the hyperbolic class of quadratic time frequency representations i constant q warping the hyperbolic paradigm properties and members the time frequency tf version of the wavelet transform and the affine quadratic bilinear tf representations can be used for a tf analysis with constant q characteristic the paper considers a new approach to constant q tf analysis a specific tf warping transform is applied to cohen s class of quadratic tf representations which results in a new class of quadratic tf representations with constant q characteristic the new class is related to a hyperbolic tf geometry and is thus called the hyperbolic class hc two prominent tf representations previously considered in the literature the bertrand p sub 0 distribution and the altes marinovic q distribution are members of the new hc the authors show that any hyperbolic tf representation is related to both the wideband ambiguity function and a hyperbolic ambiguity function it is also shown that the hc is the class of all quadratic tf representations which are invariant to hyperbolic time shifts and tf scalings operations which are important in the analysis of doppler invariant signals and self similar random processes the paper discusses the definition of the hc via constant q warping some signal theoretic fundamentals of the hyperbolic tf geometry and the description of the hc by 2d kernel functions several members of the hc are considered and a list of desirable properties of hyperbolic tf representations is given together with the associated kernel constraints

bilinear time frequency representations of signals the shift scale invariant class the authors consider the class of bilinear time frequency representations btfr s that are invariant or covariant to time shifts frequency shifts and time frequency scalings this shift scale invariant class is the intersection of the classical shift invariant cohen class and the recently defined affine class the mathematical description of shift scale invariant btfr s is in terms of a 1 d kernel and is thus particularly simple the paper concentrates on the time frequency localization properties of shift scale invariant btfr s since any shift scale invariant btfr is a superposition of generalized wigner distributions the time frequency localization of the family of generalized wigner distributions is studied first for those shift scale invariant btfr s that may be interpreted as smoothed versions of the wigner distribution e g the choi williams distribution an analysis in the fourier transform domain shows interesting peculiarities regarding time frequency concentration and interference geometry properties

the general vector solutions of such linear coupled matrix fractional differential equations by using kronecker structures in this paper we demonstrate how kronecker products and vector operator can be combined beautifully to solve and fit the non homogenous linear matrix fractional differential equations and such coupled linear matrix fractional differential equations the way exists which transform the given coupled matrix fractional differential equations by using kronecker structures into forms for which solutions may be readily computed some important and interesting special cases of the general system of non homogeneous linear matrix fractional differential equations of fractional order are also considered which includes the non homogenous linear fractional dynamical system with delays in control finally a brief comparison between the fractional and integer order vector solutions and some examples are given to illustrate our new approaches

improved signal synthesis from pseudo wigner distribution an overlapping method om for signal synthesis from modified pseudo wigner distributions pwd has been suggested the authors present a suboptimal pwd signal synthesis algorithm which like the om has a recursive structure and thus allows signal synthesis without an inherent restriction of signal length this algorithm is called the simplified partial sum method spsm while the spsm appears to be similar to the om in its formulation its results are generally quite different om and spsm are compared in a simple synthesis experiment and it is shown that while om results are clearly improper spsm yields a satisfactory performance

kernel decomposition of time frequency distributions bilinear time frequency distributions tfds offer improved time frequency resolution over linear representations but suffer from difficult interpretation higher implementation cost and the lack of associated low cost signal synthesis algorithms in the paper the authors introduce some new tools for the interpretation and quantitative comparison of high resolution tfds these tools are used in related work to define low cost high resolution tfds and to define linear low cost signal synthesis algorithms associated with high resolution tfds first each real valued tfd is associated with a self adjoint linear operator spl psi the spectral representation of spl psi expresses the tfd as a weighted sum of spectrograms sps it is shown that the sp decomposition and weyl correspondence do not yield useful interpretations for high resolution tfds due to the fact that spl psi is not positive

numerical evaluation of two and three parameter mittag leffler functions the mittag leffler ml function plays a fundamental role in fractional calculus but very few methods are available for its numerical evaluation in this work we present a method for the efficient computation of the ml function based on the numerical inversion of its laplace transform lt an optimal parabolic contour is selected on the basis of the distance and the strength of the singularities of the lt with the aim of minimizing the computational effort and reducing the propagation of errors numerical experiments are presented to show accuracy and efficiency of the proposed approach the application to the three parameter ml also known as prabhakar function is also presented

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

vector valued time frequency representations cohen s 1989 class of time frequency distributions tfds which includes the spectrogram sp wigner distribution wd and reduced interference distributions rids has become widely known as a useful signal analysis tool it has been shown that every real valued tfd can be written as a weighted sum of sps the sp decomposition has been used to construct fast approximations to desirable tfds using the sp building block for which there exist accessible and efficient hardware and software implementations we introduce a class of linear vector valued time frequency representations tfrs that are easily related to associated bilinear tfds through the sp decomposition we solve a least squares signal synthesis problem on modified vector valued tfrs that are associated with nonnegative tfds as a weighted sum of least squares short time fourier transform stft signal synthesis schemes we extend the solution to vector valued tfrs associated with high resolution tfds in order to define a high resolution alternative to stft signal synthesis as demonstrated by desirable properties and examples the resulting signal synthesis methods can be realized as a weighted sum of stft synthesis schemes for which there exist accessible and efficient hardware and software implementations

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 time frequency formulation of optimum detection a time frequency formulation is proposed for the optimum detection of gaussian signals in white gaussian noise by choosing the wigner ville distribution as the basic time frequency tool it is shown that the corresponding receivers generally take the form of a correlation between time frequency structures matching mathematical optimality with a physically meaningful interpretation the case of low snr is examined and various examples are considered deterministic signal rayleigh fading signal random jitter and random time varying channel a general class of time frequency receivers is proposed which admits as limiting cases different known structures and its suboptimum performance is evaluated possible extensions to more elaborate situations including parameter estimation are mentioned

an algorithm for synthesizing signals from partial time frequency models using the cross wigner distribution a weighted least square error criterion that optimally synthesizes a signal when only part of the desired time frequency model is available is formulated for time frequency synthesis the partial model occurs frequently in situations in which the ideal synthesis model has been truncated by a time varying mask in order to exclude unwanted signal components or when knowledge of the true time or frequency support of the ideal model is unknown a cross wigner distribution cwd synthesis algorithm is developed from the weighted least square error criterion and compared with existing wigner distribution wd synthesis algorithms the algorithm is also shown to be useful when interference or cross terms hinder the use of the quadratic auto wigner distribution awd for signal synthesis

bilinear signal synthesis the authors discuss the signal synthesis problem in the general framework of bilinear signal representations bsrs thereby obtaining a unified treatment which encompasses e g the wigner distribution and ambiguity function as special cases the inclusion of a signal space constraint serves to impart flexibility to the signal synthesis process and to relax mathematical requirements the characterization of signal spaces either by orthogonal projection operators or by orthonormal bases leads to two different signal synthesis methods both methods assume the bsr to be unitary i e satisfy moyal s formula on the signal space on which signal synthesis is performed as an application of the general signal synthesis methods band limited signal synthesis in the case of the wigner distribution is considered

the power classes quadratic time frequency representations with scale covariance and dispersive time shift covariance we consider scale covariant quadratic time frequency representations qtfrs specifically suited for the analysis of signals passing through dispersive systems these qtfrs satisfy a scale covariance property that is equal to the scale covariance property satisfied by the continuous wavelet transform and a covariance property with respect to generalized time shifts we derive an existence representation theorem that shows the exceptional role of time shifts corresponding to group delay functions that are proportional to powers of frequency this motivates the definition of the power classes pcs of qtfr s the pcs contain the affine qtfr class as a special case and thus they extend the affine class we show that the pcs can be defined axiomatically by the two covariance properties they satisfy or they can be obtained from the affine class through a warping transformation we discuss signal transformations related to the pcs the description of the pcs by kernel functions desirable properties and kernel constraints and specific pc members furthermore we consider three important pc subclasses one of which contains the bertrand 1992 p sub k distributions finally we comment on the discrete time implementation of pc qtfrs and we present simulation results that demonstrate the potential advantage of pc qtfrs

volterra series representation of time frequency distributions this paper addresses a volterra series representation of bilinear or quadratic time frequency distributions that belong to cohen s class whereby the analogy of the bilinear class with a second order double volterra series is utilized in addition a different viewpoint for the bilinear kernel and a complementary interpretation concerning the quadratic time frequency distributions are provided

blind source separation based on time frequency signal representations blind source separation consists of recovering a set of signals of which only instantaneous linear mixtures are observed thus far this problem has been solved using statistical information available on the source signals this paper introduces a new blind source separation approach exploiting the difference in the time frequency t f signatures of the sources to be separated the approach is based on the diagonalization of a combined set of spatial t f distributions in contrast to existing techniques the proposed approach allows the separation of gaussian sources with identical spectral shape but with different t f localization properties the effects of spreading the noise power while localizing the source energy in the t f domain amounts to increasing the robustness of the proposed approach with respect to noise and hence improved performance asymptotic performance analysis and numerical simulations are provided

linear redundancy of information carried by the discrete wigner distribution the discrete wigner distribution wd encodes information in a redundant fashion since it derives n by n representations from n sample signals the increased amount of data often prohibits its effective use in applications such as signal detection parameter estimation and pattern recognition as a consequence it is of great interest to study the redundancy of information it carries richard and lengelle see proc ieee int conf acost speech signal process istanbul turkey p 85 8 2000 have shown that linear relations connect the time frequency samples of the discrete wd however up until now such a redundancy has still not been algebraically characterized in this paper the problem of the redundancy of information carried by the discrete cross wd of complex valued signals is addressed we show that every discrete wd can be fully recovered from a small number of its samples via a linear map the analytical expression of this linear map is derived special cases of the auto wd of complex valued signals and real valued signals are considered the results are illustrated by means of computer simulations and some extensions are pointed out

shift covariant time frequency distributions of discrete signals many commonly used time frequency distributions are members of the cohen 1989 class this class is defined for continuous signals and since time frequency distributions in the cohen class are quadratic the formulation for discrete signals is not straightforward the cohen class can be derived as the class of all quadratic time frequency distributions that are covariant to time shifts and frequency shifts we extend this method to three types of discrete signals to derive what we call the discrete cohen classes the properties of the discrete cohen classes differ from those of the original cohen class to illustrate these properties we also provide explicit relationships between the classical wigner distribution and the discrete cohen classes

the wigner distribution of a linear signal space a time frequency representation of linear signal spaces called its wigner distribution wd is introduced similar to the wd of a signal the wd of a linear signal space describes the space s energy distribution over the time frequency plane it is shown that the wd of a signal space can be defined both in a deterministic and in a stochastic framework and it can be expressed in a simple way in terms of the space s projection operator and the bases it is shown to satisfy many interesting properties which are often analogous to corresponding properties of the wd of a signal the results obtained for some specific signal spaces are found to be intuitively satisfactory the cross wd of two signal spaces a discrete time wd version and the extension of the wd definition to arbitrary quadratic signal representation are also discussed

some notes on properties of the matrix mittag leffler function abstract we have come across with publications where some properties of the matrix exponential were incorrectly extended to the matrix mittag leffler function and then used as a key tool to solve certain linear matrix fractional differential equations the main purpose of these notes is to give some clarifications on properties of the matrix mittag leffler function by explaining in detail why some identities do not hold and by providing a list of valid properties of this function a sufficient condition to identify very special cases of pairs of matrices satisfying the semigroup property is given as well as examples illustrating the results

unitary equivalence a new twist on signal processing unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time frequency and scale implementation of these new tools involves simply preprocessing the signal by a unitary transformation performing standard processing on the transformed signal and then in some cases transforming the resulting output the resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and hence prove useful for representing and processing signals that are not well matched by current techniques as specific examples of this procedure we generalize linear time invariant systems orthonormal basis and frame decompositions and joint time frequency and time scale distributions these applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature

characterizing the radar ambiguity functions ambiguity functions are expanded relative to cross ambiguity functions associated with a special orthonormal basis of signal space related to a rectangular pulse the cross ambiguity functions are simply related to the well known ambiguity function of a rectangular pulse the description of ambiguity functions in terms of these well known and interrelated cross ambiguity functions facilitates the ease with which desired calculations can be made indeed one can compute the ambiguity function of a signal as easily as taking the fourier series of a periodic function the characterization of ambiguity functions resulting from this expansion is applied to prove two general results about the set of all ambiguity functions we prove that the set of ambiguity functions is closed on the square integrable topology and that except in a trivial case the sum of two ambiguity functions is never an ambiguity function

the hyperbolic class of quadratic time frequency representations ii subclasses intersection with the affine and power classes regularity and unitarity for pt i see ibid vol 41 p 3425 444 1993 part i introduced the hyperbolic class hc of quadratic bilinear time frequency representations qtfrs the present paper defines and studies four subclasses of the hc 1 the focalized kernel subclass of the hc is related to a time frequency concentration property of qtfrs it is analogous to the localized kernel subclass of the affine qtfr class 2 the affine subclass of the hc affine hc consists of all hc qtfrs that satisfy the conventional time shift covariance property it forms the intersection of the hc with the affine qtfr class 3 the power subclasses of the hc consist of all hc qtfrs that satisfy a power time shift covariance property they form the intersection of the hc with the recently introduced power classes 4 the power warp subclass of the hc consists of all hc qtfrs that satisfy a covariance to power law frequency warpings it is the hc counterpart of the shift scale covariant subclass of cohen s class all of these subclasses are characterized by 1d kernel functions the affine hc is contained in both the localized kernel hyperbolic subclass and the localized kernel affine subclass and that any affine hc qtfr can be derived from the bertrand unitary po distribution by a convolution we furthermore consider the properties of regularity and unitarity in the hc the calculus of inverse kernels is developed and important implications of regularity and unitarity are summarized the results comprise a general method for least squares signal synthesis and new relations for the altes marinovich q distribution

time frequency signal synthesis with time frequency extrapolation and don t care regions the application of wigner distribution wd based signal synthesis to signal separation problems is often adversely affected by wd interference terms we present a modified signal synthesis method where the use of a masked wd allows the definition of don t care regions in the don t care regions detrimental interference terms whose time frequency location is assumed to be known are ignored the synthesis result is calculated using a modified version of the quasi power algorithm previously proposed for smoothed wd s the new synthesis method is shown to possess a desirable time frequency extrapolation capability as well as a potential tendency to produce spurious signal components in the don t care regions the occurrence of spurious signal components can be avoided by the inclusion of an energy penalty

regularity and unitarity of bilinear time frequency signal representations two structural properties of bilinear time frequency representations btfrs of signals are introduced and studied the definition of these properties is based on a linear operator description of btfrs the first property termed regularity has important implications with respect to the recovery of signals from the btfr outcome the derivation of other bilinear signal representations from a btfr the btfrs reaction to linear signal transformations and the construction of bases of induced btfr domain spaces the second property called unitarity is equivalent to validity of moyal s formula 1949 unitarity is thus necessary and sufficient for a closed form solution of optimal signal synthesis and for a btfr formulation or optimal detection estimation methods unitarity also allows the systematic construction of btfr product relations like the wigner distribution s interference formula and the ambiguity function s self transformation property unitarity permits the construction of induced orthogonal projection operators and guarantees the orthonormality of induced basis functions

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

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

wideband weyl symbols for dispersive time varying processing of systems and random signals we extend the narrowband weyl symbol ws and the wideband p sub o weyl symbol pows for dispersive time frequency tf analysis of nonstationary random processes and time varying systems we obtain the new tf symbols using unitary transformations on the ws and the p sub o ws for example whereas the ws is matched to systems with constant or linear tf characteristics the new symbols are better matched to systems with dispersive nonlinear tf structures this results from matching the geometry of the unitary transformation to the specific tf characteristics of a system we also develop new classes of smoothed weyl symbols that are covariant to tf shifts or time shift and scaling system transformations these classes of symbols are also extended via unitary warpings to obtain classes of tf symbols covariant to dispersive shifts we provide examples of the new symbols and symbol classes and we list some of their desirable properties using simulation examples we demonstrate the advantage of using tf symbols that are matched to the changes in the tf characteristics of a system or random process we also provide new tf formulations for matched detection applications

a note on property of the mittag leffler function abstract recently the authors have found in some publications that the following property 0 1 of mittag leffler function is taken for granted and used to derive other properties 0 1 e a t s e a t e a s t s 0 where a is a real constant and 0 in this note it is proved that the above property is unavailable unless 1 or a 0 moreover a new equality on e a t is developed whose limit state as 1 is just the property 0 1

duality and classification of bilinear time frequency signal representations the author discusses a fundamental duality principle of btfrs bilinear time frequency representations and presents a systematic classification of btfrs which is consistent with btfr duality btfrs are first grouped into two basic domains namely the energy density domain e domain with energetic interpretation and the correlation domain c domain with correlative interpretation it is shown that these domains are related by a fourier transform duality to any btfr btfr relation or btfr property of the e domain there corresponds a dual btfr btfr relation or btfr properties of the c domain and vice versa with this duality principle as a background a classification of btfrs is given this classification is based on two dual shift invariance properties and a self dual scale invariance property of btfrs the mathematical description of btfrs by means of kernel functions is simplified inside the respective btfr classes it is shown that btfrs which are both shift and scale invariant can be represented as superpositions of generalized wigner distributions e domain or generalized ambiguity function c domain

time frequency based detection using discrete time discrete frequency wigner distributions during the last decade a comprehensive theory for optimum time frequency tf based detection has been developed this was originally proposed in the continuous time continuous frequency case this paper deals with detectors operating on discrete time discrete frequency wigner distributions wds the purpose is to discuss some existing definitions of this distribution within the context of tf based detection and selecting those that do not affect the performance of the decision device with which they are associated this question is of interest since there exist several approaches for discretizing the wd sometimes resulting in a loss of fundamental properties first the discrete time discrete frequency formulations of optimum detection are investigated next the problem of the design of tf based detectors from training data keeping in mind severe effects of the curse of dimensionality is considered

complete linear weingarten surfaces of bryant type a plateau problem at infinity in this paper we study a large class of weingarten surfaces which includes the constant mean curvature one surfaces and flat surfaces in the hyperbolic 3 space we show that these surfaces can be parametrized by holomorphic data like minimal surfaces in the euclidean 3 space and we use it to study their completeness we also establish some existence and uniqueness theorems by studing the plateau problem at infinity when is a given curve on the ideal boundary the asymptotic boundary of a complete surface in our family and how many embedded solutions are there

linear frequency modulated signal detection using radon ambiguity transform a novel time frequency technique for linear frequency modulated lfm signal detection is proposed the design of the proposed detectors is based on the radon transform of the modulus square or the envelope amplitude of the ambiguity function af of the signal a practical assumption is made that the chirp rate is the only parameter of interest since the af of lfm signals will pass through the origin of the ambiguity plane the line integral of the radon transform is performed over all lines passing through the origin of the ambiguity plane the proposed detectors yield maxima over chirp rates of the lfm signals this reduces the two dimensional 2 d problem of the conventional wigner ville distribution wvd based detection or the radon wigner transform rwt based detector to a one dimensional 1 d problem and consequently reduces the computation load and keeps the feature of built in filtering related issues such as the finite length effect the resolution and the effect of noise are studied the result is a tool for lfm detection as well as the time varying filtering and adaptive kernel design for multicomponent lfm signals

bilinear signal synthesis in array processing multiple source signals impinging on an antenna array can be separated by time frequency synthesis techniques averaging of the time frequency distributions tfds of the data across the array permits the spatial signatures of sources to play a fundamental role in improving the synthesis performance array averaging introduces a weighting function in the time frequency domain that decreases the noise levels reduces the interactions of the source signals and mitigates the crossterms this is achieved independent of the temporal characteristics of the source signals and without causing any smearing of the signal terms the weighting function may take noninteger values which are determined by the communication channel the source positions and their angular separations unlike the recently devised blind source separation methods using spatial tfds the proposed method does not require whitening or retrieval of the source directional matrix the paper evaluates the proposed method in terms of performance and computations relative to the existing source separation techniques based on quadratic tfds

extremal domains on hadamard manifolds abstract we investigate the geometry and topology of extremal domains in a hadamard manifold i e domains that support a positive solution to an overdetermined elliptic problem oep first we study narrow properties of such domains and characterize the boundary at infinity we give an upper bound for the hausdorff dimension of its boundary at infinity and how the domain behaves at infinity this shows interesting relations with the singular yamabe problem later we focus on extremal domains in the hyperbolic space symmetry and boundedness properties will be shown in a certain sense we extend levitt rosenberg s theorem to oeps which suggests a strong relation with constant mean curvature hypersurfaces in particular we are able to prove the berestycki caffarelli nirenberg conjecture under certain assumptions either on the boundary at infinity of the extremal domain or on the oep itself also a height estimate for solutions on extremal domains in a hyperbolic space will be given

convergence of an iterative time variant filtering based on discrete gabor transform an iterative time variant filtering based on the discrete gabor transform dgt has been previously proposed by the authors in this article we present a proof of the convergence of the iterative algorithm under a sufficient condition on the analysis and synthesis window functions of the dgt in the meantime we show that the iterative algorithm refines the least squares solution

the zak transform and decimated time frequency distributions in this paper the interrelation between the zak transform and the generalized discrete time frequency distribution gdtfd is examined starting with the discrete zak transform its definition is broadened to include arbitrary windows creating the windowed zak transform wzt the wzt is then combined with the spectrogram it is demonstrated that the spectrogram based upon the wzt called the zak spectrogram zs is a generalization of the standard spectrogram next building upon the idea of the weighted spectrogram the weighted zs is used to produce a new class of gdtfd called the decimated gdtfd d gdtfd the decimated gdtfd is similar to the gdtfd except it trades bandwidth for computational speed and requires significantly less storage in order to be implemented the reduction in discrete bandwidth is from 2 spl pi for the gdtfd to 2 spl pi m for the d gdtfd an important attribute of the dgdtfd is that it requires significantly less storage than the gdtfd the d gdtfd requires only 1 m sup 2 of the storage of the gdtfd an example using the binomial distribution is given to illustrate the connection between the d gdtfd and the gdtfd throughout the paper examples of multirate systems are given which could be used to implement the building blocks of the dgdtfd this makes the d gdtfd practical to implement using slower and less expensive elements

system identification using chirp signals and time variant filters in the joint time frequency domain we propose a novel method to identify an unknown linear time invariant lti system in low signal to noise ratio snr environment the method is based on transmitting chirp signals for the transmitter and using linear time variant filters in the joint time frequency tf domain for the receiver to reduce noise before identification due to the tf localization property of chirp signals a large amount of additive white noise can be reduced and therefore the snr before identification can be significantly increased this however cannot be achieved in the conventional methods where pseudo random signals are used and therefore noise reduction techniques do not apply our simulation results indicate that the method proposed outperforms the conventional methods significantly in a low snr environment this paper provides a good application of time frequency analysis and synthesis

minimal and weakly trapped submanifolds in standard static spacetimes abstract in this article we obtain some rigidity results for spacelike submanifolds of arbitrary codimension in standard static spacetimes in particular under appropriate assumptions we prove that they must be contained in a spacelike slice which enables us to characterize minimal closed submanifolds of codimension two we also prove new rigidity results for complete non compact weakly trapped submanifolds of arbitrary codimension in these ambient spacetimes

wigner space synthesis of discrete time periodic signals a procedure that facilitates at least squares synthesis of periodic discrete time signals from wigner quasi distributions is proposed the scheme is based on expanding the desired time sequence on a generally nonorthogonal gabor type basis whose associated biorthogonal function presumably exists the specific basis selection may crucially affect the efficiency and quality of the ensuing synthesis procedure the cited basis type constitutes a considerable generalization over the standardly used orthogonal variety thus creating previously unavailable degrees of freedom of primary significance is the acquired capability of generating time frequency basis functions that are well localized localization is a highly desirable property that can advantageously serve in various applications it is shown and numerically demonstrated that benefits of localization as well as the fact that achieving effective time frequency basis localization renders a certain degree of oversampling unavoidable

complete minimal varieties in hyperbolic space it is a basic problem in the subject of minimal varieties to determine the class of complete minimal and area minimizing varieties m k in a given riemannian manifold n besides being of their own intrinsic interest the cases r of euclidean space and mn sn of the sphere are fundamental in understanding the local structure of minimal varieties due to the existence of tangent cones to general minimal varieties there has been much study of the complete areaminimizing varieties in these cases in particular relating to the bernstein conjecture and minimizing cones e g l2 f1 nevertheless many deep problems remain unsolved this paper is centered around the question of existence of complete areaminimizing varieties in hyperbolic space h here by way of contrast to the situation in ir n or s we find a comparatively complete solution to the problem of existence in fact the main result of this paper exhibits a wealth of complete area minimizing varieties in h in all dimensions and codimensions more precisely we have