dynamic period doubling bifurcations of a unimodal map period doubling bifurcations of a fairly general unimodal map yn 1 y n x n are considered with linearly varying parameter x n 1 x n e e 1 the sweeping delays the apparent bifurcations there are structurally different types of trajectories sweeping forwards e and sweeping backwards e a matched asymptotic approach is used to analyse the system following baesens adiabatic manifolds are obtained for the period 1 and period 2 regions an outer expansion that is singular at the bifurcation is matched to an inner expansion valid in an o e boundary layer the inner expansion brings out the normal form in this case a pitchfork bifurcation local stability of the manifolds is examined typical trajectories sweeping down can again be described by similar outer and inner expansions sweeping up however typical trajectories remain at least o e close to the unstable period 1 manifold before a rapid transition to period 2 a discrete canard an inner inner expansion is needed to describe how perturbations or noise are critical in determining where the rapid transition occurs trajectories sweeping up are thus described by a uniformly valid triple deck matched asymptotic expansion a specific example of a quadratic map is used to compare this expansion with numerical simulations the example shows explicitly the effect of both sweep rate and initial value or noise on determining where the rapid transition occurs

on the generalized likelihood ratio test for a class of nonlinear detection problems the authors examine the generalized likelihood ratio test glrt for a certain class of detection problems this class is characterized by a model which is linear in some parameters and nonlinear in others they show that the classical asymptotic analysis of the glrt fails for this class and demonstrate the existence of ill behaved cases in this class they then propose a modification of the glrt the main advantage of this modification is that its probability of false alarm is easily computable thus facilitating the choice of threshold according to the neyman pearson criterion performance analysis of the modified glrt is provided and supported by simulations

a test for aliasing using bispectral analysis abstract aliasing is a signal confounding problem that arises when a continuous time signal is sampled at a rate slower than twice the highest frequency component of a fourier series representation of the signal aliasing can be especially serious for social science time series applications since the sampling designs used to construct most social science data bases are fixed by considerations other than the nature of the underlying continuous time mechanisms after collecting sampled data it is of value to test the observations for the presence of aliasing it is shown that the nature of the support set of a sampled band limited stationary signal can be used to motivate an amended version of the hinich bispectrum test for gaussianity hinich 1982 as a test for aliasing

the unique limit of the glimm scheme we introduce the definitions of a standard riemann semigroup and of a viscosity solution for a nonlinear hyperbolic system of conservation laws for a class including general 2 2 systems it is proved that the solutions obtained by a wavefront tracking algorithm or by the glimm scheme are precisely the semigroup trajectories in particular these solutions are unique and depend lipschitz continuously on the initial data in the l1 norm

performance analysis of transient detectors based on a class of linear data transforms the problem of detecting short duration nonstationary signals which are commonly referred to as transients is addressed transients are characterized by a signal model containing some unknown parameters and by a model mismatch representing the difference between the model and the actual signal both linear and nonlinear signal models are considered the transients are assumed to undergo a noninvertible linear transformation prior to the application of the detection algorithm examples of such transforms include the short time fourier transform the gabor transform and the wavelet transform closed form expressions are derived for the worst case detection performance for all possible mismatch signals of a given energy these expressions make it possible to evaluate and compare the performance of various transient detection algorithms for both single channel and multichannel data numerical examples comparing the performance of detectors based on the wavelet transform and the short time fourier transform are presented

time phase bispectral analysis bispectral analysis a technique based on high order statistics is extended to encompass time dependence for the case of coupled nonlinear oscillators it is applicable to univariate as well as to multivariate data obtained respectively from one or more of the oscillators it is demonstrated for a generic model of interacting systems whose basic units are the poincare oscillators their frequency and phase relationships are explored for different coupling strengths both with and without gaussian noise the distinctions between additive linear or quadratic and parametric frequency modulated interactions in the presence of noise are illustrated

inherent limitations in the localization of a coherently scattered source this paper addresses the problem of localizing a single coherently scattered far field narrowband source emitting a gaussian signal and observed in additive gaussian noise an explicit expression for the cramer rao bound crb of the unknown spatial and spectral i e source and noise power level parameters of the source is presented for arbitrary array geometry the crb is used to study the inherent limitations in the estimation of the mean angle of a scattered source in comparison to the case of a point source at the same mean angle

linear systems in gabor time frequency space a new approach for the description and operation of linear time varying systems is presented the proposed formalism implements the superposition integral describing a general linear operation in gabor time frequency space enabling the use of its joint properties the method is based on transforming both the input and the time varying impulse response function into the gabor space the 2 and 4 d arrays corresponding to the gabor spectra of the input signal and the impulse response respectively are multiplied yielding a 2 d array corresponding to the output gabor spectrum from which the output time signal is subsequently reconstructed unlike other time varying operation methods carried out in different mixed time frequency spaces e g wigner space the suggested approach when employing the critically sampled gabor expansion generates a legal output spectrum and eliminates the need to resort to cumbersome and numerically taxing approximate synthesis techniques the proposed formalism can be implemented in the areas of time variant filtering speech scrambling and any other linear operations that vary their characterizations in time

robust detection with the gap metric in a multipath communication channel the optimal receiver is matched to the maximum likelihood ml estimate of the multipath signal in general this leads to a computationally intensive multidimensional nonlinear optimization problem that is not feasible in most applications we develop a detection algorithm that avoids finding the ml estimates of the channel parameters while still achieving good performance our approach is based on a geometric interpretation of the multipath detection problem the ml estimate of the multipath signal is the orthogonal projection of the received signal on a suitable signal subspace s we design a second subspace g which is the representation subspace that is close to s but whose orthogonal projection is easily computed the closeness is measured by the gap metric the subspace g is designed by using wavelet analysis tools coupled with a reshaping algorithm in the zak transform domain we show examples where our approach significantly outperforms the conventional correlator receiver cr and other alternative suboptimal detectors

gabor representation of generalized functions this paper deals with gabor representation of generalized functions by this we mean that a given function is to be expanded in a series involving gabor functions that are located in the points of a given lattice in the time frequency plane we shall mainly consider lattices in which the area of the elementary cells of the lattice equals 1 in 1946 gabor used these expansions for the simultaneous analysis of signals in time and frequency cf 181 gabor stated that the above mentioned expansions exist for every reasonable signal and that the coefficients in the expansion are uniquely determined by the signal this statement is true when interpreted carefully and the aim of this paper is to find out what kind of generalized functions are sufficiently well behaved to allow a development in a gabor series we shall also consider the question of the uniqueness of the coefficients in the expansions as well as questions concerning convergence it turns out that the uniqueness questions can be handled with the aid of the main results of io in particular 2 12 and 2 13 the questions on the existence of expansions are harder to answer and require special care depending on the particular function we consider lpfunctions 1 p 2 in detail and show existence of gabor representation for tempered distribution in general

robustness of oversampled gabor transient detectors a comparison of energy and known location detectors this correspondence provides a context for previous studies on the use of linear time frequency transforms for transient signal detection in the case where signal component locations are assumed to be known the robustness of a known location detector kld based on the oversampled gabor transform is compared with that of the corresponding energy detector in the gabor domain as expected the kld was sensitive to location mismatch unexpectedly it was extremely sensitive to location mismatch

robust transient signal detection using the oversampled gabor representation the gabor representation has been investigated previously as an effective and efficient means of detecting transient signals the major problem associated with the most commonly used form of the gabor representation is that it assumes that signals have integer arrival times and modulation frequencies an assumption that if violated causes signal miss match and deterioration in detector performance the present correspondence presents the concept of oversampling the gabor representation which makes the representation more robust to certain types of signal mismatch to show this the performance of an oversampled gabor detector is compared to that of critically sampled gabor detectors gabor coefficients are calculated in the oversampled representation via the least squares method which has been shown to be superior to the more commonly used biorthogonal function method in terms of corresponding detector performance

bifurcations in a stock market model abstract a theoretical framework is laid out where a stock exchange is represented as a process under decentralized control attention is devoted to a specific case in which the trading activity is described by a second order dynamical system three economically significant modes of behavior are identified the stock market can 1 adjust to a stable equilibrium 2 approach a stable limit cycle 3 diverge to infinity the transition from mode 1 to mode 2 is a supercritical hopf bifurcation whereas the transition from mode 2 to mode 3 is a homoclinic bifurcation

transient signal detection using prior information in the likelihood ratio test a uniform approach to the problem of detecting a deterministic transient signal of unknown waveshape in gaussian noise that is applicable for a general class of signals is provided it is assumed that the vector representation consists of a group of zero coefficients plus a group of unknown nonzero coefficients starting at a certain index performance indices for a likelihood ratio test detector of such a generalized transient signal are derived for three cases a both the starting index and the number of unknown nonzero signal coefficients are known b only the number of unknown nonzero signal coefficients is known and c neither of these is known it is shown that the performance of detector a is always better than that of b and c and conditions under which the performance of detector b is better than that of c are derived the theoretical results are demonstrated by considering signals of different assumed structures

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

primary bifurcations in two non linearly coupled oscillators abstract a study is described of periodically perturbed primary bifurcations in two non linearly coupled oscillators in both the non resonant and resonant cases the krylov bogoliubov mitrolposky kbm averaging method is used to derive the bifurcation equations the concept of normal form singularity unfolding theory and theory of z2 symmetry bifurcations are employed to analyze the bifurcation equations and to enumerate the bifurcation diagrams in different components of bifurcation hypersurface in parameter space the formation of several interesting patterns is presented in the non resonant case periodic perturbation is shown to have small effect on the primary bifurcations the bifurcations in the subharmonic resonant case are z2 symmetry ones and they have codimension 3 on the other hand the bifurcations in the main resonant case are shown to possess no symmetry properties and their codimension increases to 5 these bifurcation problems are analyzed in detail and the quasiglobal bifurcation classifications as well as bifurcation diagrams in the system are presented it is shown that one can control vibration in non linear systems with an appropriate choice of system parameters as suggested by some regions in the hypersurface where the amplitude of bifurcating solution is always zero the study of periodically perturbed secondary bifurcation problems will be reported in a companion paper

hopf bifurcation analysis of a rotor seal system abstract the hopf bifurcation behaviour of a symmetric rotor seal system was investigated using muszynska s non linear seal fluid dynamic force model for a perfectly balanced system the instability from certain critical equilibrium positions is proved to be the result of hopf bifurcation and only the supercritical type is found for a specific rotor system using poore s algebraic criteria hence a stable periodic orbit bifurcates from the critical equilibrium position after the threshold speed is exceeded due to the dimensionless whirl frequency being found to be close to 1 2 over quite a large range of system parameters the periodically perturbed hopf bifurcation in 1 2 subharmonic resonance is dealt with for an imbalanced rotor system the bifurcation of the averaged system obtained using the centre manifold procedure and averaging method is analyzed the results show that non synchronized whirl of the imbalanced rotor can either be a quasi periodic motion resulting from a hopf bifurcation or a half frequency whirl from period doubling bifurcation determined by the structure parameters of the system and operation conditions numerical simulation verifies the analytical results

uniqueness of weak solutions to systems of conservation laws consider a strictly hyperbolic system of conservation laws in one space dimension relying on the existence of the standard riemann semigroup generated by we establish the uniqueness of entropy admissible weak solutions to the cauchy problem under a mild assumption on the variation of along space like segments

constrained epsilon minimax test for simultaneous detection and classification a constrained epsilon minimax test is proposed to detect and classify nonorthogonal vectors in gaussian noise with a general covariance matrix and in presence of linear interferences this test is epsilon minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability this loss is even more negligible as the signal to noise ratio is large furthermore it is also an epsilon equalizer test since its classification error probabilities are equalized up to a negligible difference when the signal to noise ratio is sufficiently large an asymptotically equivalent test with a very simple form is proposed this equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of euclidean distance numerical experiments on active user identification in a multiuser system confirm the theoretical findings

detecting a suddenly arriving dynamic profile of finite duration this paper addresses the detection of a suddenly arriving dynamic profile of a finite duration often called a transient change in contrast to the traditional abrupt change detection where the post change period is assumed to be infinitely long the detection of a suddenly arriving transient change should be done before it disappears the detection of transient changes after their disappearance is considered as missed hence the traditional quickest change detection criterion minimizing the average detection delays provided a prescribed false alarm rate is compromised the proposed optimality criterion minimizes the worst case probability of missed detection provided that the worst case probability of false alarm during a certain period is upper bounded a suboptimal cusum type transient change detection algorithm based on a subclass of truncated sequential probability ratio tests is proposed the optimization of the proposed algorithm in this subclass leads to a specially designed finite moving average test the proposed method is analyzed theoretically and by simulation a special attention is paid to the case of gaussian observations with a dynamic profile

global dynamics of parametrically excited nonlinear reversible systems with nonsemisimple 1 1 resonance abstract in this paper we analytically investigate the global dynamics associated with the nonlinear reversible systems that exhibit hopf bifurcation in the presence of one to one nonsemisimple internal resonance the effect of periodic parametric excitations is examined on such systems near the principal subharmonic resonance in presence of dissipation the nonlinear and nonautonomous system is simplified considerably by reducing it to the corresponding four dimensional normal form the normal form associated with the reversible systems is obtained as a special case from the general normal form equations obtained in n sri namachchivaya m m doyle w f langford and n evans normal form for generalized hopf bifurcation with non semisimple 1 1 resonance z angew math phys zamp 45 1994 312 335 under small perturbations arising from parametric excitations and nonreversible dissipation two mechanisms are identified in such systems that may lead to chaotic dynamics explicit restrictions on the system parameters are obtained for both of these mechanisms which lead to this complex behavior finally the results are demonstrated through a two degree of freedom model of a thin rectangular beam vibrating under the action of a pulsating follower force

discrete gabor transform a feasible algorithm for implementing the gabor expansion the coefficients of which are computed by the discrete gabor transform dgt is presented for a given synthesis window and sampling pattern computing the auxiliary biorthogonal function of the dgt is nothing more than solving a linear system the dgt presented applies for both finite as well as infinite sequences by exploiting the nonuniqueness of the auxiliary biorthogonal function at oversampling an orthogonal like dgt is obtained as the discrete fourier transform dft is a discrete realization of the continuous time fourier transform similarly the dgt introduced provides a feasible vehicle to implement the useful gabor expansion

resonant parametric perturbations of the hopf bifurcation abstract the effects of periodic parametric perturbations on a system undergoing hopf bifurcation are studied in detail of primary interest is the case of resonance between the hopf bifurcation frequency and the perturbation frequency method of alternative problems is used to obtain the small nonlinear periodic solutions it is shown that for a certain range of parameters the hopf solution is modified to give rise to jump response as well as isolated solutions for some parameter combinations stable solutions can get unstable and may bifurcate into aperiodic or amplitude modulated motions

multi dimensional scalar balance laws with discontinuous flux abstract we consider scalar balance laws with a dissipative source term the flux function may be discontinuous with respect to both the space variable x and the unknown quantity u we formulate the definition of entropy weak solutions and provide existence and uniqueness to the considered problem the problem is formulated in the framework of multi valued mappings the notion of entropy measure valued solutions is used to prove the so called contraction principle and comparison principle

detection of random transient signals via hyperparameter estimation difficulties arise with the generalized likelihood ratio test glrt in situations where one or more of the unknown signal parameters requires an enumeration that is computationally intractable in the transient signal detection problem the frequency characteristics of the signal are typically unknown therefore even if an aggregate signal bandwidth is assumed the estimation problem intrinsic to the glrt requires an enumeration of all possible sets of signal locations within the monitored band in this paper a prior distribution is imposed over those portions of the signal parameter space that traditionally require enumeration by replacing intractable enumeration over possible signal characteristics with an a priori signal distribution and by estimating the hyperparameters of the prior distribution jointly with other signal parameters it is possible to obtain a new formulation of the glrt that avoids enumeration and is computationally feasible the glrt philosophy is not changed by this approach what is different from the original glrt is the underlying signal model the performance of this new approach appears to be competitive with that of a scheme of emerging acceptance the power law detector

on unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown abstract we deal with the cauchy problem for multi dimensional scalar conservation laws where the fluxes and the source terms can be discontinuous functions of the unknown the main novelty of the paper is the introduction of a kinetic formulation for the considered problem to handle the discontinuities we work in the framework of re parametrization of the flux and the source functions which was previously used for kru kov entropy solutions within this approach we obtain a fairly complete picture existence of entropy measure valued solutions entropy weak solutions and their equivalence to the kinetic solution the results of existence and uniqueness follow under the assumption of holder continuity at zero of the flux the source term what is another novelty for the studies on problems with discontinuous flux is only assumed to be one side lipschitz not necessarily monotone function

relationships involving third moments and bispectra of a harmonic process relationships between third moments of a harmonic random process and its bispectrum are presented the skewness and asymmetry with respect to a vertical axis of the process and its derivative can be obtained by integrating the real imaginary and frequency scaled real and imaginary parts of the bispectrum respectively triads of fourier coefficients containing a high frequency component can contribute substantially to the third moments of the derivative of the process

time frequency transfer function calculus symbolic calculus of linear time varying systems linear operators based on a generalized underspread theory we introduce a generalized concept of underspread linear time varying systems linear operators which contains a previous definition as a special case we show that an existing approximate transfer function calculus symbolic calculus can be extended to this wider and practically more relevant class of underspread operators as a mathematical underpinning of this calculus we establish explicit bounds on various error quantities associated with it the transfer function calculus provides a theoretical basis for various methods recently proposed for nonstationary signal processing and it has important implications in the theory of time varying power spectra

the bispectrum and bicoherence for quadratically nonlinear systems subject to non gaussian inputs in the analysis of data from nonlinear systems both the bispectrum and the bicoherence have emerged as useful tools both are frequently used to detect the influence of a nonlinear system on the joint probability distribution of the system input previous work has provided an analytical expression for the bispectrum of a quadratically nonlinear system output if the input is stationary jointly gaussian distributed this work significantly generalizes the previous analysis by providing an analytical expression for the bispectrum of the response of quadratically nonlinear systems subject to stationary jointly non gaussian inputs possessing arbitrary auto correlation function the expression is then used to determine the optimal input probability density function for detecting a quadratic nonlinearity in a second order system it is also shown how the expression can be used to design an optimal nonlinear filter for detecting deviations from normality in the probability density of a signal

oversampling in the gabor scheme a method for calculating the coefficients of the gabor expansion in the case of oversampling is presented the method is based on the concept of frames and utilizes the zak transform as such the zak transform highlights the meaning and importance of frames in the context of oversampling and other aspects of signal representation by means of nonorthogonal bases

bispectral based tests for the detection of gaussianity and linearity in time series abstract statistical techniques have been developed that use estimated bispectrum values to test whether a sample of a time series is consistent with the hypothesis that the observations are generated by a linear process the magnitude of the test statistics indicates the amount of divergence between the observations and the linear model hypothesis it is important to investigate such a divergence since the usual linear model coefficients can be shown to be biased in the face of nonlinear time series structure the tests presented here can thus be considered diagnostic as well as confirmatory these tests are applied to a variety of real series previously modeled with linear models the results indicate nonlinear models may yield better results because many of the series analyzed appear to have considerable nonlinear lagged interactions

gabor transform of time varying systems exact representation and approximation approximate modeling of discrete time linear time varying systems is studied based on a representation of linear systems in the gabor time frequency space the time varying system is assumed to be given in input output or kernel representation this representation has previously received attention because of its applicability in frozen time analysis and design of optimal control for time varying systems but requires a large number of coefficients motivated by its application to signal analysis the gabor transform is considered as a tool for the representation and approximation of linear time variant systems in order to show the main results the class of systems considered is restricted to the one usually considered in the frozen time approach an example is included to illustrate the potential application of the technique

the semigroup generated by 2 2 conservation laws consider the cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension ie1 01 assuming that each characteristic field is either linearly degenerate or genuinely nonlinear this paper develops a new algorithm based on wave front tracking which yields a cauchy sequence of approximate solutions converging to a unique limit depending continuously on the initial data the solutions that we obtain constitute a semigroup s defined on a set ie1 02 of integrable functions with small total variation for some lipschitz constant l we have the estimate ie1 03

detection of transient signals by the gabor representation gabor representation is used for the detection of transient signals with unknown arrival times a one sided exponential window function is used which seems to be most appropriate for transient modelling explicit expressions for the gabor coefficients are given for this window function when the given signal is random so are the coefficients the second order moments of the gabor coefficients are computed for a white noise signal these are then used to introduce a detection statistic based on the gabor coefficients the proposed detector is capable of separating transients having different arrival times even in this case where their waveforms partially overlap

pattern recognition using invariants defined from higher order spectra one dimensional inputs a new approach to pattern recognition using in variant parameters based on higher order spectra is presented in particular invariant parameters derived from the bispec trum are used to classify one dimensional shapes the bispec trum which is translation invariant is integrated along straight lines passing through the origin in bifrequency space the phase of the integrated bispectrum is shown to be scale and amplifi cation invariant as well a minimal set of these invariants is selected as the feature vector for pattern classification and a minimum distance classifier using a statistical distance measure is used to classify test patterns the classification technique is shown to distinguish two similar but different bolts given their one dimensional profiles pattern recognition using higher or der spectral invariants is fast suited for parallel implementa tion and has high immunity to additive gaussian noise sim ulation results show very high classification accuracy even for low signal to noise ratios

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

a parametric class of discrete gabor expansions the gabor expansion and its discretization have been widely studied and many potential applications have been suggested in various signal processing problems a new approach to the study of the discrete gabor expansion dge is introduced and analyzed in detail using the theory of pseudoframe decompositions a parametric and analytical formula for a class of different gabor analysis sequences is derived it is a simple algebraic formula rather than another abstract system of equations for the first time the structure of analysis sequences is questioned we show that while there is a class of infinite analysis sequences that possess the gabor translation and complex modulation structure there are also infinite analysis sequences of arbitrary forms simulation results are provided to demonstrate the proposed algorithms the study of the dge by means of the theory of pseudoframe decompositions reveals a much broader mathematical perspective on the dge the general algorithm derived provides a feasible platform for optimizations in discrete gabor expansions arising from various applications this is an area that can surely be exploited as algorithms of dges become known and applications become more and more intensive

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

wigner higher order moment spectra definition properties computation and application to transient signal analysis the wigner higher order moment spectra whos are defined as extensions of the wigner ville distribution wd to higher order moment spectra domains a general class of time frequency higher order moment spectra is also defined in terms of arbitrary higher order moments of the signal as gen eralizations of the cohen s general class of time frequency rep resentations the properties of the general class of time fre quency higher order moment spectra can be related to the properties of whos which are in fact extensions of the prop erties of the wd discrete time and frequency wigner higher order moment spectra dtf whos distributions are intro duced for signal processing applications and are shown to be implemented with two fft based algorithms one application is presented where the wigner bispectrum wb which is a whos in the third order moment domain is utilized for the detection of transient signals embedded in noise the wb is compared with the wd in terms of simulation examples and analysis of real sonar data it is shown that better detection schemes can be derived in low signal to noise ratio when the wb is applied

can one evaluate the gabor expansion using gabor s iterative algorithm d gabor s original 1946 approach for calculation of expansion coefficients was examined and it was found that convergence of the suggested algorithm is conditional on the window function chosen the method of analysis enables a process of synthesis whereby eligible windows can be defined ensuring convergence of the algorithm for every represented signal for windows having a finite support of width d the coefficients calculated according to the algorithm are obtained after a single iteration it is proved that in the special case of a gaussian window the algorithm converges only for specific signals on the basis of the conclusions drawn conditions are formulated which ensure convergence of the gabor algorithm permitting examination of alternative windows

periodically perturbed hopf bifurcation in this paper the influence of small periodic perturbations on systems exhibiting hopf bifurcation is studied in detail in two dimensional systems that ordinarily exhibit hopf bifurcation the addition of small periodic parametric excitation gives rise to interesting secondary phenomena explicit results for various primary and secondary bifurcations along with their stabilities are obtained in this work the ideas related to method of averaging poincare birkhoff normal forms and center manifold theorem are used appropriately at different stages it is found that various results obtained using these techniques agree in their common regions of validity

the use of the wavelet transform in the detection of an unknown transient signal for the detection of a not perfectly known signal in noise usually no uniformly most powerful test exists and thus a detector performance depends on the signal representation the use of the wavelet representation of signals to perform a new detection scheme is discussed the advantage of using this particular representation is shown it is shown that prior information regarding the relative bandwidth and the time bandwidth product of the signal to be detected is efficiently incorporated into the detection problem formulation thus the proposed detection scheme is most suitable for detection of unknown transient signals when prior information about the signal time bandwidth product and relative bandwidth exists in these cases the wavelet representation based detector performs better than any other the structure of the proposed detectors is discussed and its performance is evaluated using monte carlo simulations

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

adaptive detection of transient signals the paper discusses the problem of detecting transient signals of unknown waveforms in white gaussian noise the signals are modeled as impulse responses of rational transfer functions with unknown parameters a modified generalized likelihood ratio test mglrt is proposed and its statistical properties are analyzed for both known and unknown noise variances the mglrt involves constrained maximum likelihood estimation of the signal parameters the performance of the mglrt is compared to that of an optimal matched filter and an energy detector for some test cases also the theoretical distributions of the likelihood ratios under h 0 and h 1 are compared to experimental distributions obtained by monte carlo simulations

higher order spectra hos invariants for shape recognition abstract this paper describes a shape feature based invariant object recognition method first a set of features invariant to rotation translation and scaling rts is generated using the radon transform and bispectral analysis in order to improve the noise resistance of the invariants the ensemble averaging technique is introduced into the estimation of bispectra the feature data are further reduced to a smaller set using thresholding and principal component analysis the resultant feature invariants are proved to be more reliable and discriminable in the classification stage than the original ones it is shown experimentally that the extracted higher order spectra hos invariants form compact and isolated clusters in the feature space and that a simple minimum distance classifier yields high classification accuracy with low snr inputs the comparison study with hu s moment invariants and fourier descriptors also shows that the performance of the proposed method is better than these two methods especially in the presence of background noise the hos invariants algorithm is also applied to shape similarity based image indexing a new similarity matching technique based on tanimoto measure is employed for fast image retrieval the retrieval accuracy is high as shown in the experimental results

detecting a transient signal by bispectral analysis a method for detecting a transient waveform of unknown shape in additive stationary noise is presented the method uses a statistic computed from the sample bispectrum of a sampled record of the signal plus noise of length t n tau where 1 tau is the sampling rate the key result underlying the method is that the bispectrum of the noise is zero in a triangle that is a proper subset of the principal domain triangle it is shown that the probability of detecting the signal is high if 3 16 sup 1 2 n sup 5 6 is larger than rho sup 1 where rho is the energy signal to noise ratio the result implies that the bispectrum based test may detect a weak signal of unknown form which evades detection by other methods

oversampled gabor representation for transient signals considers the gabor representation that uses a one sided exponential window for detection and analysis of transient signals earlier results on the critically sampled case are extended to the more practically useful oversampled case for oversampling by an integer factor the authors derive an explicit analytical expression for the dual window dual frame function required for computing the gabor representation based on this expression they develop an efficient procedure for computing the gabor coefficients finally they demonstrate the performance of the method by numerical examples

self tuning to the hopf bifurcation in fluctuating systems the problem of self tuning a system to the hopf bifurcation in the presence of noise and periodic external forcing is discussed we find that the response of the system has a non monotonic dependence on the noise strength and displays an amplified response which is more pronounced for weaker signals the observed effect is to be distinguished from stochastic resonance for the feedback we have studied the unforced self tuned hopf oscillator in the presence of fluctuations exhibits sharp peaks in its spectrum the implications of our general results are briefly discussed in the context of sound detection by the inner ear

multivalued equations for granular avalanches we study existence and uniqueness for the scalar equation of first order hyperbolic type the rhs is in the form of a multifunction which is physically motivated by an avalanche flow model therefore some kind of monotonicity to the rhs has to be assumed

performance analysis of a class of transient detection algorithms a unified framework the detection of short duration nonstationary signals which are commonly referred to as transients is often performed in the time frequency transform domain an analytical framework within which the performance of different detectors based on linear transforms can be easily compared for different classes of signals is developed a given class of transients is modeled as a signal existing in a linear subspace plus a mismatch signal closed form expressions are derived for the best and the worst detection performance for all possible transients in a given class using this framework the performance of detectors based on the gabor transform and on the short time fourier transform is evaluated and compared

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

on the principal domain of the discrete bispectrum of a stationary signal the paper presents a simplifying yet general approach to determining the symmetry structure of a bispectrum the principal domain pd of the bispectrum and its region of positive support are derived in a way that illuminates the controversy surrounding the triangle in the pd which is called the outer triangle ot by hinich and wolinsky 1988 where the bispectrum is zero for a stationary random sampled process that is not aliased the basic statistical issues of testing for nonzero bispectral structure are reviewed

on the sliding window representation in digital signal processing the short time fourier transform of a discrete time signal which is the fourier transform of a windowed version of the signal is interpreted as a sliding window spectrum this sliding window spectrum is a function of two variables a discrete time index which represents the position of the window and a continuous frequency variable it is shown that the signal can be reconstructed from the sampled sliding window spectrum i e from the values at the points of a certain time frequency lattice this sampling lattice is rectangular and the rectangular cells occupy an area of 2 in the time frequency domain it is shown that an elegant way to represent the signal directly in terms of the sample values of the sliding window spectrum is in the form of gabor s signal representation therefore a reciprocal window is introduced and it is shown how the window and the reciprocal window are related gabor s signal representation then expands the signal in terms of properly shifted and modulated versions of the reciprocal window and the expansion coefficients are just the values of the sampled sliding window spectrum

adaptive window length detection of underwater transients using wavelets this paper describes a detection method that adapts to unknown characteristics of the underlying transient signal such as location length and time frequency content it applies a set of embedded detectors tuned to a number of signal partitions the detectors are based on the wavelet theory whereby two different techniques are examined one using local fourier transform and the other using discrete wavelet transform the detection statistics are computed so as to enable prewhitening of unknown colored noise and to allow for a constant false alarm rate detection an adapted segmentation of the signal is next obtained with a goal of finding the largest detection statistics within each segment of the partition the detectors are tested using several underwater acoustic transient signals buried in ambient sea noise

recursive time frequency reassignment a fast algorithm for creating time frequency representations based on a special case of the short time fourier transform stft is presented the algorithm is extended with the method known as time frequency reassignment this approach makes time frequency reassignment well suited for real time implementations

known source detection predictions for higher order correlators the problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal if additional receiver information is included in the higher order correlations while the cross correlation is the optimal linear detector for white noise additional receiver information in the higher order correlations makes them nonlinear in this paper formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal given the first through fourth order signal moments and the noise variance the formulas predict the snr for which the detectors achieve a probability of detection of 0 5 for any level of false alarm when noise at each receiver is independent and identically distributed results show that the performance of the cross correlation bicorrelation and tricorrelation detectors are proportional to the second fourth and s