generalized sampling expansions with multiple sampling rates for lowpass and bandpass signals in the fractional fourier transform domain the objective of generalized sampling expansion gse is the reconstruction of an unknown continuously defined function f left t right from samples of the responses from m linear time invariant lti systems that are each sampled using the 1 m th nyquist rate in this paper we investigate the gse for lowpass and bandpass signals with multiple sampling rates in the fractional fourier transform frft domain first we propose an improvement of papoulis gse which has multiple sampling rates in the frft domain based on the proposed gse we derive the periodic nonuniform sampling scheme and the derivative interpolation method by designing different fractional filters and selecting specific sampling rates in addition the papoulis gse and the previous gse associated with frft are shown to be special instances of our results second we address the problem of the gse of fractional bandpass signals a new gse for fractional bandpass signals with equal sampling rates is derived we show that the restriction of an even number of channels in the gse for fractional bandpass signals is unnecessary and perfect signal reconstruction is possible for any arbitrary number of channels further we develop the gse for a fractional bandpass signal with multiple sampling rates lastly we discuss the application of the proposed method in the context of single image super resolution reconstruction based on gse illustrations and simulations are presented to verify the validity and effectiveness of the proposed results

an effective method for solving the hyper singular integral equations in 3 d acoustics the application of the boundary integral methods to the problem of acoustics exterior to a three dimensional surface suffers in general from the nonexistence of nonuniqueness of its solutions at frequencies that are characteristic of the associated interior problem the formulation that is most suitable for numerical implementation still appears to be that proposed by burton and miller proc r soc london ser a 323 201 210 1971 however the hypersingular kernels present in such a formulation render it computationally unattractive previous attempts to regularize such hypersingular kernels involved the use of double surface integrals or implicit use of tangential operators or closed form evaluations of hypersingular integrals the method of double surface integrals is computationally highly inefficient even though it allows higher order interpolation schemes on the surface the other two approaches are more conducive to the assumption of a constant value for each of the variables pressure a

a bi hamiltonian formulation for triangular systems by perturbations a bi hamiltonian formulation is proposed for triangular systems resulting from perturbations around solutions from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed provided that one operator of the hamiltonian pair is invertible through our formulation four examples of triangular systems are exhibited which also show that bi hamiltonian systems in both lower dimensions and higher dimensions are many and varied two of four examples give local 2 1 dimensional bi hamiltonian systems and illustrate that multiscale perturbations can lead to higher dimensional bi hamiltonian systems

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

filtering in rotated time frequency domains with unknown noise statistics the concept of rotation in the joint time frequency plane can be exploited in order to generalize classical fourier based operations it is known that filtering in rotated time frequency domains can lead to significant performance advantages for certain types of signals as compared to conventional linear time invariant systems in this correspondence we revisit the design problem of such a scheme and derive a formulation that does not require knowledge of the statistics of the corrupting noise simulations have been used to confirm the validity of the proposed solution

wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

fractional cosine sine and hartley transforms in previous papers the fourier transform ft has been generalized into the fractional fourier transform frft the linear canonical transform lct and the simplified fractional fourier transform sfrft because the cosine sine and hartley transforms are very similar to the ft it is reasonable to think they can also be generalized by the similar way we introduce several new transforms they are all the generalization of the cosine sine or hartley transform we first derive the fractional cosine sine and hartley transforms frct frst frht they are analogous to the frft then we derive the canonical cosine and sine transforms cct cst they are analogous to the lct we also derive the simplified fractional cosine sine and hartley transforms sfrct sfrst sfrht they are analogous to the sfrft and have the advantage of real input real output we also discuss the properties digital implementation and applications e g the applications for filter design and space variant pattern recognition of these transforms the transforms introduced in this paper are very efficient for digital implementation we can just use one half or one fourth of the real multiplications required for the frft and lct to implement them when we want to process even odd or pure real imaginary functions we can use these transforms instead of the frft and lct besides we also show that the frct frst cct cst and sfrct sfrst are also useful for the one sided t spl isin 0 spl infin signal processing

integrable counterparts of the d kaup newell soliton hierarchy two integrable counterparts of the d kaup newell soliton hierarchy are constructed from a matrix spectral problem associated with the three dimensional special orthogonal lie algebra so 3 r an application of the trace identity presents hamiltonian or quasi hamiltonian structures of the resulting counterpart soliton hierarchies thereby showing their liouville integrability i e the existence of infinitely many commuting symmetries and conserved densities the involved hamiltonian and quasi hamiltonian properties are shown by computer algebra systems

time frequency projection filters and time frequency signal expansions we consider the problems of designing a linear time varying filter with a specified time frequency tf pass region and of constructing an orthonormal basis for the parsimonious expansion of signals located in a given tf support region these problems of tf filtering and tf signal expansion are reduced to the problem of designing a tf subspace i e a linear signal space comprising all signals located in a given tf legion specifically the tf filter is taken to be the orthogonal projection operator on the tf subspace we present an optimum design of tf subspaces that is based on the wigner distribution of a linear signal space and is an extension of the well known signal synthesis problem the optimum tf subspace is shown to be an eigenspace of the tf region and some properties of eigenspaces are discussed the performance of tf projection filters and tf signal expansions is studied both analytically and via computer simulation

the numerical evaluation of hadamard finite part integrals a quadrature rule is described for the numerical evaluation of hadamard finite part integrals with a double pole singularity within the range of integration the rule is based upon the observation that such an integral is the derivative of a cauchy principal value integral

nonlinear continuous integrable hamiltonian couplings based on a kind of special non semisimple lie algebras a scheme is presented for constructing nonlinear continuous integrable couplings variational identities over the corresponding loop algebras are used to furnish hamiltonian structures for the resulting continuous integrable couplings the application of the scheme is illustrated by an example of nonlinear continuous integrable hamiltonian couplings of the akns hierarchy of soliton equations

second order time frequency synthesis of nonstationary random processes we present time frequency methods for the synthesis of finite energy nonstationary random processes the energetic characteristics of the process to be synthesized are specified in a joint time frequency domain via a time frequency model function the synthesis methods optimize the autocorrelation function of the process such that the process wigner ville spectrum is closest to the given model function an optional signal subspace constraint allows the incorporation of additional properties such as bandlimitation and also permits the reformulation of the synthesis methods in a discrete time setting the synthesized process is expressed either in terms of an orthonormal basis of the constraint subspace or via its karhunen loeve expansion an example involving the prolate spheroidal functions is given and computer simulation results are provided

a unified framework for the fractional fourier transform the paper investigates the possibility for giving a general definition of the fractional fourier transform frt for all signal classes one dimensional 1 d and multidimensional continuous and discrete periodic and aperiodic since the definition is based on the eigenfunctions of the ordinary fourier transform ft the preliminary conditions is that the signal domain periodicity be the same as the ft domain periodicity within these classes a general frt definition is formulated and the frt properties are established in addition the multiplicity which is intrinsic in a fractional operator is clearly developed the general definition is checked in the case in which the frt is presently available and moreover to establish the frt in new classes of signals

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

the estimation of time delay and doppler stretch of wideband signals the problem of estimating the time delay and the doppler stretch for wideband signals from a moving target is considered the cramer rao bound and the maximum likelihood ml method of estimation are derived due to the uncertainty of the reflection coefficient the ml method may not be practicable an alternative method involving the location of the peak of the wideband ambiguity function of the signal is suggested the performance of the method is analysed and under high signal to noise ratios snrs the method is asymptotically unbiased and the variances of the estimates are closed to the cramer rao bound for a large variety of signals optimum signals for the joint estimation of the time delay and the doppler stretch under practical constraints are designed and through computer simulations their performance are shown to be superior to the commonly used signals

constructing nonlinear discrete integrable hamiltonian couplings beginning with lax pairs from special non semisimple matrix lie algebras we establish a scheme for constructing nonlinear discrete integrable couplings discrete variational identities over the associated loop algebras are used to build hamiltonian structures for the resulting integrable couplings we illustrate the application of the scheme by means of an enlarged volterra spectral problem and present an example of nonlinear discrete integrable hamiltonian couplings for the volterra lattice equations

optimal filtering in fractional fourier domains for time invariant degradation models and stationary signals and noise the classical fourier domain wiener filter which can be implemented in o n log n time gives the minimum mean square error estimate of the original undistorted signal for time varying degradations and nonstationary processes however the optimal linear estimate requires o n sup 2 time for implementation we consider filtering in fractional fourier domains which enables significant reduction of the error compared with ordinary fourier domain filtering for certain types of degradation and noise especially of chirped nature while requiring only o n log n implementation time thus improved performance is achieved at no additional cost expressions for the optimal filter functions in fractional domains are derived and several illustrative examples are given in which significant reduction of the error by a factor of 50 is obtained

evaluation of 2 d green s boundary formula and its normal derivative using legendre polynomials with an application to acoustic scattering problems this paper presents the non singular forms in a global sense of two dimensional green s boundary formula and its normal derivative the main advantage of the modified formulations is that they are amenable to solution by directly applying standard quadrature formulas over the entire integration domain that is the proposed element free method requires only nodal data the approach includes expressing the unknown function as a truncated fourier legendre series together with transforming the integration interval a b to 1 1 the series coefficients are thus to be determined the hypersingular integral interpreted in the hadamard finite part sense and some weakly singular integrals can be evaluated analytically the remaining integrals are regular with the limiting values of the integrands defined explicitly when a source point coincides with a field point the effectiveness of the modified formulations is examined by an elliptic cylinder subject to prescribed boundary conditions the regularization is further applied to acoustic scattering problems the well known burton miller method using a linear combination of the surface helmholtz integral equation and its normal derivative is adopted to overcome the non uniqueness problem a general non singular form of the composite equation is derived comparisons with analytical solutions for acoustically soft and hard circular cylinders are made copyright 2001 john wiley sons ltd

the quadratic form identity for constructing the hamiltonian structure of integrable systems a usual loop algebra not necessarily the matrix form of the loop algebra is also made use of for constructing linear isospectral problems whose compatibility conditions exhibit a zero curvature equation from which integrable systems are derived in order to look for the hamiltonian structure of such integrable systems a quadratic form identity is created in the present paper whose special case is just the trace identity that is when taking the loop algebra the quadratic form identity presented in this paper is completely consistent with the trace identity

tridiagonal commuting matrices and fractionalizations of dct and dst matrices of types i iv v and viii in this paper we first establish new relationships in matrix forms among discrete fourier transform dft generalized dft gdft and various types of discrete cosine transform dct and discrete sine transform dst matrices two new independent tridiagonal commuting matrices for each of dct and dst matrices of types i iv v and viii are then derived from the existing commuting matrices of dft and gdft with these new commuting matrices the orthonormal sets of hermite like eigenvectors for dct and dst matrices can be determined and the discrete fractional cosine transform dfrct and the discrete fractional sine transform dfrst are defined the relationships among the discrete fractional fourier transform dfrft fractional gdft and various types of dfrct and dfrst are developed to reduce computations for dfrft and fractional gdft

short time fractional fourier methods for the time frequency representation of chirp signals the fractional fourier transform frft provides a valuable tool for the analysis of linear chirp signals this paper develops two short time frft variants which are suited to the analysis of multicomponent and nonlinear chirp signals outputs have similar properties to the short time fourier transform stft but show improved time frequency resolution the frft is a parameterized transform with parameter a related to chirp rate the two short time implementations differ in how the value of a is chosen in the first a global optimization procedure selects one value of a with reference to the entire signal in the second a values are selected independently for each windowed section comparative variance measures based on the gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains for appropriately chosen frft orders the derived fractional domain uncertainty relationship is minimized for gaussian windowed linear chirp signals the two short time frft algorithms have complementary strengths demonstrated by time frequency representations for a multicomponent bat chirp a highly nonlinear quadratic chirp and an output pulse from a finite difference sonar model with dispersive change these representations illustrate the improvements obtained in using frft based algorithms compared to the stft

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

two integrable couplings of the tu hierarchy and their hamiltonian structures the double integrable couplings of the tu hierarchy are worked out by use of vector loop algebras g 6 and g 9 respectively also the hamiltonian structures of the obtained system are given by the quadratic form identity

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

fractional convolution and correlation via operator methods and an application to detection of linear fm signals using operator theory methods together with our previously introduced unitary fractional operator we derive explicit definitions of fractional convolution and correlation operations in a systematic and comprehensive manner via operator manipulations we also provide alternative formulations of those fractional operations that suggest efficient algorithms for discrete implementation through simulation examples we demonstrate how well the proposed efficient method approximates the continuous formulation of fractional autocorrelation it is also shown that the proposed fractional autocorrelation corresponds to radial slices of the ambiguity function af we also suggest an application of the fast fractional autocorrelation for detection and parameter estimation of linear fm signals

tangential derivative of singular boundary integrals with respect to the position of collocation points this paper investigates the evaluation of the sensitivity with respect to tangential perturbations of the singular point of boundary integrals having either weak or strong singularity both scalar potential and elastic problems are considered a proper definition of the derivative of a strongly singular integral with respect to singular point perturbations should accommodate the concomitant perturbation of the vanishing exclusion neighbourhood involved in the limiting process used in the definition of the integral itself this is done here by esorting to a shape sensitivity approach considering a particular class of infinitesimal domain perturbations that move individual points and especially the singular point but leave the initial domain globally unchanged this somewhat indirect strategy provides a proper mathematical setting for the analysis moreover the resulting sensitivity expressions apply to arbitrary potential type integrals with densities only subjected to some regularity requirements at the singular point and thus are applicable to approximate as well as exact bem solutions quite remarkable is the fact that the analysis is applicable when the singular point is located on an edge and simply continuous elements are used the hypersingular bie residual function is found to be equal to the derivative of the strongly singular bie residual when the same values of the boundary variables are substituted in both sbie and hbie formulations with interesting consequences for some error indicator computation strategies 1998 john wiley sons ltd

time variant filtering of signals in the mixed time frequency domain a new approach to the problem of time variant filtering is presented this approach is based upon the generation of the mixed time frequency representation mtfr of a signal multiplication of that representation by a time frequency function h t and obtaining a filtered output by an inverse operation the resultant filter is linear if the time frequency representation used is the complex spectrogram in contrast the filter is nonlinear if the wigner distribution function is used not every function of two variables is an allowed mtfr of a signal some conditions must be satisfied if the function produced by the product of the signal mtfr and the filter function is not an allowed mtfr an approximation based on projection onto the space of allowed mtfr functions is investigated this approximation yields a filtered function whose mtfr is as close as possible in the least squared sense to the desired

acoustic scattering by a hard or soft body across a wide frequency range by the helmholtz integral equation method in this paper the acoustic scattering by an obstacle across a wide frequency range of sound waves is investigated on the basis of the helmholtz integral formulation to overcome the nonuniqueness difficulties the methods proposed by burton npl report nac 30 jan 1973 and by burton and miller proc r soc london ser a 323 201 210 1971 are adopted for the dirichlet and neumann problems respectively the aim of this paper is twofold the first is to bring together completely regular formulations of the helmholtz integral equation and its normal derivative the second is to extend these formulations to treat the higher frequency problems the weakly singular integrals are regularized by subtracting out one term and adding it back depending on the problem concerned the additional integral can finally be expressed in an explicit form or results in solving a surface source distribution of the equipotential body the hypersingular kernels are regularized by the method of using some properties of the associated laplace equation originally proposed by chien et al j acoust soc am 88 918 937 1990 the completely regularized integral equations are amenable to computation by direct use of the standard quadrature methods to study the acoustic scattering due to higher frequency waves filon s quadrature method proc r soc edinburgh 49 38 47 1928 is extended to treat the rapidly oscillatory integrands numerical examples consist of acoustic scattering from a hard or soft sphere of radius a across a wide spectrum of wave numbers ka 20 comparisons of the numerical results with the exact solutions demonstrate the validity and efficiency of the implementation

some notes on singular integral techniques in boundary element analysis the paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed the numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive gaussian quadrature and subdivision techniques

digital computation of the fractional fourier transform an algorithm for efficient and accurate computation of the fractional fourier transform is given for signals with time bandwidth product n the presented algorithm computes the fractional transform in o nlogn time a definition for the discrete fractional fourier transform that emerges from our analysis is also discussed

multiple 3d far field near field moving target localization using wideband echo chirp signals in this paper we propose a technique for active detection and estimation of the range radial velocity and direction of arrival doa of multiple moving targets in the three dimensional space for both far field and near field cases using wideband chirp signals the proposed technique is an extension of the method recently proposed by leong in multiple target localization using wideband echo chirp signals ieee trans signal process vol 61 no 16 pp 4077 4089 aug 2013 for the localization of multiple far field targets in the two dimensional space in our approach the received signals at a sensor array are first decomposed into the spherical harmonic components and a modal preprocessing step is then carried out on the received wideband signals so that they can be further processed using narrowband techniques for parameter estimation the application of fractional fourier transform on the modal preprocessed signals allows the proposed method to identify closely spaced targets this is demonstrated via computer simulations where the proposed technique achieved low root mean square errors in the parameters estimated in a scenario with closely spaced targets

time varying filtering and signal estimation using wigner distribution synthesis techniques the short time fourier transform stft the ambiguity function af and the wigner distribution wd are mixed time frequency signal representations that use fourier transform techniques to map a one dimensional function of time into a two dimensional function of time and frequency these mixed time frequency mappings have been used to analyze the local frequency characteristics of a variety of signals and systems although much work has also been done to develop stft and af synthesis algorithms that can be used to implement a variety of time varying signal processing operations no such synthesis techniques have thus far been developed for the wd in this paper a signal synthesis algorithm that works directly with the real valued high resolution wd will be derived examples of how this wd synthesis procedure can be used to perform time varying filtering operations or signal separation will be given

on the singularities of green s formula and its normal derivative with an application to surface wave body interaction problems the paper presents the non singular forms of green s formula and its normal derivative of exterior problems for three dimensional laplace s equation the main advantage of these modified formulations is that they are amenable to solution by directly using quadrature formulas thus the conventional boundary element approximation which locally regularizes the singularities in each element is not required the weak singularities are treated by both the gauss flux theorem and the property of the associated equipotential body the hypersingularities are treated by further using the boundary formula for the associated interior problems the efficacy of the modified formulations is examined by a sphere in an infinite domain subject to neumann and dirichlet conditions respectively the modified integral formulations are further applied to a practical problem i e surface wave body interactions using the conventional boundary integral equation formulation is known to break down at certain discrete frequencies for such a problem removing the irregular frequencies is performed by linearly combining the standard integral equation with its normal derivative computations are presented of the added mass and damping coefficients and wave exciting forces on a floating hemisphere comparing the numerical results with that by other approaches demonstrates the effectiveness of the method copyright 2000 john wiley sons ltd

a boundary integral method for acoustic radiation and scattering in this article a computational method is proposed for computing the helmholtz integral equation for acoustic radiation and scattering problems with a three dimensional body shape unlike the previous boundary element method the integration of acoustic properties is based on the global body surface instead of local elements the approximation function of body geometry and the weighting function of numerical integration are independently chosen when the singular kernels of helmholtz equation are regularized as bounded discontinuous functions the order of integration polynomials for acoustic properties can be arbitrarily chosen therefore the accuracy and efficiency of computation can be increased

multiple target localization using wideband echo chirp signals active target detection and localization is a classical signal processing problem that arises in various military and biomedical applications a novel method for the detection and estimation of the range velocity and direction of arrival doa of multiple far field targets using wideband chirp signals is proposed in this paper using the plane wave representation of the signals reflected from far field targets a modal preprocessing procedure is designed for the echo signals received at a concentric circular array following that the parameter estimation method for the multiple targets present is developed based on i the fractional fourier transform which projects a signal onto an orthonormal basis formed by chirps and ii the root music algorithm which is a high resolution doa estimation method originally proposed for narrowband signals received at a uniform linear array there is no limit on the number of targets detectable by the proposed method as long as the echo signals are separable in the chosen fractional fourier domain simulation results show that the proposed method demonstrates good performance with low root mean square errors in the parameters estimated under difficult conditions such as closely spaced targets and low signal to noise ratio

radon transformation of time frequency distributions for analysis of multicomponent signals the radon transform of a time frequency distribution produces local areas of signal concentration that facilitate interpretation of multicomponent signals the radon wigner transform can be efficiently implemented with dechirping in the time domain however only half of the possible projections through the time frequency plane can be realized because of aliasing we show here that the frequency dual to dechirping exists so that all of the time frequency plane projections can be calculated efficiently both time and frequency dechirping are shown to warp the time frequency plane rather rotating it producing an angle dependent dilation of the radon wigner projection axis we derive the discrete time equations for both time and frequency dechirping and highlight some practical implementation issues discrete dechirping is shown to correspond to line integration through the extended discrete rather than the discrete wigner ville distribution computationally dechirping is o 2n log 2n instead of o n sup 3 for direct projection and the computation is dominated by the fast fourier transform calculation the noise and cross term suppression of the radon wigner transform are demonstrated by several examples using dechirping and using direct radon wigner transformation

a boundary integral equation method for radiation and scattering of elastic waves in three dimensions etude du rayonnement et de la diffusion d ondes elastiques par des obstacles de forme arbitraire

a direct method for integrable couplings of td hierarchy a direct method for establishing integrable couplings is proposed in this paper as an example illustration integrable couplings of td hierarchy are obtained by constructing a suitable transformation of lax pairs and a new lie algebra

hamiltonian structure of discrete soliton systems we describe an approach for investigating the hamiltonian structures of the lattice isospectral evolution equations associated with a general discrete spectral problem by using the so called implicit representations of the isospectral flows we demonstrate the existence of the recursion operator l which is a strong and hereditary symmetry of the flows it is then proven that every equation in the isospectral hierarchy possesses the hamiltonian structure if l has a skew symmetric factorization and the first equation ut k 0 in the hierarchy satisfies some simple condition we obtain related properties such as the implectic symplectic factorization of l the liouville complete integrability and the multi hamiltonian structures of the isospectral hierarchy four examples are given

semidirect sums of lie algebras and discrete integrable couplings a relation between semidirect sums of lie algebras and integrable couplings of lattice equations is established and a practicable way to construct integrable couplings is further proposed an application of the resulting general theory to the generalized toda spectral problem yields two classes of integrable couplings for the generalized toda hierarchy of lattice equations the construction of integrable couplings using semidirect sums of lie algebras provides a good source of information on complete classification of integrable lattice equations

non singular boundary integral formulations for plane interior potential problems in this article a non singular formulation of the boundary integral equation is developed to solve smooth and non smooth interior potential problems in two dimensions the subtracting and adding back technique is used toregularize the singularity of green s function and to simplify the calculation of the normal derivative of green s function after that a global numerical integration is directly applied at the boundary and those integration points are also taken as collocation points to simplify the algorithm of computation the result indicates that this simple method gives the convergence speed of order n 3 in the smooth boundary cases for both dirichlet and mix type problems for the non smooth cases the convergence speed drops at o n 1 2 for the dirichlet problems

hamiltonian and quasi hamiltonian structures associated with semi direct sums of lie algebras the trace variational identity is generalized to zero curvature equations associated with non semi simple lie algebras or equivalently lie algebras possessing degenerate killing forms an application of the resulting generalized variational identity to a class of semi direct sums of lie algebras in the akns case furnishes hamiltonian and quasi hamiltonian structures of the associated integrable couplings three examples of integrable couplings for the akns hierarchy are presented one hamiltonian and two quasi hamiltonian

sampling and sampling rate conversion of band limited signals in the fractional fourier transform domain the fractional fourier transform frft has become a very active area in signal processing community in recent years with many applications in radar communication information security etc this study carefully investigates the sampling of a continuous time band limited signal to obtain its discrete time version as well as sampling rate conversion for the frft firstly based on product theorem for the frft the sampling theorems and reconstruction formulas are derived which explain how to sample a continuous time signal to obtain its discrete time version for band limited signals in the fractional fourier domain secondly the formulas and significance of decimation and interpolation are studied in the fractional fourier domain using the results the sampling rate conversion theory for the frft with a rational fraction as conversion factor is deduced which illustrates how to sample the discrete time version without aliasing the theorems proposed in this study are the generalizations of the conventional versions for the fourier transform finally the theory introduced in this paper is validated by simulations