phase correlation of foreign exchange time series abstract correlation of foreign exchange rates in currency markets is investigated based on the empirical data of usd dem and usd jpy exchange rates for a period from february 1 1986 to december 31 1996 the return of exchange time series is first decomposed into a number of intrinsic mode functions imfs by the empirical mode decomposition method the instantaneous phases of the resultant imfs calculated by the hilbert transform are then used to characterize the behaviors of pricing transmissions and the correlation is probed by measuring the phase differences between two imfs in the same order from the distribution of phase differences our results show explicitly that the correlations are stronger in daily time scale than in longer time scales the demonstration for the correlations in periods of 1986 1989 and 1990 1993 indicates two exchange rates in the former period were more correlated than in the latter period the result is consistent with the observations from the cross correlation calculation

studies of spectral properties of short genes using the wavelet subspace hilbert huang transform wshht abstract this paper presents a new algorithm for the analysis of spectral properties of short genes using the wavelet transform and the hilbert huang transform hht a wavelet subspace algorithm combined with the empirical mode decomposition emd is introduced to create subdivided intrinsic mode functions imfs and a cross correlation analysis is applied to remove pseudo spectral components experiments are carried out on dna sequences with the double base db curve representation and the results show that the signal to noise ratio of buried signals can be enhanced using the proposed method yielding significant patterns that are rarely observed with conventional methods the wavelet subspace hilbert huang transform wshht algorithm is able to correctly identify spectral patterns of very short genes below 70 bp in dna sequences

empirical mode decomposition and correlation properties of long daily ozone records sreceived 16 november 2004 revised manuscript received 17 march 2005 published 27 may 2005d correlations for daily data of total ozone column are investigated by detrended fluctuation analysis sdfad the removal of annual periodicity does not result in a background free signal for the tropical station mauna loa in order to identify the remaining quasiperiodic constituent the relatively new method of empirical mode decomposition semdd is tested we found that the so called intrinsic mode functions do not represent real signal components of the ozone time series their amplitude modulation is very sensitive to local changes such as random data removal or smoothing tests on synthetic data further corroborate the limitations of decomposing quasiperiodic signals from noise with emd nevertheless the emd algorithm helps to identify dominating frequencies in the time series which allows to separate fluctuations from the remaining background we demonstrate that dfa analysis for the cleaned mauna loa record yields scaling comparable to a mid latitude station

general solutions of the pseudo diffusion equation of squeezed states we show that the projection operator mod pq yei phi yei phi pq mod where mod pq yei phi is a squeezed state obeys a partial differential equation in which the squeeze parameter y plays the role of time it follows that related functions such as the probability distribution functions and the wigner function are solutions of this equation this equation will be called a pseudodiffusion equation because it resembles a diffusion equation in minkowski space we give general solutions of the pseudo diffusion equation first by the method of separation of variables and then by the fourier transform method and discuss the limitations of the latter method the fourier method is used to introduce squeezing into the number states the thermal light and the wigner function

a wavelet based approach for the identification of linear time varying dynamical systems a novel procedure is developed for the identification of linear discrete models of dynamical systems from noisy data of particular interest is the application of the methodology to time varying systems the procedure is based on a representation of the governing differential equations with respect to a wavelet basis and the formulation of an inverse algebraic problem in the associated subspace the effect of noisy data is considered and numerical simulations demonstrating the applicability of the method to single and multi degree of freedom dynamical systems are presented

survival probability for the stadium billiard abstract we consider the open stadium billiard consisting of two semicircles joined by parallel straight sides with one hole situated somewhere on one of the sides due to the hyperbolic nature of the stadium billiard the initial decay of trajectories due to loss through the hole appears exponential however some trajectories bouncing ball orbits persist and survive for long times and therefore form the main contribution to the survival probability function at long times using both numerical and analytical methods we concur with previous studies that the long time survival probability for a reasonably small hole drops like c o n s t a n t t i m e 1 here we obtain an explicit expression for the constant

entropic bounds on semiclassical measures for quantized one dimensional maps quantum ergodicity asserts that almost all infinite sequences of eigenstates of quantized ergodic hamiltonian systems are equidistributed in phase space this however does not prohibit existence of exceptional sequences which might converge to different non liouville classical invariant measures it has been recently shown by n anantharaman and s nonnenmacher in 20 21 with h koch that for anosov geodesic flows the metric entropy of any semiclassical measure must satisfy a certain bound this remarkable result seems to be optimal for manifolds of constant negative curvature but not in the general case where it might become even trivial if the negative curvature of the riemannian manifold varies a lot it has been conjectured by the same authors that in fact a stronger bound valid in the general case should hold

quantum mechanics in the gaussian wave packet phase space representation abstract we present here some results related to an alternative mapping formulation to the well known wigner weyl transform which makes use of the gaussian wave packet or coherent states representation pq the pair p q which labels this state defines a phase space in which the abstract operators p q of momentum and position are represented as differential operators in the mapped expression of an operator a p q the quantum effects appear when they are absent in the corresponding wigner weyl transform

quantum ergodicity and symmetry reduction abstract we study the spectral and ergodic properties of schrodinger operators on a compact connected riemannian manifold m without boundary in case that the examined system possesses certain symmetries more precisely if m carries an isometric and effective action of a compact connected lie group g we prove a generalized equivariant version of the semiclassical weyl law with an estimate for the remainder using a semiclassical functional calculus for h dependent functions and relying on recent results on singular equivariant asymptotics we then deduce an equivariant quantum ergodicity theorem under the assumption that the symmetry reduced hamiltonian flow on the principal stratum of the singular symplectic reduction of m is ergodic in particular we obtain an equivariant version of the shnirelman zelditch colin de verdiere theorem as well as a representation theoretic equidistribution theorem if m g is an orbifold similar results were recently obtained by kordyukov when g is trivial one recovers the classical results

reversible joint hilbert and linear canonical transform without distortion generalized analytic signal associated with the linear canonical transform lct was proposed recently by fu and li generalized analytic signal associated with linear canonical transform opt commun vol 281 pp 1468 1472 2008 however most real signals especially for baseband real signals cannot be perfectly recovered from their generalized analytic signals therefore in this paper the conventional hilbert transform ht and analytic signal associated with the lct are concerned to transform a real signal into the lct of its ht two integral transforms i e the ht and lct are required the goal of this paper is to simplify cascades of multiple integral transforms which may be the ht analytic signal lct or inverse lct the proposed transforms can reduce the complexity when realizing the relationships among the following six kinds of signals a real signal its ht and analytic signal and the lct of these three signals most importantly all the proposed transforms are reversible and undistorted using the proposed transforms several signal processing applications are discussed and show the advantages and flexibility over simply using the analytic signal or the lct

quantum ergodicity of boundary values of eigenfunctions suppose that n is a bounded piecewise smooth domain we prove that the boundary values cauchy data of eigenfunctions of the laplacian on with various boundary conditions are quantum ergodic if the classical billiard map on the ball bundle b is ergodic our proof is based on the classical observation that the boundary values of an interior eigenfunction 2 is an eigenfunction of an operator fh on the boundary of with h 1 in the case of the neumann boundary condition fh is the boundary integral operator induced by the double layer potential we show that fh is a semiclassical fourier integral operator quantizing the billiard map plus a small remainder the quantum dynamics defined by fh can be exploited on the boundary much as the quantum dynamics generated by the wave group were exploited in the interior of domains with corners and ergodic billiards in the work of zelditch zworski 1996 novelties include the facts that fh is not unitary and consequently the boundary values are equidistributed by measures which are not invariant under and which depend on the boundary conditions ergodicity of boundary values of eigenfunctions on domains with ergodic billiards was conjectured by s ozawa 1993 and was almost simultaneously proved by gerard leichtnam 1993 in the case of convex c1 1 domains with continuous tangent planes and with dirichlet boundary conditions our methods seem to be quite different motivation to study piecewise smooth domains comes from the fact that almost all known ergodic domains are of this form

recent progress on the quantum unique ergodicity conjecture we report on some recent striking advances on the quantum unique ergodicity or que conjecture concerning the distribution of large frequency eigenfunctions of the laplacian on a negatively curved manifold the account falls naturally into two categories the first concerns the general conjecture where the tools are more or less limited to micro local analysis and the dynamics of the geodesic flow the second is concerned with arithmetic such manifolds where tools from number theory and ergodic theory of flows on homogeneous spaces can be combined with the general methods to resolve the basic conjecture as well as its holomorphic analogue the recent account by zelditch zel4 covers some of the same material and his and our discussion complement each other nicely as he goes into more detail with the first category and we with the second this note is not meant to be a survey of these topics and the discussion is not chronological our aim is to expose these recent developments after introducing the necessary backround which places them in their proper context recent progress on que 2 1 the general que conjecture in figure 1 the domains e s and b are an ellipse a stadium and a barnett billiard table respectively superimposed on these are the densities of a consecutive sequence of high frequency eigenfunctions states modes of the laplacian that is they are solutions to 4 j j j 0 in 0 dirichlet boundary conditions j dxdy 1 0 here 4 divgrad 2 x2 2 y2 1 2 3 are the eigenvalues and the eigenfunctions are normalized to have unit l norm the sequences are of 12 consecutive modes around the 5600 eigenvalue they are ordered from left to right and then down and the grayscale represents the probability density with zero white and larger values darker

ergodicity of eigenfunctions for ergodic billiards we give a simple proof of ergodicity of eigenfunctions of the laplacian with dirichlet boundary conditions on compact riemannian manifolds with piecewise smooth boundaries and ergodic billiards examples include the bunimovich stadium the sinai billiard and the generic polygonal billiard tables of kerckhoff masur and smillie

scarred eigenstates for quantum cat maps of minimal periods in this paper we construct a sequence of eigenfunctions of the quantum arnold s cat map that in the semiclassical limit shows a strong scarring phenomenon on the periodic orbits of the dynamics more precisely those states have a semiclassical limit measure that is the sum of 1 2 the normalized lebesgue measure on the torus plus 1 2 the normalized dirac measure concentrated on any a priori given periodic orbit of the dynamics it is known the schnirelman theorem that most sequences of eigenfunctions equidistribute on the torus the sequences we construct therefore provide an example of an exception to this general rule our method of construction and proof exploits the existence of special values of h for which the quantum period of the map is relatively short and a sharp control on the evolution of coherent states up to this time scale we also provide a pointwise description of these states in phase space which uncovers their hyperbolic structure in the vicinity of the fixed points and yields more precise localization estimates

singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series we distinguish between two dimensions of a dynamical system given by experimental time series statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe tje attractor up to the accuracy of the data taking into account sampling and noise problems the dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data singular spectrum analysis ssa provides estimates of the statistical dimension ssa also describes the main physical phenomena reflected by the data it gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data we apply ssa to four paleoclimatic records the principal climatic oscillations and the regime changes in their amplitude are detected about 10 degrees of freedom are statistically significant in the data large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension

instantaneous vortex shedding behaviour in periodically varying flow vortex shedding behind a stationary t shaped cylinder in a circular pipe subjected to periodically varying flow was studied at reynolds numbers between 6 17 103 and 2 46 104 whereas the frequency ratio fs fo ranged from 0 29 to 14 64 fs denotes the natural vortex shedding frequency referred to the mean flow and fo denotes the frequency of periodically varying flow by adopting the hilbert transform to analyse the velocity signals measured the instantaneous vortex shedding frequency was obtained based on this quantity one could categorize the vortex shedding phenomenon observed into three regimes namely quasi steady vortex shedding for fs fo 4 37 hysteresis vortex shedding for fs fo 1 56 4 37 and non interactive vortex shedding for 0 29 fs fo 1 56 in the regime of quasi steady vortex shedding the instantaneous vortex shedding frequency follows the periodically varying flow without phase lag in the regime of hysteresis vortex shedding the instantaneous vortex shedding frequency lags behind the periodically varying flow phase lag roughly varies linearly with fs fo further the variations of non dimensionalized instantaneous vortex shedding frequencies obtained in the accelerating and decelerating portions of the periodically varying flow are found to depend on fs fo and u in the regime of non interactive vortex shedding the vortex shedding frequency tends to vary with the mean velocity of periodically varying flow excluding the occurrences of primary and secondary lock on at fs fo 0 97 1 03 and 0 495 0 514 respectively

marginal and correlation distribution functions in the squeezed states representation here we consider the husimi function hf p for the squeezed states and calculate the marginal and correlation distribution functions mdfs and cdfs when p is projected onto the photon number states according to the value of the squeezing parameter one verifies the occurence of oscillations and beats as already appointed in the literature we verify that these phenomena are entirely contained in the correlation function in particular we show that since the husimi and its mdfs satisfy partial differential equations where the squeeze parameter plays the role of time the solutions the squeezed functions obtained from initial unsqueezed functions can be expressed by means of kernels responsible for the propagation of squeezing from the calculational point of view this method presents advantages for calculating the mdfs compared with a direct integration over one of the two phase space variables of p since one can use the symmetry properties of the differential equations

localized eigenfunctions in seba billiards we describe some new families of quasimodes for the laplacian perturbed by the addition of a potential formally described by a dirac delta function as an application we find under some additional hypotheses on the spectrum subsequences of eigenfunctions of seba billiards that localize around a pair of unperturbed eigenfunctions

brownian motion on a pseudo sphere in minkowski space mathbb r l_v for a brownian motion moving on a pseudo sphere in minkowski space mathbb r l v of radius r starting from point x we obtain the distribution of hitting a fixed point on this pseudo sphere with l ge 3 by solving dirichlet problems the proof is based on the method of separation of variables and the orthogonality of trigonometric functions and gegenbauer polynomials

entropy of semiclassical measures in dimension 2 we study the high energy asymptotic properties of eigenfunctions of the laplacian in the case of a compact riemannian surfacem of anosov type to do this we look at families of distributions associated to them on the cotangent bundle t m and we derive entropic properties on their accumulation points in the high energy limit the so called semiclassical measures we show that the kolmogorov sinai entropy of a semiclassical measure for the geodesic ow gt is bounded from below by half of the ruelle upper bound i e hks g 1 2 s m d where is the upper lyapunov exponent at point

hilbert transform and its engineering applications the hilbert transform is useful in calculating instantaneous attributes of a time series especially the envelope amplitude and instantaneous frequency the instantaneous envelope is the amplitude of the complex hilbert transform the instantaneous frequency is the time rate of change of the instantaneous phase angle these properties can be applied to identify dynamic characteristics of a linear as well as a nonlinear system however the conventional discrete hilbert transform which is based on fast fourier transform and inverse fourier transform has shown the lack of accuracy for time derivative calculations in this paper we first introduce the hilbert transform and its applications to the nonlinear system parameter identification then we address the practical issues in applying the hilbert transform to engineering applications to increase the accuracy of the envelope detection we propose a hilbert transform technique based on local maxima interpolation analyses and simulations are carried out to demonstrate the advantages of the proposed technique finally we employ the proposed local maxima interpolation technique in identifying the nonlinear dynamic characteristics of industrial examples

the fourier decomposition method for nonlinear and non stationary time series analysis for many decades there has been a general perception in the literature that fourier methods are not suitable for the analysis of nonlinear and non stationary data in this paper we propose a novel and adaptive fourier decomposition method fdm based on the fourier theory and demonstrate its efficacy for the analysis of nonlinear and non stationary time series the proposed fdm decomposes any data into a small number of fourier intrinsic band functions fibfs the fdm presents a generalized fourier expansion with variable amplitudes and variable frequencies of a time series by the fourier method itself we propose an idea of zero phase filter bank based multivariate fdm mfdm for the analysis of multivariate nonlinear and non stationary time series using the fdm we also present an algorithm to obtain cut off frequencies for mfdm the proposed mfdm generates a finite number of band limited multivariate fibfs mfibfs the mfdm preserves some intrinsic physical properties of the multivariate data such as scale alignment trend and instantaneous frequency the proposed methods provide a time frequency energy tfe distribution that reveals the intrinsic structure of a data numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms

pseudo diffusion equation and information entropy of squeezed coherent states abstract as the squeezed coherent states are labeled by 3 tuple the momentum the coordinate and the squeeze parameter a phase space probability distribution function associated with a generic wavefunction can be introduced we verify that this probability function is the solution of a partial differential equation the pseudo diffusion equation hence permitting to extend the concept of information entropy as introduced by wehrl for the coherent states to the squeezed coherent states it is shown that the entropy functionals can be used as a measure of quantum correlations between the phase space variables for a given wavefunction we also present several properties and discuss the use of the entropic inequality as a concept that complements the heisenberg uncertainty relationship

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

invariant measures and arithmetic quantum unique ergodicity we classify measures on the locally homogeneous space i sl 2 r l which are invariant and have positive entropy under the diagonal subgroup of sl 2 r and recurrent under l this classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces and a similar but slightly weaker result for the finite volume case other applications are also presented in the appendix joint with d rudolph we present a maximal ergodic theorem related to a theorem of hurewicz which is used in theproof of the main result

adaptive ecg denoising using genetic algorithm based thresholding and ensemble empirical mode decomposition this paper proposes an adaptive denoising methodology for electrocardiogram ecg signals that employs ensemble empirical mode decomposition eemd and a genetic algorithm ga based thresholding technique in this method a noisy ecg signal is first decomposed by means of eemd into a series of intrinsic mode functions imfs which are then separated into signal and noise dominant groups using a similarity measure based on kullback leibler divergence and a probability density function a ga based thresholding technique is then used adaptively to remove the noise inherent in noise dominant imfs finally a denoised signal is reconstructed by combining the signal dominant imfs and the denoised noise dominant imfs the performance of the proposed denoising methodology is evaluated in the present work by using the mit bih arrhythmia ecg database and results from the proposed method are compared with those of other conventional approaches in various noisy environments experimental results indicate that the proposed denoising method outperforms other denoising methodologies in terms of signal to noise ratio mean square error and percent root mean square difference

ergodic billiards that are not quantum unique ergodic partially rectangular domains are compact two dimensional riemannian manifolds x either closed or with boundary that contain a flat rectangle or cylinder in this paper we are interested in partially rectangular domains with ergodic billiard flow examples are the bunimovich stadium the sinai billiard or donnelly surfaces we consider a one parameter family x t of such domains parametrized by the aspect ratio t of their rectangular part there is convincing theoretical and numerical evidence that the laplacian on x t with dirichlet or neumann boundary conditions is not quantum unique ergodic que we prove that this is true for all t in 1 2 excluding possibly a set of lebesgue measure zero this yields the first examples of ergodic billiard systems proven to be non que

quantum mechanics in the gaussian wave packet phase space representation iii from phase space probability functions to wave functions abstract using a mapping formalism the wave packet phase space representation we show that for phase space probability distributions that do not violate the uncertainty principle one can associate a density matrix x x when some conditions are fulfilled furthermore if condition tr 2 1 is satisfied it becomes possible to find a wave function associated to the probability distribution

non linear free vibration identification via the hilbert transform a time domain non parametric method for non linear vibration system identification based on the hilbert transform is introduced the method is demonstrated using computer simulations of different types of non linear elastic and damping dynamic systems

identification of linear time varying mdof dynamic systems from forced excitation using hilbert transform and emd method an algorithm is developed for the identification of linear time varying ltv multiple degrees of freedom systems it is based on the hilbert transform and the empirical mode decomposition with forced vibration response data the proposed identification algorithm is applied to single degree of freedom and multi degrees of freedom dynamic systems three ideal cases of ltv systems with smoothly varying abruptly varying and periodically varying stiffness and damping are studied to illustrate the capability of the algorithm to track the variations of the system simulation results demonstrate the effectiveness and the robustness of the proposed identification algorithm and the lack of complete orthogonality for any two intrinsic mode functions is one of the sources of error in the identification

generalized entropy as a measure of quantum uncertainty abstract a generalized entropy is used in order to advance a different form of expressing the uncertainty principle of quantum mechanics we consider the generalized entropic formulation for different pairs of incompatible observables in particular we study the number phase entropic uncertainty measure for the case of coherent states within the pegg barnett theory we also tackle the situation of operators with continuous spectra where a correlation functional is calculated in terms of generalized joint and marginal entropies for harmonic oscillator wavefunctions

identification of weakly nonlinearities in multiple coupled oscillators this paper considers the analysis of free nonlinear response of multi degree of freedom mdof vibration systems demonstrating that system skeleton curves are significantly changed in the presence of coupling the hilbert transform vibration decomposition together with the modal spatial coordinate transform allow precise identification of initial nonlinear characteristics

automatic noise removal signal removal based on general cross validation thresholding in synchrosqueezed domain and its application on earthquake data abstractrecorded seismic signals are often corrupted by noise we have developed an automatic noise attenuation method for single channel seismic data based upon high resolution time frequency analysis synchrosqueezing is a time frequency reassignment method aimed at sharpening a time frequency picture noise can be distinguished from the signal and attenuated more easily in this reassigned domain the threshold level is estimated using a general cross validation approach that does not rely on any prior knowledge about the noise level the efficiency of the thresholding has been improved by adding a preprocessing step based on kurtosis measurement and a postprocessing step based on adaptive hard thresholding the proposed algorithm can either attenuate the noise either white or colored and keep the signal or remove the signal and keep the noise hence it can be used in either normal denoising applications or preprocessing in ambient noise studies we tested the performance of the proposed method on s

study of boundary conditions in the iterative filtering method for the decomposition of nonstationary signals abstract nonstationary and non linear signals are ubiquitous in real life their decomposition and analysis is an important research topic of signal processing recently a new technique called iterative filtering has been developed with the goal of decomposing such signals into simple oscillatory components several papers have been devoted to the investigation of this technique from a mathematical point of view all these works start with the assumption that each compactly supported signal is extended periodically outside the boundaries in this work we tackle the problem of studying the influence of different boundary conditions on the decompositions produced by the iterative filtering method in particular the choice of boundary conditions gives rise to different types of structured matrices thus we describe their spectral properties and the convergence properties of iterative filtering algorithm when such matrices are involved numerical results on artificial and real life signals provide interesting insight on important aspects such as accuracy and error propagation of the proposed technique and pave the way for further promising developments

coupling of bouncing ball modes to the chaotic sea and their counting function we study the coupling of bouncing ball modes to chaotic modes in two dimensional billiards with two parallel boundary segments analytically we predict the corresponding decay rates using the fictitious integrable system approach agreement with numerically determined rates is found for the stadium and the cosine billiard we use this result to predict the asymptotic behavior of the counting function n text bb e ensuremath sim e ensuremath delta for the stadium billiard we find agreement with the previous result ensuremath delta 3 4 for the cosine billiard we derive ensuremath delta 5 8 which is confirmed numerically and is well below the previously predicted upper bound ensuremath delta 9 10

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

vibration signal component separation by iteratively using basis pursuit and its application in mechanical fault detection abstract using different transform basis the vibration signal components such as impulses harmonics and modulated components can be effectively separated by basis pursuit for multicomponent vibration signals this paper proposes a new vibration signal component separation approach by iteratively using basis pursuit the signal is firstly denoised by basis pursuit denoising and the impulsive component can be separated by using identity matrix and redundant fourier basis then signal components with different frequency ranges can be separated by using short time fourier transform basis with different window lengths and the components with high frequency are separated after each iteration to choose the best basis from the dictionary the separation coefficient is proposed for evaluating the separating performance of the transform basis the proposed approach empirical mode decomposition emd and matching pursuit are respectively applied to analyzing a simulated faulty vibration and a simulated faulty gear vibration signal the comparison results demonstrate its superiority to emd and matching pursuit in separation accuracy finally the proposed approach is used for detecting the faults of a rotor and rolling bearings the results further show that this proposed method can be effectively applied to mechanical fault diagnosis

a sampling theorem for non bandlimited signals using generalized sinc functions a ladder shaped filter of two real parameters a 1 a 2 1 1 is introduced in this note the impulse response of the corresponding linear time invariant lti system is a generalized sinc function of two parameters consequently a generalized shannon type sampling theorem is established for a class of non bandlimited signals with special spectrum properties associated with a ladder shaped filter of two parameters finally a mathematical characterization for the class of non bandlimited signals satisfying the generalized sampling theorem is offered these signals are restrictions to the real line of certain analytic functions in stripped domains symmetric about the real axis in the complex plane for these signals their spectra in higher frequency bands are measured by the spectrum of their base bands

on fourier interpolation error for band limited signals fourier interpolation is a useful tool to reconstruct continuous signals from discrete samples this correspondence derives fourier interpolation expression from fourier series for periodic signals and investigates its error expression and upper bound for general band limited signals two numerical examples are given to interpret the meaning of the formulas

a green s function based bi dimensional empirical mode decomposition a new git bemd algorithm is developed based on green s function with tension much faster than canonical bemd algorithms easy to implement and very robust superior performance tested on artificial and real images bidimensional empirical mode decomposition bemd interprets an image as a superposition of bidimensional intrinsic mode functions bimfs they are extracted by a process called sifting which encompasses two dimensional surface interpolations connecting a set of local maxima or minima to form corresponding envelope surfaces existing surface interpolation schemes are computationally very demanding and often induce artifacts in the extracted modes this paper suggests a novel method of envelope surface interpolation based on green s functions including surface tension greatly improves the stability of the new method which we call green s function in tension based bemd git bemd simulation results using toy images with various textures facial images and functional neuroimages demonstrate the superior performance of the new method when compared to its canonical bemd counterpart git bemd strongly speeds up computations and achieves a higher quality of the extracted bimfs furthermore git bemd can be extended simply to an ensemble based variant git beemd if needed in summary the study suggests the new variant git bemd as a highly competitive fast and stable alternative to existing bemd techniques for image analysis

the semiclassical theory of discontinuous systems and ray splitting billiards we analyze the semiclassical limit of spectral theory on manifolds whose metrics have jump like discontinuities such systems are quite different from manifolds with smooth riemannian metrics because the semiclassical limit does not relate to a classical flow but rather to branching ray splitting billiard dynamics in order to describe this system we introduce a dynamical system on the space of functions on phase space to identify the quantum dynamics in the semiclassical limit we compute the principal symbols of the fourier integral operators associated to reflected and refracted geodesic rays and identify the relation between classical and quantum dynamics in particular we prove a quantum ergodicity theorem for discontinuous systems in order to do this we introduce a new notion of ergodicity for the ray splitting dynamics

entropy and the localization of eigenfunctions we study the large eigenvalue limit for the eigenfunctions of the laplacian on a compact manifold of negative curvature in fact we only assume that the geodesic flow has the anosov property in the semi classical limit we prove that the wigner measures associated to eigenfunctions have positive metric entropy in particular they cannot concentrate entirely on closed geodesies 1 introduction statement of results we consider a compact riemannian manifold m of dimension d 2 and assume that the geodesic flow ter acting on the unit tangent bundle of m has a chaotic behaviour this refers to the asymptotic properties of the flow when time t tends to infinity ergodicity mixing hyperbolicity we assume here that the geodesic flow has the anosov property the main example being the case of negatively curved manifolds the words quantum chaos express the intuitive idea that the chaotic features of the geodesic flow should imply certain special features for the corresponding quantum dynamical system that is according to schrodinger the unitary flow exp iht t r acting on the hilbert space l2 m where a stands for the laplacian on m and h is proportional to the planck constant recall that the quantum flow converges in a sense to the classical flow g in the so called semi classical limit h 0 one can imagine that for small values ofh the quantum system will inherit certain qualitative properties of the classical flow one expects for instance a very different behaviour of eigenfunctions of the laplacian or the distribution of its eigenvalues if the geodesic flow is anosov or in the other extreme completely integrable see sa95 the convergence of the quantum flow to the classical flow is stated in the egorov theorem consider one of the usual quantization procedures op which associates an operator oph a acting on l2 m to every smooth compactly supported function a e c t m on the cotangent bundle t m according to the egorov theorem we have for any fixed t

variational mode decomposition during the late 1990s huang introduced the algorithm called empirical mode decomposition which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands emd is known for limitations like sensitivity to noise and sampling these limitations could only partially be addressed by more mathematical attempts to this decomposition problem like synchrosqueezing empirical wavelets or recursive variational decomposition here we propose an entirely non recursive variational mode decomposition model where the modes are extracted concurrently the model looks for an ensemble of modes and their respective center frequencies such that the modes collectively reproduce the input signal while each being smooth after demodulation into baseband in fourier domain this corresponds to a narrow band prior we show important relations to wiener filter denoising indeed the proposed method is a generalization of the classic wiener filter into multiple adaptive bands our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand the variational model is efficiently optimized using an alternating direction method of multipliers approach preliminary results show attractive performance with respect to existing mode decomposition models in particular our proposed model is much more robust to sampling and noise finally we show promising practical decomposition results on a series of artificial and real data

decomposition of the wigner ville distribution and time frequency distribution series using the orthogonal like gabor expansion the authors decompose the wigner ville distribution wvd to a linear combination of localized and symmetric functions wvd sub h h t w the wvd of the gabor elementary functions h sub m n t and h sub m n t since the influence of the wvd sub h h t w to the useful properties is inversely proportional to the distance between h sub m n t and h sub m n t the wvd sub h h t w are further grouped as a series of the function p sub d t w the authors name the resulting representation the time frequency distribution series tpds also known as the gabor spectrogram in industry the tfdsd consists of up to a dth order p sub d t w while tfds sub 0 t w p sub 0 t w is similar to the spectrogram tfds sub spl infin t w converges to the wvd sub s t w numerical simulations demonstrate that adjusting the order d of the tfds one could effectively balance the cross term interference and the useful properties

arbitrary order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders in this paper we present an extended version of hilbert huang transform namely arbitrary order hilbert spectral analysis to characterize the scale invariant properties of a time series directly in an amplitude frequency space we first show numerically that due to a nonlinear distortion traditional methods require high order harmonic components to represent nonlinear processes except for the hilbert based method this will lead to an artificial energy flux from the low frequency large scale to the high frequency small scale part thus the power law if it exists is contaminated we then compare the hilbert method with structure functions sf detrended fluctuation analysis dfa and wavelet leader wl by analyzing fractional brownian motion and synthesized multifractal time series for the former simulation we find that all methods provide comparable results for the latter simulation we perform simulations with an intermittent parameter 0 15 we find that the sf underestimates scaling exponent when q 3 the hilbert method provides a slight underestimation when q 5 however both dfa and wl overestimate the scaling exponents when q 5 it seems that hilbert and dfa methods provide better singularity spectra than sf and wl we finally apply all methods to a passive scalar temperature data obtained from a jet experiment with a taylor s microscale reynolds number re 250 due to the presence of strong ramp cliff structures the sf fails to detect the power law behavior for the traditional method the ramp cliff structure causes a serious artificial energy flux from the low frequency large scale to the high frequency small scale part thus dfa and wl underestimate the scaling exponents however the hilbert method provides scaling exponents q quite close to the one for longitudinal velocity indicating a less intermittent passive scalar field than what was believed before 2011 american physical society

a synchrosqueezed wavelet transform enhanced by extended analytical mode decomposition method for dynamic signal reconstruction abstract a synchrosqueezed wavelet transform combined by wavelet analysis and time frequency reallocation method was recently developed to improve the quality of time frequency representation and construct the components of a signal however the quality of this transform highly depends on the parameters of wavelet functions to overcome the effects of wavelet function parameters on signal decomposition an analytical mode decomposition method was proposed to reconstruct each component the analytical mode decomposition selects the bisecting frequency between any two adjacent instantaneous frequencies estimated from a preliminary synchrosqueezed wavelet analysis and analytically extracts the individual components from a signal between any two bisecting frequencies two examples including a frequency modulated amplitude decayed signal and seismic responses of a two story building are analyzed it is demonstrated that the analytically derived components are insensitive to the selection parameters of wavelet function and bisecting frequency the proposed method is superior to the synchrosqueezed wavelet transform method for dynamic signal reconstruction

detecting intrinsic dynamics of traffic flow with recurrence analysis and empirical mode decomposition abstract in this paper we apply the empirical mode decomposition emd method to the recurrence plot rp and recurrence quantification analysis rqa to evaluate the frequency and time evolving dynamics of the traffic flow based on the cumulative intrinsic mode functions extracted by the emd the frequency evolving rp regarding different oscillation of modes suggests that apparent dynamics of the data considered are mainly dominated by its components of medium and low frequencies while severely affected by fast oscillated noises contained in the signal noises are then eliminated to analyze the intrinsic dynamics and consequently the denoised time evolving rqa diversely characterizes the properties of the signal and marks crucial points more accurately where white bands in the rp occur whereas a strongly qualitative agreement exists between all the non denoised rqa measures generally the emd combining with the recurrence analysis sheds more reliable abundant and inherent lights into the traffic flow which is meaningful to the empirical analysis of complex systems

time varying vibration decomposition and analysis based on the hilbert transform this paper introduces a simple method for time varying vibration decomposition based on the hilbert transform the non stationary frequency of the largest component is estimated as an average function of the instantaneous frequency of the composition and the corresponding envelope is estimated according to synchronous demodulation the method is demonstrated using computer simulation of different types of non stationary and nonlinear vibration

uniform distribution of eigenfunctions on compact hyperbolic surfaces on demontre que les fonctions propres k du laplacien sur une surface hyperbolique compacte x devient uniformement distribuee sur x quand k

squeezed states generalized hermite polynomials and pseudo diffusion equation abstract we show that the wavefunctions pq n of the harmonic oscillator in the squeezed state representation have the generalized hermite polynomials as their natural orthogonal polynomials these wavefunctions lead to generalized poisson distribution pn pq which satisfy an interesting pseudo diffusion equation p n p q 1 4 2 p 2 1 2 2 q 2 p 2 p q in which the squeeze parameter plays the role of time th entropies sn have minima at the unsqueezed states 1 which means that squeezing or stretching decreases the correlation between momentum p and position q

o n symmetries sum rules for generalized hermite polynomials and squeezed states quantum optics has been dealing with coherent states squeezed states and many other non classical states the associated mathematical framework makes use of special functions as hermite polynomials laguerre polynomials and others in this connection we here present some formal results that follow directly from the group o n of complex transformations motivated by the squeezed states structure we introduce the generalized hermite polynomials which include as particular cases the hermite polynomials as well as the heat polynomials using generalized raising operators we derive new sum rules for the which are covariant under o n transformations the and the associated sum rules become useful for evaluating wigner functions in a straightforward manner as a byproduct we use one of these sum rules on the operator level to obtain raising and lowering operators for the laguerre polynomials and show that they generate an sl 2 r su 1 1 algebra

on the analytic wavelet transform an exact and general expression for the analytic wavelet transform of a real valued signal is constructed resolving the time dependent effects of nonnegligible amplitude and frequency modulation the analytic signal is first locally represented as a modulated oscillation demodulated by its own instantaneous frequency and then taylor expanded at each point in time the terms in this expansion called the instantaneous modulation functions are time varying functions which quantify at increasingly higher orders the local departures of the signal from a uniform sinusoidal oscillation closed form expressions for these functions are found in terms of bell polynomials and derivatives of the signal s instantaneous frequency and bandwidth the analytic wavelet transform is shown to depend upon the interaction between the signal s instantaneous modulation functions and frequency domain derivatives of the wavelet inducing a hierarchy of departures of the transform away from a perfect representation of the signal the form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal in which case our expressions simplify considerably one may then quantify the time varying bias associated with signal estimation via wavelet ridge analysis and choose wavelets to minimize this bias

a hybrid detrending method for fractional gaussian noise abstract determining trend and implementing detrending operations are important steps in data analysis yet there is neither precise definition of trend nor any logical algorithm for extracting it in this paper we propose a hybrid detrending method hdm which is based on the empirical mode decomposition emd and the detrended fluctuation analysis dfa our method can remove the polynomial and sinusoidal trends from the fractional gaussian noise fgn background we illustrate the method by selected examples from artificial time series and climate data in comparison with existing frequency domain based detrending methods our method is a posteriori the trend defined by our method is only derived from the data further our method also preserves the scaling behavior of the original signals

a class of multivariate denoising algorithms based on synchrosqueezing univariate thresholding techniques based on high resolution time frequency algorithms such as the synchrosqueezing transform have emerged as important tools in removing noise from real world data low cost multichannel sensor technology has highlighted the need for direct multivariate denoising and to this end we introduce a class of multivariate denoising techniques based on the synchrosqueezing transform this is achieved by partitioning the time frequency domain so as to identify a set of modulated oscillations common to the constituent data channels within multivariate data and by employing a modified universal threshold in order to remove noise components while retaining signal components of interest this principle is used to introduce both the wavelet and fourier based multivariate synchrosqueezing denoising algorithms the performance of the proposed multivariate denoising algorithm is illustrated on both synthetic and real world data

on the equivalence between the wave packet phase space representation wppsr and the phase space generated by the squeezed states departamento de fisica universidade federal de sao carlos rodovia washington luiz km 235 13560 sao carlos sp

the behaviour of eigenstates of arithmetic hyperbolic manifolds in this paper we study some problems arising from the theory of quantum chaos in the context of arithmetic hyperbolic manifolds we show that there is no strong localization scarring onto totally geodesic submanifolds arithmetic examples are given which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom