exponentially with the channel memory a suboptimal trellis search algorithm is proposed whose complexity at best is slightly higher than that of the adaptive viterbi algorithm operating with a known channel response a simplified channel estimation algorithm when the number of data alphabets is greater than 2 is also proposed fast convergence of the algorithm in estimating the channel is demonstrated for binary pulse amplitude modulation over a variety of channels convergence over a wide range of snr occurs within 100 symbols the channel estimation algorithm for multi level signals converges within 500 1000 symbols we finally present an application of this algorithm to the problem of sequence estimation in the presence of rapidly time varying intersymbol interference the algorithm provides reliable zero delay decisions which results in a better channel tracking algorithm when compared to previously proposed schemes

multimodal admittance method in waveguides and singularity behavior at high frequencies this work presents a multimodal method for the propagation in a waveguide with varying height and its relation to trapped modes or quasi trapped modes the coupled mode equations are obtained by projecting the helmholtz equation on the local transverse modes to solve this problem we integrate the riccati equation governing the admittance matrix dirichlet to neumann operator for many propagating modes i e at high frequencies the numerical integration of the riccati equation shows that the rule is that this matrix has quasi singularities associated to quasi trapped modes

lamb wave propagation in inhomogeneous elastic waveguides the problem of lamb wave propagation in an axially multilayered waveguide is treated by a multimodal approach a general formalism is proposed that avoids the numerical divergence due to evanescent

a study of wave propagation in varying cross section waveguides by modal decomposition part i theory and validation the propagation of acoustic waves in waveguides with variable cross section is considered using multimodal decomposition the approach adopted is to construct two infinite first order differential equations for the components of the pressure and the velocity projected over the normal modes from these an infinite matricial riccati equation is derived for the impedance matrix these equations are ordinary differential equations that can be integrated after truncation at a sufficient number of modes and take into account the coupling between modes the stiffness of the pressure velocity equations induced by the presence of evanescent modes is avoided by first calculating the impedance matrix along the guide the method is checked using different examples where the solutions of the plane wave approximation or the finite element method are known results show the method provides simple and accurate means to obtain the acoustic field with correct boundary conditions in a nonuniform guide with no restriction on the flare

a wavelet based kl like expansion for wide sense stationary random processes we describe a wavelet based series expansion for wide sense stationary processes the expansion coefficients are uncorrelated random variables a property similar to that of a karhunen loeve kl expansion unlike the kl expansion however the wavelet based expansion does not require the solution of the eigen equation and does not require that the process be time limited this expansion also has advantages over fourier series which is often used as an approximation to the kl expansion in that it completely eliminates correlation and that the computation for its coefficients are more stable over large time intervals the basis functions of this expansion can be obtained easily from wavelets of the lemaire meyer 1990 type and the power spectral density of the process finally the expansion can be extended to some nonstationary processes such as those with wide sense stationary increments

on coupled modes theory of two dimensional wave motion in elastic waveguides with slowly varying parameters in curvilinear orthogonal coordinates coupled modes theory as applied to 2 d wave propagation in range dependent isotropic elastic waveguides in curvilinear orthogonal coordinates is proposed the model consists of one or more curvilinear layers with interfaces and outer boundaries departing slowly from the coordinate surfaces the material parameters are supposed to be slowly dependent on the longitudinal coordinate four dimensional vector valued functions with the displacements rotation and divergence as the components are shown to be a convenient form of wave field description to extend the coupled modes theory from liquid to elastic waveguides for this case the cross section operator is defined and the generalized bi orthogonality property of its eigenfunctions is established using the generalized bi orthogonality the coupling equations are derived wave propagation in a tube which narrows slowly to a conic rod and in a disk of radially dependent thickness are considered as the examples the differences between the results obtained by the coupled modes theory and those the multiple scales theory leads to are discussed the theory modification for dealing with a cutoff phenomenon and the general algorithm of computation of the wave field excited by a point source are considered

coupled mode theory of intrinsic modes in a wedge recent theoretical studies of acoustic wave propagation in a model waveguide consisting of a homogeneous wedge with one reflecting and one penetrable boundary have established the utility of the concept of an intrinsic mode which generalizes for nonseparable problems the normal mode of separable configurations in this paper it is shown by explicit calculations on the same model problem that direct orthogonal expansion in local normal modes of the intrinsic mode produces the same expansion coefficients as those obtained by a perturbation analysis of the coupled mode equations the perturbation method used is that of renormalization in which the mode coupling operator is iteratively diagonalized up to a certain order in the nonseparability parameter which in this case is the wedge angle

a hierarchy of rational timoshenko dispersion relations abstract this paper shows that the conventional timoshenko dispersion relation for bending waves is the 0 1 member of a two parameter family m n of approximations to the exact dispersion relation obtained from linear elasticity higher members of the family are shown to converge rapidly to the exact dispersion relation in particular any number of branches can be captured accurately over their entire length i e up to arbitrarily high frequencies and wavenumbers the theory admits a rigorous accuracy analysis and demonstrates that the conventional timoshenko dispersion relation is a completely rational approximation thus answering some previous doubts about this matter lower members of the two parameter family include the euler bernoulli dispersion relation and a rayleigh type inertia correction especially useful is the timoshenko 1 2 dispersion relation which extends the conventional timoshenko 0 1 dispersion relation by capturing the first four branches of the exact dispersion relation rather than merely the first two and is accurate over a wide range an inertia corrected timoshenko dispersion relation is also derived and is shown to include many previous approximations as special cases

time domain deconvolution when the kernal has no spectral inverse deconvolution of data in the fourier domain is sometimes hampered by the presence of zeros in the kernel a time domain deconvolution method is proposed that can circumvent such difficulty added advantages are 1 a higher signal to noise ratio often attainable in the deconvolved result compared to the fourier domain solution even with nonsingular kernels and 2 a saving in computational speed when the unknown signal is short compared to the kernel numerical illustrations and application to motion blur correction are also given

factorization of second order elliptic boundary value problems by dynamic programming we present a method to factorize a second order boundary value problem in a cylindrical domain in a system of uncoupled first order initial value problems together with a nonlinear riccati type equation for functional operators this uncoupling is obtained by a space invariant embedding technique along the axis of the cylinder this method can be viewed as an infinite dimensional generalization of the block gauss lu factorization

lamb wave propagation in elastic waveguides with variable thickness the problem of lamb wave propagation in waveguides with varying height is treated by a multimodal approach the technique is based on a rearrangement of the equations of elasticity that provides a new system of coupled mode equations preserving energy conservation these coupled mode equations avoid the usual problem at the cut offs with zero wavenumber thereafter we define an impedance matrix that is governed by a riccati equation yielding a stable numerical computation of the solution incidentally the versatility of the multimodal method is exemplified by treating analytically the case of slowly varying guide and by showing how to get easily the green tensor in any geometry the method is applied for a waveguide whose height is described by a gaussian function and the energy conservation in verified numerically we determine the green tensor in this geometry

am fm energy detection and separation in noise using multiband energy operators this paper develops a multiband or wavelet approach for capturing the am fm components of modulated signals immersed in noise the technique utilizes the recently popularized nonlinear energy operator psi s s sup 2 ss to isolate the am fm energy and an energy separation algorithm esa to extract the instantaneous amplitudes and frequencies it is demonstrated that the performance of the energy operator esa approach is vastly improved if the signal is first filtered through a bank of bandpass filters and at each instant analyzed via psi and the esa using the dominant local channel response moreover it is found that uniform worst case performance across the frequency spectrum is attained by using a constant q or multiscale wavelet like filter bank the elementary stochastic properties of psi and of the esa are developed first the performance of psi and the esa when applied to bandpass filtered versions of an am fm signal plus noise combination is then analyzed the predicted performance is greatly improved by filtering if the local signal frequencies occur in band these observations motivate the multiband energy operator and esa approach ensuring the in band analysis of local am pm energy in particular the multi bands must have the constant q or wavelet scaling property to ensure uniform performance across bands the theoretical predictions and the simulation results indicate that improved practical strategies are feasible for tracking and identifying am fm components in signals possessing pattern coherencies manifested as local concentrations of frequencies

analysis of higher order mode effects in an expansion chamber using modal theory and equivalent electrical circuits abstract modal theory for propagation in an acoustic waveguide with variable cross section in particular in an expansion chamber can lead to several different numerical or approximate analytical solutions the advantages of these are compared and one of their number is shown to be a generalization of the plane piston inlet outlet approximation made by ih and lee the results are expressed in the form of two kinds of equivalent electrical circuits connecting the plane modes in the inlet and outlet in the first one the higher modes are described by two series inductances and one shunt inductance in the second one there is no shunt inductance and series inductances are replaced by complex series impedances the existence of resistive elements is discussed in terms of energy transport by higher modes especially at low frequencies when tunneling occurs approximate analytical numerical and experimental results for the elements of circuits are given with a study of coupling between the two step discontinuities

unidimensional models of acoustic propagation in axisymmetric waveguides this paper presents a model of the linear acoustic propagation in axisymmetric waveguides the pressure depending on a single space variable the approach consists of writing the wave equation and the boundary conditions for a coordinate system rectifying the isobaric map at each time the two dimensional dependence of the problem is thus transferred from the pressure to the coefficients of the wave equation from this result an exclusively geometrical necessary condition is deduced for the admissibility of isobaric maps however the knowledge of the waveguide geometry is not sufficient to separate the pressure and the isobaric map solutions in order to develop a unidimensional wave equation a geometrical hypothesis is discussed for lossless and motionless rigid waveguides the deduced equation leads to exact results for tubes and cones it may be interpreted as a webster equation for a particular coordinate system so that the particular profiles for which analytical solutions of the pressure exist are redefined the wave equation is also established for pipes with visco thermal losses and more generally for mobile walls having a small admittance the compatibility of the geometrical hypothesis with the exact model is specified for this general case

multimodal method and conformal mapping for the scattering by a rough surface the scattering of a wave from a periodic rough surface in two dimensions is considered the proposed method is based on the use of a conformal mapping and of the multimodal admittance method the use of the conformal mappings induces a spatially varying refractive index and transforms the boundary condition on the rough surface into a boundary condition on a flat surface then the multimodal admittance method reduces this problem to a riccati equation for the modal admittance matrix which is solved numerically with a magnus mobius scheme the method is shown to converge exponentially with the number of fourier modes the method also allows to find geometries having trapped modes or quasi trapped modes at a given frequency by looking at singularities or quasi singularities of this riccati equation besides a simple perturbation expansion based on a small roughness approximation is developed

coarse grid computation of the one way propagation of coupled modes in a varying cross section waveguide a one way approximation is investigated for the computation of wave propagation in varying cross section waveguides the proposed method derives as a basic approximation of the extensively studied multimodal admittance method when integrated with a magnus scheme this matrix one way equation exhibits an unexpected behavior as the deviation from the exact solution is minimum when only two discretization points per wavelength are taken this peculiar property makes this method efficient to compute the wave propagation for a large variety of geometries beyond the initially stated framework of weakly non uniform waveguides

sound propagation in rigid bends a multimodal approach the sound propagation in a waveguide with bend of finite constant curvature is analyzed using multimodal decomposition two infinite first order differential equations are constructed for the pressure and velocity in the bend projected on the local transverse modes a riccati equation for the impedance matrix is then derived which can be numerically integrated after truncation at a sufficient number of modes an example of validation is considered and results show the accuracy of the method and its suitability for the formulation of radiation conditions reflection and transmission coefficients are also computed showing the importance of higher order mode generation at the junction between the bend and the straight ducts the case of varying cross section curved ducts is also considered using multimodal decomposition

optimal deconvolution based on polynomial methods the problem of estimating the input to a known linear system is treated in a shift operator polynomial formulation the mean square estimation error is minimized the input and a colored measurement noise are described by independent arma autoregressive moving average processes the filter is calculated by performing a spectral factorization and solving a polynomial equation the approach can be applied to input prediction filtering and smoothing problems as well as to the use of prefilters in the quadratic criterion it applies to nonminimum phase as well as unstable systems as illustrated by two examples

estimation of communications channels using discrete wavelet transform based deconvolution in this paper a technique for the deconvolution of signals in the wavelet domain is presented it makes use of the discrete wavelet transform dwt implemented with filter banks and is based on expressing the convolution of two signals using the forward merge approach for dwt based convolution the dwt based deconvolution technique is then applied to the problem of pilot based channel estimation which can be used in the design of wavelet based agile radio systems par dwt based deconvolution is first described analytically and is then implemented in matlab to validate the theory and evaluate its performance monte carlo simulations of dwt based deconvolution of transmitted signals from received signals both known a priori are performed to estimate channel impulse responses transmitted signals are corrupted by additive white gaussian noise awgn resulting in e b n 0 ratios ranging from 0 db to 30 db fast fading channels with gaussian and hilly area power delay profiles pdps are used along with four different wavelets for the dwts the results of the simulations show that dwt based deconvolution is a viable technique and its performance in some cases is comparable to direct discrete time domain deconvolution

wave propagation in a waveguide containing restrictions with circular arc shape a multimodal method is used to analyze the wave propagation in waveguides containing restrictions or corrugations with circular arc shapes this is done using a geometrical transformation which transforms the waveguide with complex geometry in the real space to a straight waveguide in the transformed space or virtual space in this virtual space the helmholtz equation has a modified structure which encapsulates the complexity of the geometry it is solved using an improved modal method which was proposed in a paper by a maurel j f mercier and s felix proc r soc a 470 20130743 2014 that increases the accuracy and convergence of usual multimodal formulations results show the possibility to solve the wave propagation in a waveguide with a high density of circular arc shaped scatterers

systems of convolution equations deconvolution shannon sampling and the wavelet and gabor transforms linear translation invariant systems e g sensors linear filters are modeled by the convolution equation s f mu where f is the input signal mu is the system impulse response function or more generally impulse response distribution and s is the output signal in many applications the output s is an inadequate approximation of f which motivates solving the convolution equation for f i e deconvolving f from mu if the function mu is time limited compactly supported and nonsingular it is proven that this deconvolution problem is ill posed a theory of solving such equations has been developed by berenstein et al it circumvents ill posedness by using a multichannel system if the signal f is overdetermined by using a system of convolution equations s i f mu i i 1 ldots n the problem of solving for f is well posed if the set of convolvers mu i satisfies the condition of being what is called strongly coprime in this case there exist compactly suppor

the finite product method in the theory of waves and stability this paper presents a method of analysing the dispersion relation and field shape of any type of wave field for which the dispersion relation is transcendental the method involves replacing each transcendental term in the dispersion relation by a finite product polynomial the finite products chosen must be consistent with the low frequency low wavenumber limit but the method is nevertheless accurate up to high frequencies and high wavenumbers full details of the method are presented for a non trivial example that of anti symmetric elastic waves in a layer the method gives a sequence of polynomial approximations to the dispersion relation of extraordinary accuracy over an enormous range of frequencies and wavenumbers it is proved that the method is accurate because certain gamma function expressions which occur as ratios of transcendental terms to finite products largely cancel out nullifying runge s phenomenon the polynomial approximations which are unrelated to taylor series introduce no spurious branches into the dispersion relation and are ideal for numerical computation the method is potentially useful for a very wide range of problems in wave theory and stability theory

determination of the complex acoustic scattering matrix of a right angled duct a method for determining the complete higher order scattering matrix of an acoustic discontinuity is developed the method is demonstrated for a right angled waveguide bend and the magnitude and phase of the reflection and transmission coefficients are extracted precisely the procedure is straightforward and based on the solutions to the helmholtz equation by the finite element method fem the consistency of the scattering coefficients found by this method is verified by their properties of symmetry and their accuracy is established by the conservation of energy the reliability of the new technique is further proved by means of an arbitrary sound source and by comparing the direct fem response to the reflection matrix calculation some features of the scattering matrix as a function of frequency are surprising such as the steps and reversion of the phase evolution or the complete loss of transmission of the incoming wave the methodology detailed in this paper can be extended to other multiport junctions such as t junctions or size discontinuities in ducts

a new method for d dimensional exact deconvolution deconvolution is an important problem of signal processing and conventional approaches including fourier methods have stability problems due to the zeros of the convolution kernel we present a new method of multidimensional exact deconvolution this method is always stable even when the convolution kernel h n has zeros on the unit circle and there exist closed form solutions for the one dimensional 1 d case d 1 for the multidimensional case d 1 the proposed method yields stable solutions when det h d this solution set covers a portion of all possible convolution kernels including the ones that have zeros on the multidimensional unit circle this novel time domain method is based on the fact that the convolution inverse of a first order kernel can be found exactly in multidimensional space convolution inverses for higher order kernels are obtained using this fact and the zeros of the convolution kernel the presented method is exact stable and computationally efficient several examples are given in order to show the performance of this method in 1 d and multidimensional cases

improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow we present an efficient multimodal method to describe the acoustic propagation in the presence of a uniform flow in a waveguide with locally a wall impedance treatment the method relies on a variational formulation of the problem which allows to derive a multimodal formulation within a rigorous mathematical framework notably to properly account for the boundary conditions on the walls being locally the myers condition and the neumann condition otherwise also the method uses an enriched basis with respect to the usual cosine basis able to absorb the less converging part of the modal series and thus to improve the convergence of the method using the cosine basis the modal method has a low convergence 1 n with n the order of truncation using the enriched basis the improvement in the convergence is shown to depend on the mach number from 1 n5 to roughly 1 n1 5 for m 0 to m close to unity the case of a continuously varying wall impedance is considered and we discuss the limiting case of piecewise constant impedance which defines pressure edge conditions at the impedance discontinuities

revisiting the edge resonance for lamb waves in a semi infinite plate the resonance for the elastic plate with a free edge is studied from the point of view of complex resonance the variations of the real part and of the imaginary part of the complex resonance frequency as a function of the poisson ratio are determined numerically the results confirm the real resonance frequency theoretically predicted in i roitberg et al q j mech appl math 51 1 13 1998 for a zero poisson ratio 1 0 and a real resonance frequency that corresponds to a lame mode is discovered for a poisson ratio 2 0 2248 it is shown that both real resonance frequencies may exist at these two particular values of because of the decoupling between the propagating lamb mode and the set of evanescent lamb modes

wavelet based linear system modeling and adaptive filtering it is shown how linear time varying systems can be modeled in several different ways by discrete time wavelets or more generally by some set of functions interpretation of physical meanings possible efficiency and other characteristics of the modeling are considered system identification minimizing the mean square output error is studied optimal coefficients and the corresponding minimum mean square error are found and they are in general time varying least mean square adaptive filtering algorithms are derived for on line filtering and system identification theoretically and by simulations the advantages of using wavelet based filtering are shown separation of adaptation effects from unknown time varying system behavior and fast convergence adaptive coefficients estimated by a recursive least square algorithm can tend toward constants even in the case of time varying systems time invariant system identification and adaptive filtering is given as a special case of the general time varying setting

differential eigenvalue problems in which the parameter appears nonlinearly several methods are examined for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly the equations are the result of the discretization of differential eigenvalue problems using a finite chebyshev series two global methods are considered which determine the spectrum of eigenvalues without an initial estimate a local iteration scheme with cubic convergence is presented calculations are performed for a model second order differential problem and the orr sommerfeld problem for plane poiseuille flow

wavelet representations of stochastic processes and multiresolution stochastic models deterministic signal analysis in a multiresolution framework through the use of wavelets has been extensively studied very successfully in recent years in the context of stochastic processes the use of wavelet bases has not yet been fully investigated we use compactly supported wavelets to obtain multiresolution representations of stochastic processes with paths in l sup 2 defined in the time domain we derive the correlation structure of the discrete wavelet coefficients of a stochastic process and give new results on how and when to obtain strong decay in correlation along time as well as across scales we study the relation between the wavelet representation of a stochastic process and multiresolution stochastic models on trees proposed by basseville et al see ieee trans inform theory vol 38 p 766 784 mar 1992 we propose multiresolution stochastic models of the discrete wavelet coefficients as approximations to the original time process these models are simple due to the strong decorrelation of the wavelet transform experiments show that these models significantly improve the approximation in comparison with the often used assumption that the wavelet coefficients are completely uncorrelated

some general properties of the exact acoustic fields in horns and baffles abstract the propagation of the fundamental longitudinal acoustic mode in a duct of variable cross section is considered and the webster wave equations for the sound pressure and velocity are used to establish some general properties of the exact acoustic fields the equipartition of kinetic and compression energies is shown section 2 1 to hold at all stations only for i a duct of constant cross section and ii an exponential horn these are the two cases for which the wave equations for the acoustic velocity and pressure coincide it is proved section 2 3 that there are only five duct shapes forming two dual families which have constant cut off frequency ies namely i the exponential duct which is self dual and is the only shape with constant and coincident cut offs both for the velocity and pressure ii the catenoidal horns of cross section s cosh 2 sinh 2 which with their duals iii the inverse catenoidal ducts s sech 2 csch 2 have one constant cut off frequency respectively for the acoustic pressure and velocity the existence of at least one constant cut off frequency implies that the corresponding wave equation can be transformed into one with constant coefficients and thus the acoustic fields calculated exactly in terms of elementary exponential circular and hyperbolic functions this property also applies to the imaginary transformations of the above shapes viz the sinusoidal s sin 2 and inverse sinusoidal s csc 2 ducts that have no cut off frequency i e are acoustically transparent it is shown that elementary exact solutions of the webster equation exist only section 3 1 for these seven shapes namely the exponential catenoidal sinusoidal and inverse ducts it is implied that for all other duct shapes the exact acoustic fields involve special functions in infinite or finite terms e g bessel and hermite functions respectively for power law and gaussian horns examples of the method of analysis are given by calculating in elementary form the exact acoustic fields in inverse catenoidal ducts for all cases of a propagating waves above b non oscillating modes below and c transition fields at the cut off frequency the inverse catenoidal ducts consist of a the horn of cross section s sech 2 ressembling the soliton of non linear water wave fame and b the baffle of cross section s csch 2 which also matches two exponentially converging ducts but has infinite instead of finite flare at the origin the geometrical and acoustic properties of these ducts are illustrated by sets of six plots in figure 1 a for the sech horn and in figure 1 b for the csch baffle the exact acoustic fields are described by amplitude and phase decompositions of the sound velocity and pressure plotted as functions of position along the duct for four frequencies ranging from the cut off condition to the ray limit or w k b j approximation

multiresolution sequence detection in rapidly fading channels based on focused wavelet decompositions the problem of detecting a sequence using the maximum likelihood strategy when the time varying multipath channel is unknown can be in principle solved using the generalized likelihood detector gld the gld metric involves finding the orthogonal projection of the received signal onto the subspace of the transmitted signal distorted by the multipath channel the faded signal corresponding to one of the transmitted sequences is in fact known to lie in a subspace but its exact location is not known because the channel parameters are unknown this detector which in the case of a static channel collapses to the per survivor processing method is also called a matched subspace detector because its statistic is matched to the a priori known signal subspace unfortunately the computation of the perfectly matched orthogonal projection of the received signal onto the multipath faded signal subspace is in the general time varying case impossible we introduce in this work the idea of using new wavelet based subspaces that approximate the original signal subspace the nested sequence of linear vector spaces defined by a wavelet based multiresolution decomposition of the fading channel time variations provides a set of subspaces that at an increasingly high level of detail are efficient representations of the original signal subspace for each of these representations sequence detection at different levels of resolution can be performed

time varying system identification and model validation using wavelets parametric identification of time varying tv systems is possible if each tv coefficient can be expanded onto a finite set of basis sequences the problem then becomes time invariant with respect to the parameters of the expansion the authors address the question of selecting this set of basis sequences they advocate the use of a wavelet basis because of its flexibility in capturing the signal s characteristics at different scales and discuss how to choose the optimal wavelet basis for a given system trajectory they also develop statistical tests to keep only the basis sequences that significantly contribute to the description of the system s time variation by formulating the problem as a regressor selection problem they apply an p test and an aic based approach for multiresolution analysis of tv systems the resulting algorithm can estimate tv ar or armax models and determine their orders they apply this algorithm to both synthetic and real speech data and compare it with the kalman filtering tv parameter estimator

transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide this work concerns the numerical finite element computation in the frequency domain of the diffracted wave produced by a defect crack inclusion perturbation of the boundaries etc located in a 3d infinite elastic waveguide the objective is to use modal representations to build transparent conditions on some artificial boundaries of the computational domain this cannot be achieved in a classical way due to non standard properties of elastic modes however a biorthogonality relation allows us to build an operator relating hybrid displacement stress vectors an original mixed formulation is then derived and implemented whose unknowns are the displacement field in the bounded domain and the normal component of the normal stresses on the artificial boundaries numerical validations are presented in the 2d case

fir perfect signal reconstruction from multiple convolutions minimum deconvolver orders given p co prime finite impulse response fir filters h sub i spl isin r m sub h it well known that there exist q sub i spl isin r m sub q such that spl sigma sub i h sub i q sub i spl delta importantly this enables signal recovery from its convolutions with p spl ges 2 co prime fir filters by fir filtering we show that such q sub i exist almost surely if and only if m sub q spl ges m sub h 1 p 1 where x is the smallest integer greater than or equal to x the results also provide conditions for full rank of certain key matrices arising in the blind multichannel deconvolution problem

trumpet with near perfect harmonicity design and acoustic results this paper presents a mathematical design methodology for determining the shape of a trumpet air column that has near perfect harmonicity whose components are discontinuity free and whose input impedance peak heights are balanced over the playing range the simulation model employed assumes linear wave propagation and uses cylindrical element discretization with a plane wave approximation acoustic measurements are made using a test set up with an estimated relative measurement error of 3 cents comparisons of measured results are given for the presented design macaluso trumpet and the same trumpet air column with the bell replaced by a commercially used generic trumpet bell of unknown shape generic trumpet for acoustic resonance modes 2 13 233 1515 hz the measured root mean square rms harmonicity deviation is 5 cents for the macaluso trumpet whereas it is 18 cents for the generic trumpet however considering the estimated measurement uncertainty each of those deviations is somewhat over s

an adaptive regularized method for deconvolution of signals with edges by convex projections a new adaptive deconvolution method based on the projection operators onto convex sets pocs is presented a minimum norm least squares mnls is obtained for signals with edges by means of an estimation detection protection scheme the regularized differentiation technique is necessary for a reasonable detection of the signal edges the improvement introduced with this method is illustrated through a simulation example finally a discussion of the wide series of possibilities open along these lines closes this article

a class of reduced order models in the theory of waves and stability this paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental the approximations have two defining characteristics i they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the frequency wavenumber plane and ii the approximate dispersion relations are polynomials that pass exactly through points on this grid thus the method is interpolatory in nature but the interpolation takes place in frequency wavenumber space rather than in physical space full details are presented for a non trivial example that of antisymmetric elastic waves in a layer the method is related to partial fraction expansions and barycentric representations of functions an asymptotic analysis is presented involving stirling s approximation to the psi function and a logarithmic correction to the polynomial dispersion relation

mlse for an unknown channel i optimality considerations the problem of performing joint maximum likelihood ml estimation of a digital sequence and unknown dispersive channel impulse response is considered starting from a continuous time ct model previous investigations of this problem have not considered the front end fe processing in detail rather a discrete time signal model has been assumed we show that a fractionally spaced whitened matched filter matched to the known data pulse provides a set of sufficient statistics when a tapped delay line channel model is assumed and that the problem is ill posed when the channel impulse response is generalized to a ct finite length model practical approximations are considered that circumvent this ill posed condition recursive computation of the joint ml metric is developed together the fe processing and metric recursion provide a receiver structure which may be interpreted as the theoretical foundation for the previously introduced technique of per survivor processing and they lead directly to generalizations several fe processors representative of those suggested in the literature are developed and related to the practically optimal fe

noncommuting limits in electromagnetic scattering asymptotic analysis for an array of highly conducting inclusions we consider formulations for the helmholtz operator for periodic media containing high contrast inclusions in the limit when the wavelength outside the inclusions tends to infinity applications are to problems of electromagnetism the main focus is on the analysis of the effect of noncommuting limits an effect which indicates that linear boundary value problems of electromagnetism give formally different results for the long wavelength limits in cases where highly conducting inclusions have refractive indices of different orders of magnitude specifically the effective moduli of the homogenized material will depend on the path used to approach the origin in the coordinate space wave number normalized refractive index of the inclusions 1 this mathematical observation gives a physical subtlety which is studied in this paper the dispersion relation for the lowest frequency or acoustic mode is investigated as are the conditions for existence of an acoustic mode cases of both nondispersive and di

bloch waves in periodic multi layered acoustic waveguides the band spectrum and associated floquet bloch eigensolutions arising in acoustic and electromagnetic waveguides which have periodic structure along the guide while remaining of finite width are found homogeneous dirichlet or neumann conditions along the guide walls or an alternation of them are taken importantly in some cases a total stop band at zero frequency is identified providing space for low frequency localized modes geometric defects in the structured waveguide also create these modes numerical and asymptotic techniques identify dispersion curves and trapped modes some cases demonstrate maxima and minima of the spectral edges within the brillouin zone and also allow for ultraslow light or sound imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated

kolmogorov n widths and wavelet representations for signal classes we address the problem of basis selection and wavelet representations for two important signal classes the ellipsoidal signal class and the bounded cone class we define time frequency concentrated signals in this paper as the class of signals whose wigner distributions are concentrated in some region of the wigner domain we use the concept of the kolmogorov n width and the constrained n width to quantitatively measure the ability of a basis to represent a signal class we select the best wavelet representation by comparing the constrained widths of different wavelet bases explicit formulas are given to compute the kolmogorov n width for both signal models a globally convergent algorithm is proposed to calculate the constrained n width for a given basis

determination of lamb mode eigenvalues an original method is presented to determine the complex lamb wave spectrum by using a numerical spectral method applied to the elasticity equations this method presents the advantage to directly determine complex wave numbers for a given frequency via a classical matricial eigenvalue problem and allows the wave numbers to be determined at relatively high frequencies i e corresponding to many propagating modes it does not need initial guess values for the wave numbers contrary to the usual method of root finding of the rayleigh lamb frequency equations dispersion relation in the complex plane results are presented and the method is discussed

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

a discrete time multiresolution theory multiresolution analysis and synthesis for discrete time signals is described concepts of scale and resolution are first reviewed in discrete time the resulting framework allows one to treat the discrete wavelet transform octave band perfect reconstruction filter banks and pyramid transforms from a unified standpoint this approach is very close to previous work on multiresolution decomposition of functions of a continuous variable and the connection between these two approaches is made it is shown that they share many mathematical properties such as biorthogonality orthonormality and regularity however the discrete time formalism is well suited to practical tasks in digital signal processing and does not require the use of functional spaces as an intermediate step

wiener filter design using polynomial equations a simplified way of deriving realizable and explicit wiener filters is presented discrete time problems are discussed in a polynomial equation framework optimal filters predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations a tool for obtaining these equations for a given problem structure is described it is based on the evaluation of orthogonality in the frequency domain by means of canceling stable poles with zeros comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical wiener solution the simplicity of the proposed derivation method is particularly evident in multistage filtering problems to illustrate two examples are discussed a filtering and a generalized deconvolution problem a new solvability condition for linear polynomial equation appearing in scalar problems is also presented

environmentally adaptive wedge modes the notion of environmentally adaptive curvilinear uncoupled normal modes is developed by writing the helmholtz equation in curvilinear coordinates the depth dependent vertical scaling function provides some coordinate freedom missing from the cartesian formulation this freedom permits adaptation of the normal mode approach to variable depth and variable sound speed problems for environments that change slowly in range a w k b approximation to the eigenfunctions shows modal decoupling can be realized when the vertical scaling function is chosen equal to the reciprocal of the depth dependent vertical wave number of the lowest mode numerical simulations demonstrate that a requirement for constant inter modal ratios of the vertical wave number is valid throughout several wedges with different bottom boundary conditions the horizontal refraction of such modes agrees closely with analytic solutions for a wide angle wedge the acoustic field agrees qualitatively well with the benchmark solution of dean and buckingham j acoust soc am 93 1319 1328 1993

oblique propagation of electromagnetic and elastic waves for an array of cylindrical fibres this paper presents analysis of electromagnetic and elastodynamic waves propagating through a doubly periodic array of cylindrical channels in oblique incidence a new method based on a multipole scattering approach has been proposed to reduce these spectral problems for partial differential equations to certain algebraic problems of the rayleigh type we obtain a formulation in terms of an eigenvalue problem that enables us to construct the high order dispersion curves and to study both photonic and phononic band gap structures in oblique incidence we also address the question of a singular perturbation induced by the conical incidence and discuss some effective properties for ferromagnetic photonic crystal fibres in the long wavelength limit

consistent coupled mode theory of sound propagation for a class of nonseparable problems this article examines the effects of boundary condition approximations that arise whenever the coupled mode theories of a d pierce j acoust soc am 37 19 27 1965 and d m milder j acoust soc am 46 1259 1263 1969 are applied to propagation problems involving range dependent boundaries this boundary condition approximation requires that the depth derivative rather than the normal derivative of the field be continuous across a sloping interface the approximation is necessary in order to carry out the partial separation of depth and range variables effected in the mathematical formulation of the theory this article will show that a consequence of this approximation is that conventional coupled mode theory applied to dissipationless media with nonhorizontal boundaries does not conserve energy it is shown that a correction to coupled mode theory can be derived such that the proper boundary conditions are satisfied and energy is conserved to first order in the local bottom slope moreover the corrections are not prohibitive in terms of added computational complexity numerical examples are presented which illustrate the nonconservation of energy effect and the corrections to the theory

improved precision in measurements of acoustic impedance spectra using resonance free calibration loads and controlled error distribution resonances and or singularities during measurement and calibration often limit the precision of acoustic impedance spectra this paper reviews and compares several established techniques and describes a technique that incorporates three features that considerably improve precision the first feature is to minimize problems due to resonances by calibrating the instrument using up to three different acoustic reference impedances that do not themselves exhibit resonances the second involves using multiple pressure transducers to reduce the effects of measurement singularities the third involves iteratively tailoring the spectrum of the stimulus signal to control the distribution of errors across the particular measured impedance spectrum examples are given of the performance of the technique on simple cylindrical waveguides

the acoustical klein gordon equation the wave mechanical step and barrier potential functions the transformed form of the webster equation is investigated usually described as analogous to the schrodinger equation of quantum mechanics it is noted that the second order time dependency defines a klein gordon problem this acoustical klein gordon equation is analyzed with particular reference to the acoustical properties of wave mechanical potential functions u x that give rise to geometry dependent dispersions at rapid variations in tract cross section such dispersions are not elucidated by other one dimensional cylindrical or conical duct models since sturm liouville analysis is not appropriate for inhomogeneous boundary conditions the exact solution of the klein gordon equation is achieved through a green s function methodology referring to the transfer matrix of an arbitrary string of square potential functions including a square barrier equivalent to a radiation impedance the general conclusion of the paper is that in the absence of precise knowledge of initial conditions on the area function any given potential function will map to a multiplicity of area functions of identical relative resonance characteristics since the potential function maps uniquely to the acoustical output it is suggested that the one dimensional wave physics is both most accurately and most compactly described within the klein gordon framework

localized and propagating modes in acoustical waveguides with variable cross section a method of determining the propagating and the localized modes in an acoustic waveguide with continuously varying cross section is studied for the rectangular and circular waveguides where the area of the cross section is dependent on the distance from the center of the waveguide the wave equation with dirichlet pressure release boundary condition can be transformed into an infinite set of coupled ordinary differential equations with variable coefficients this set of differential equations has a first integral which is the flux of the wave and is constant along the length of the waveguide if the cross section approaches a constant value at the two ends of the waveguide then there are a finite number of propagating modes plus a number of localized modes a technique for the numerical integration of the stiff ordinary differential equations resulting from the partial wave projection is discussed and applied to different examples

on webster s horn equation and some generalizations sound waves along a rigid axisymmetric tube with a variable cross section are considered the governing helmholtz equation is solved using power series expansions in a stretched radial coordinate leading to a hierarchy of one dimensional ordinary differential equations in the longitudinal direction the lowest approximation for axisymmetric motion turns out to be webster s horn equation fourth order differential equations are obtained at the next level of approximation comparisons with existing asymptotic theories for waves in slender tubes are made

lse and mse optimum partition based fir iir deconvolution filters with best delay we considered the least squares error lse and mean square error mse optimum best delay deconvolution filter design we presented the partition based finite impulse response infinite impulse response fir iir filters where the channel zeros are partitioned into two regions the first region is composed of the selected channel zeros inside the unit circle and the second region is composed of the remaining channel zeros outside the first region two methods for obtaining partitions are proposed namely optimum partitioning and ring based partitioning resulting fir iir filters are compared with the fir and fir iir unit circle best delay inverse filters in terms of their lse it is shown that the partition based fir iir filter performances are about 4 5 db better than their fir counterpart for the same complexity then starting with the best delay fir wiener deconvolution filter formulation we extended our results for the design of fir iir mse optimum deconvolution filters we have compared the optimum partitioning and ring based fir iir inverse filters with the fir and iir wiener deconvolution filters it is shown that fir iir best delay inverse filters are less sensitive to the estimation errors compared with the iir wiener filters and they perform better than the fir wiener filters furthermore they are always causal and stable making them suitable for real time implementations

exact semi separation of variables in waveguides with non planar boundaries series expansions of unknown fields nzn in elongated waveguides are commonly used in acoustics optics geophysics water waves and other applications in the context of coupled mode theories

legendre and laguerre polynomial approach for modeling of wave propagation in layered magneto electro elastic media a numerical method to compute propagation constants and mode shapes of elastic waves in layered piezoelectric piezomagnetic composites potentially deposited on a substrate is described the basic feature of the method is the expansion of particle displacement stress fields electric and magnetic potentials in each layer on different polynomial bases legendre for a layer of finite thickness and laguerre for the semi infinite substrate the exponential convergence rate of the method for propagation of love waves is numerically verified the main advantage of the method is to directly determine complex wave numbers for a given frequency via a matricial eigenvalue problem in a way that no transcendental equation has to be solved results are presented and the method is discussed

lamb quasi modes in curved plates wave propagation in slowly varying elastic waveguides is analysed in terms of mutually uncoupled quasi modes these are a generalization of the lamb modes that exist in a uniform guide to a weakly non uniform guide quasi modal propagation is dependent upon the wavelength and two geometrical length scales that of the longitudinal variations and the guide thickness by changing these length scales one enters different asymptotic regimes in this paper the emphasis is on the mid frequency regime where only a few propagating modes can exist our aim is to present an asymptotic theory for quasi modal propagation in a canonical geometry an arbitrarily curved two dimensional plate of constant thickness we derive practically useful asymptotic expressions of the quasi modes of a weakly curved plate these are particularly important since an adiabatic approximation for this problem coincides with the expression for the lamb modes of a flat plate of the same thickness

wave evolution reflection and transmission along inhomogeneous waveguides abstract one dimensional wave propagation along an inhomogeneous waveguide such as an acoustic horn a plate strip a rod or a beam is considered the equations of motion of a generic waveguide are written in first order form and the properties of the position dependent eigenvalues and eigenvectors of the system are deduced by considering the symmetry and or the energetics of the system the equations of motion are then transformed to wave co ordinates based on the right eigenvectors of the system and a perturbation method is employed to study wave propagation along deterministic periodic and random waveguides attention is then turned to wave reflection at a cut off cross section and a general result for the phase of the reflection coefficient is derived the general theory is illustrated by application to rod and beam examples the method can be likened to a coupled modes approach in which the properties of the eigenvectors or modes arising from symmetry and or energetics are exploited

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed