instantaneous frequency estimation using the wigner distribution with varying and data driven window length the estimation of the instantaneous frequency if of a harmonic complex valued signal with an additive noise using the wigner distribution is considered if the if is a nonlinear function of time the bias of the estimate depends on the window length the optimal choice of the window length based on the asymptotic formulae for the variance and bias can be used in order to resolve the bias variance tradeoff however the practical value of this solution is not significant because the optimal window length depends on the unknown smoothness of the if the goal of this paper is to develop an adaptive if estimator with a time varying and data driven window length which is able to provide quality close to what could be achieved if the smoothness of the if were known in advance the algorithm uses the asymptotic formula for the variance of the estimator only its value may be easily obtained in the case of white noise and relatively high sampling rate simulation shows good accuracy for the proposed adaptive algorithm

the hilbert spectrum via wavelet projections non stationary signals are increasingly analysed in the time frequency domain to determine the variation of frequency components with time it was recently proposed in this journal that such signals could be analysed by projections onto the time frequency plane giving a set of monocomponent signals these could then be converted to analytic signals using the hilbert transform and their instantaneous frequency calculated which when weighted by the energy yields the hilbert energy spectrum for that projection agglomeration over projections yields the complete hilbert spectrum we show that superior results can be obtained using waveletbased projections the maximal overlap undecimated stationary translation invariant discrete wavelet transform and wavelet packet transforms are used with

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

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

a confidence limit for the empirical mode decomposition and hilbert spectral analysis the confidence limit is a standard measure of the accuracy of the result in any statistical analysis most of the confidence limits are derived as follows the data are first divided into subsections and then under the ergodic assumption the temporal mean is substituted for the ensemble mean next the confidence limit is defined as a range of standard deviations from this mean however such a confidence limit is valid only for linear and stationary processes furthermore in order for the ergodic assumption to be valid the subsections have to be statistically independent for non stationary and nonlinear processes such an analysis is no longer valid the confidence limit of the method here termed emd hsa for empirical mode decomposition hilbert spectral analysis is introduced by using various adjustable stopping criteria in the sifting processes of the emd step to generate a sample set of intrinsic mode functions imfs the emd technique acts as a pre processor for hsa on the original data producing a set of components imfs from the original data that equal the original data when added back together each imf represents a scale in the data from smallest to largest the ensemble mean and standard deviation of the imf sample sets obtained with different stopping criteria are calculated and these form a simple random sample set the confidence limit for emd hsa is then defined as a range of standard deviations from the ensemble mean without evoking the ergodic assumption subdivision of the data stream into short sections is unnecessary hence the results and the confidence limit retain the full frequency resolution of the full dataset this new confidence limit can be applied to the analysis of nonlinear and non stationary processes by these new techniques data from length of day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied by providing a confidence limit for this new approach a stable range of stopping criteria for the decomposition or sifting phase emd has been established making the results of the final processing with hsa and the entire emd hsa method more definitive

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

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

properties of linear integral equations related to the six vertex model with disorder parameter ii we study certain functions arising in the context of the calculation of correlation functions of the xxz spin chain and of integrable field theories related to various scaling limits of the underlying six vertex model we show that several of these functions that are related to linear integral equations can be obtained by acting with deformed difference operators on a master function the latter is defined in terms of a functional equation and of its asymptotic behavior concentrating on the so called temperature case we show that these conditions uniquely determine the high temperature series expansions of the master function this provides an efficient calculation scheme for the high temperature expansions of the derived functions as well

b splines of blaschke product type in this paper we construct a class of new splines related to a blaschke product they emerge naturally when studying the filter functions of a class of linear time invariant systems which are related to the boundary values of a blaschke product for the purpose of sampling non bandlimited signals using nonlinear fourier atoms the new splines generalize the well known symmetric b splines we establish their properties such as integral representation property a partition of unity property a recurrence relation and difference property we also investigate their random behaviour finally our numerical experiments confirm our theories

applications of high resolution time frequency transforms to attenuation estimation abstractattenuation estimates quantify the loss of energy of propagating seismic waves due to anelastic processes it is often carried out in the frequency domain the most well known methods for attenuation estimation such as the spectral ratio and frequency shift methods compare spectral shapes of waveforms along a given raypath they require broad spectra such as those obtained with the fourier transform and the continuous wavelet transform these methods are incompatible with high resolution time frequency transforms which drastically localize time frequency information on the other hand these transforms indicate stronger resistance to noise and can be used in combination with the peak frequency method to estimate attenuation we have applied high resolution transforms namely the synchrosqueezing transform basis pursuit and complete ensemble empirical mode decomposition to a synthetic wedge example and two seismic data set examples a seismic reflection profile and a vertical seismic profile

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

the application of the hilbert spectrum to the analysis of electromyographic signals this paper investigates the application of the hilbert spectrum hs which is a recent tool for the analysis of nonlinear and nonstationary time series to the study of electromyographic emg signals the hs allows for the visualization of the energy of signals through a joint time frequency representation in this work we illustrate the use of the hs in two distinct applications the first is for feature extraction from emg signals our results showed that the instantaneous mean frequency imnf estimated from the hs is a relevant feature to clinical practice we found that the median of the imnf reduces when the force level of the muscle contraction increases in the second application we investigated the use of the hs for detection of motor unit action potentials muaps the detection of muaps is a basic step in emg decomposition tools which provide relevant information about the neuromuscular system through the morphology and firing time of muaps we compared visually how muap activity is perceived on the hs with visualizations provided by some traditional e g scalogram spectrogram wigner ville time frequency distributions furthermore an alternative visualization to the hs for detection of muaps is proposed and compared to a similar approach based on the continuous wavelet transform cwt our results showed that both the proposed technique and the cwt allowed for a clear visualization of muap activity on the time frequency distributions whereas results obtained with the hs were the most difficult to interpret as they were extremely affected by spurious energy activity

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

audio denoising by time frequency block thresholding removing noise from audio signals requires a nondiagonal processing of time frequency coefficients to avoid producing ldquomusical noise rdquo state of the art algorithms perform a parameterized filtering of spectrogram coefficients with empirically fixed parameters a block thresholding estimation procedure is introduced which adjusts all parameters adaptively to signal property by minimizing a stein estimation of the risk numerical experiments demonstrate the performance and robustness of this procedure through objective and subjective evaluations

nonparametric estimation of instantaneous frequency the local polynomial approximation of time varying phase is used in order to estimate the instantaneous frequency and its derivatives for a complex valued harmonic signal given by discrete time observations with a noise the considered estimators are high order nonparametric generalizations of the short time fourier transform and the wigner ville distribution the asymptotic variance and bias of the estimates are obtained

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

on the physical part of the factorized correlation functions of the xxz chain it was recently shown by jimbo et al 2008 arxiv 0811 0439 that the correlation functions of a generalized xxz chain associated with an inhomogeneous six vertex model with a disorder parameter and with arbitrary inhomogeneities on the horizontal lines factorize and can all be expressed in terms of only two functions and here we approach the description of the same correlation functions and in particular of the function from a different direction we start from a novel multiple integral representation for the density matrix of a finite chain segment of length m in the presence of a disorder field we explicitly factorize the integrals for m 2 based on this we present an alternative description of the function in terms of the solutions of certain linear and nonlinear integral equations we then prove directly that the two definitions of describe the same function the definition in the work of jimbo et al 2008 arxiv 0811 0439 was crucial for the proof of the factorization the definition given here together with the known description of in terms of the solutions of nonlinear integral equations is useful for performing e g the trotter limit in the finite temperature case or for obtaining numerical results for the correlation functions at short distances we also address the issue of the construction of an exponential form of the density matrix for finite

parameter estimation for locally linear fm signals using a time frequency hough transform an estimator for the phase parameters of mono and multicomponent fm signals with both good numerical properties and statistical performance is proposed the proposed approach is based on the hough transform of the pseudo wigner ville time frequency distribution pwvd it is shown that the numerical properties of the estimator can be improved by varying the pwvd window length the effect of the window time extent on the statistical performance of the estimator is delineated experimental data is used for validation of the statistical properties

maximal subgroups of the classical groups associated with non isotropic subspaces of a vector space in 6 we showed that if v is a finite dimensional vector space and if h is a symplectic special orthogonal orthogonal special unitary or unitary group acting on i then with a few exceptions the stabilizer in h of a totally singular subspace is maximal we further indicated that if the stabilizer in h of an arbitrary subspace is maximal then that subspace will usually be totally singular non isotropic or isotropic but non singular of dimension 1 this only occurs in the case of an orthogonal group over a field of characteristic two in this paper we consider the stabilizer of a non isotropic subspace with the restriction that either the subspace or its conjugate will have a singular l dimensional subspace there is one general exception when h contains elements that interchange the subspace and its conjugate we show that in this case the subgroup of h consisting of the elements that either stabilize the subspace or interchange it with its conjugate is in most cases maximal there are a number of more specific exceptions listed in the next section as in 6 our approach is geometric in nature we show that any subgroup of h properly containing the given stabilizer contains every transvection or every semi transvection in h and deduce that it must therefore be the whole of h

hidden grassmann structure in the xxz model ii creation operators in this article we unveil a new structure in the space of operators of the xxz chain for each we consider the space mathcal w alpha of all quasi local operators which are products of the disorder field q alpha sum j infty 0 sigma 3 j with arbitrary local operators in analogy with cft the disorder operator itself is considered as primary field in our previous paper we have introduced the annhilation operators b c which mutually anti commute and kill the primary field here we construct the creation counterpart b c and prove the canonical anti commutation relations with the annihilation operators we conjecture that the creation operators mutually anti commute thereby upgrading the grassmann structure to the fermionic structure the bosonic operator t is the generating function of the adjoint action by local integrals of motion and commutes entirely with the fermionic creation and annihilation operators operators b c t create quasi local operators starting from the primary field we show that the ground state averages of quasi local operators created in this way are given by determinants

nonlinear chirp mode decomposition a variational method variational mode decomposition vmd a recently introduced method for adaptive data analysis has aroused much attention in various fields however the vmd is formulated based on the assumption of narrow band property of the signal model to analyze wide band nonlinear chirp signals ncss we present an alternative method called variational nonlinear chirp mode decomposition vncmd the vncmd is developed from the fact that a wideband ncs can be transformed to a narrow band signal by using demodulation techniques our decomposition problem is thus formulated as an optimal demodulation problem which is efficiently solved by the alternating direction method of multipliers our method can be viewed as a time frequency filter bank which concurrently extracts all the signal modes some simulated and real data examples are provided showing the effectiveness of the vncmd in analyzing ncss containing close or even crossed modes

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

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

rbf based technique for statistical demodulation of pathological tremor this paper presents an innovative technique based on the joint approximation capabilities of radial basis function rbf networks and the estimation capability of the multivariate iterated hilbert transform iht for the statistical demodulation of pathological tremor from electromyography emg signals in patients with parkinson s disease we define a stochastic model of the multichannel high density surface emg by means of the rbf networks applied to the reconstruction of the stochastic process characterizing the disease modeled by the multivariate relationships generated by the karhunen loeve transform in hilbert spaces next we perform a demodulation of the entire random field by means of the estimation capability of the multivariate iht in a statistical setting the proposed method is applied to both simulated signals and data recorded from three parkinsonian patients and the results show that the amplitude modulation components of the tremor oscillation can be estimated with signal to noise ratio close to 30 db with root mean square error for the estimates of the tremor instantaneous frequency additionally the comparisons with a large number of techniques based on all the combinations of the rbf extreme learning machine backpropagation support vector machine used in the first step of the algorithm and iht empirical mode decomposition multiband energy separation algorithm periodic algebraic separation and energy demodulation used in the second step of the algorithm clearly show the effectiveness of our technique these results show that the proposed approach is a potential useful tool for advanced neurorehabilitation technologies that aim at tremor characterization and suppression

methodology for nonlinear quantification of a flexible beam with a local strong nonlinearity abstract this study presents a methodology for nonlinear quantification i e the identification of the linear and nonlinear regimes and estimation of the degree of nonlinearity for a cantilever beam with a local strongly nonlinear stiffness element the interesting feature of this system is that it behaves linearly in the limits of extreme values of the nonlinear stiffness an euler bernoulli cantilever beam with two nonlinear configurations is used to develop and demonstrate the methodology one configuration considers a cubic spring attached at a distance from the beam root to achieve a smooth nonlinear effect the other configuration considers a vibro impact element that generates non smooth effects both systems have the property that in the limit of small and large values of a configuration parameter the system is almost linear and can be modeled as such with negligible error for the beam with a cubic spring attachment the forcing amplitude is the varied parameter while for the vibro impact beam this parameter is the clearance between the very stiff stops and the beam at static equilibrium proper orthogonal decomposition is employed to obtain an optimal orthogonal basis used to describe the nonlinear system dynamics for varying parameter values the frequencies of the modes that compose the basis are then estimated using the rayleigh quotient the variations of these frequencies are studied to identify parameter values for which the system behaves approximately linearly and those for which the dynamical response is highly nonlinear moreover a criterion based on the betti maxwell reciprocity theorem is used to verify the existence of nonlinear behavior for the set of parameter values suggested by the described methodology the developed methodology is general and applicable to discrete or continuous systems with smooth or nonsmooth nonlinearities

on demodulation ridge detection and synchrosqueezing for multicomponent signals in this paper we present a novel technique for the retrieval of the modes of a multicomponent signal using a time frequency tf representation of the signal our approach is based on a novel ridge extraction method that takes into account the fact that the tf representation is both discrete in time and frequency followed by a demodulation procedure numerical results show the benefits of the proposed approach for mode reconstruction in comparison to similar techniques that do not make use of demodulation furthermore numerical investigations show that the proposed approach sharpens the tf representation on which it is built

emd revisited a new understanding of the envelope and resolving the mode mixing problem in am fm signals empirical mode decomposition emd is an adaptive and data driven approach for analyzing multicomponent nonlinear and nonstationary signals the stop criterion envelope technique and mode mixing problem are the most important topics that need to be addressed in order to improve the emd algorithm in this paper we study the envelope technique and the mode mixing problem caused by separating multicomponent am fm signals with the emd algorithm we present a new necessary condition on the envelope that questions the current assumption that the envelope passes through the extreme points of an intrinsic mode function imf then we present a solution to the mode mixing problem that occurs when multicomponent am fm signals are separated we experiment on several signals including simulated signals and real life signals to demonstrate the efficacy of the proposed method in resolving the mode mixing problem

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

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

applications of the synchrosqueezing transform in seismic time frequency analysis abstracttime frequency representation of seismic signals provides a source of information that is usually hidden in the fourier spectrum the short time fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components known limitations such as trade offs between time and frequency resolution may be overcome by alternative techniques that extract instantaneous modal components empirical mode decomposition aims to decompose a signal into components that are well separated in the time frequency plane allowing the reconstruction of these components on the other hand a recently proposed method called the synchrosqueezing transform sst is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques this new tool produces a well defined time frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight

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

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

high order synchrosqueezing transform for multicomponent signals analysis with an application to gravitational wave signal this paper puts forward a generalization of the short time fourier based synchrosqueezing transform using a new local estimate of instantaneous frequency such a technique enables not only to achieve a highly concentrated time frequency representation for a wide variety of amplitude and frequency modulated multicomponent signals but also to reconstruct their modes with a high accuracy numerical investigation on synthetic and gravitational wave signals shows the efficiency of this new approach

on the analytic signal the teager kaiser energy algorithm and other methods for defining amplitude and frequency this paper compares the teager kaiser algorithm tka and other similar local methods to the analytic signal as procedure the general concepts of the instantaneous amplitude and frequency are discussed it is shown that only as meets certain physical conditions for the amplitude phase and frequency apf the advantage of accuracy and simplicity of the as is also demonstrated

fermionic screening operators in the sine gordon model abstract extending our previous construction in the sine gordon model we show how to introduce two kinds of fermionic screening operators in close analogy with conformal field theory with c 1

lagrangian single particle turbulent statistics through the hilbert huang transform the hilbert huang transform is applied to analyze single particle lagrangian velocity data from numerical simulations of hydrodynamic turbulence the velocity trajectory is described in terms of a set of intrinsic mode functions c i t and of their instantaneous frequency i t on the basis of this decomposition we define the conditioned statistical moments of the c i modes named q order hilbert spectra hs we show that such quantities have enhanced scaling properties as compared to traditional fourier transform or correlation based structure functions statistical indicators thus providing better insights into the turbulent energy transfer process we present clear empirical evidence that the energylike quantity i e the second order hs displays a linear scaling in time in the inertial range as expected from a dimensional analysis we also measure high order moment scaling exponents in a direct way without resorting to the extended self similarity procedure this leads to an estimate of the lagrangian structure function exponents which are consistent with the multifractal prediction in the lagrangian frame as proposed by biferale et al

an improved design of high resolution quadratic time frequency distributions for the analysis of nonstationary multicomponent signals using directional compact kernels this paper presents a new advanced methodology for designing high resolution time frequency distributions tfds of multicomponent nonstationary signals that can be approximated using piece wise linear frequency modulated pw lfm signals most previous kernel design methods assumed that signals auto terms are mostly centered around the origin of the nu tau ambiguity domain while signal cross terms are mostly away from the origin this study uses a multicomponent test signal for which each component is modeled as a pw lfm signal it finds that the above assumption is a very rough approximation of the location of the auto terms energy and cross terms energy in the ambiguity domain and it is only valid for signals that are well separated in the t f domain a refined investigation led to improved specifications for separating cross terms from auto terms in the nu tau ambiguity domain the resulting approach first represents the signal in the ambiguity domain and then applies a multidirectional signal dependent compact kernel that accounts for the direction of the auto terms energy the resulting multidirectional distribution mdd approach proves to be more effective than classical methods like extended modified b distribution s method or compact kernel distribution in terms of auto terms resolution and cross terms suppression results on simulated and real data validate the improved performance of the mdd showing up to 8 gain as compared to more standard state of the art tfds

the spillover effects between natural gas and crude oil markets the correlation network analysis based on multi scale approach abstract this paper proposes a new compound model to investigate the dynamic linkage mechanism between the natural gas and crude oil markets from the multi scale perspective in the proposed model two main steps are involved multi scale analysis and network research based on the bivariate empirical mode decomposition bemd and fine to coarse algorithm the multi scale analysis ensures the relationship between price fluctuations can be studied under three different time scales which corresponding to market disequilibrium significant events and long term trend by integrating the grey correlation degree and coarse gaining algorithm the network research reveals the dynamic spillover effects of the two markets at different time scales to capture the different linked characteristic in different periods the sample data of henry hub and wti spot prices from 1997 to 2017 is divided into three periods we transfer the daily correlations between the price fluctuations with specific time scale into the correlation patterns and establish the network based on their transmission relations the crucial correlation patterns and the significant transmission relations are revealed by some network indicators and the proposed approach in this paper can be applied to other field of research

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

completeness of a fermionic basis in the homogeneous xxz model with the aid of the creation operators introduced in our previous works we show how to construct a basis of the space of quasilocal operators for the homogeneous xxz chain

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

a time frequency based method for the detection and tracking of multiple non linearly modulated components with births and deaths the estimation of the components which contain the characteristics of a signal attracts great attention in many real world applications in this paper we address the problem of the tracking of multiple signal components over discrete time series we propose an algorithm to first detect the components from a given time frequency distribution and then to track them automatically in the first place the peaks corresponding to the signal components are detected using the statistical properties of the spectral estimator then an original classifier is proposed to automatically track the detected peaks in order to build components over time this classifier is based on a total divergence matrix computed from a peak component divergence matrix that takes account of both amplitude and frequency information the peak component pairs are matched automatically from this divergence matrix we propose a stochastic discrimination rule to decide upon the acceptance of the peak component pairs in this way the algorithm can estimate the number the amplitude and frequency modulation functions and the births and the deaths of the components without any limitation on the number of components the performance of the proposed method a post processing of a time frequency distribution is validated on simulated signals under different parameter sets the method is also applied to four real world signals as a proof of its applicability

hidden grassmann structure in the xxz model for the critical xxz model we consider the space mathcal w alpha of operators which are products of local operators with a disorder operator we introduce two anti commutative families of operators bf b zeta bf c zeta which act on mathcal w alpha these operators are constructed as traces over representations of the q oscillator algebra in close analogy with baxter s q operators we show that the vacuum expectation values of operators in mathcal w alpha can be expressed in terms of an exponential of a quadratic form of bf b zeta bf c zeta

hidden grassmann structure in the xxz model iv cft limit the grassmann structure of the critical xxz spin chain is studied in the limit to conformal field theory a new description of virasoro verma modules is proposed in terms of zamolodchikov s integrals of motion and two families of fermionic creation operators the exact relation to the usual virasoro description is found up to level 6

analysis of multicomponent lfm signals by a combined wigner hough transform the aim of the paper is the performance evaluation of a method for the analysis of mono or multicomponent linear frequency modulation lfm signals based on the hough transform of the wigner ville distribution of the signals a closed form expression is found for the signal to noise ratio and the parameter estimation accuracy the overall method as any nonlinear method exhibits a threshold effect nevertheless it is shown to be asymptotically efficient and offers a good rejection capability of the cross terms

data adaptive evolutionary spectral estimation we present a novel data adaptive estimator for the evolutionary spectrum of nonstationary signals we model the signal at a frequency of interest as a sinusoid with a time varying amplitude which is accurately represented by an orthonormal basis expansion we then compute a minimum mean squared error estimate of this amplitude and use it to estimate the time varying spectrum at that frequency all while minimizing the interference from the signal components at other frequencies repeating the process over all frequencies we obtain a power distribution that is consistent with the wold cramer evolutionary spectrum and reduces to capon s 1969 method for the stationary case our estimator possesses desirable properties in terms of time frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data we also propose a new estimator for the autocorrelation of nonstationary signals this autocorrelation estimate is needed in the data adaptive spectral estimation we illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time frequency distribution with exponential kernels

integral representations for correlation functions of the xxz chain at finite temperature we derive a novel multiple integral representation for a generating function of the z z correlation functions of the spin xxz chain at finite temperature and finite longitudinal magnetic field our work combines algebraic bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics

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 new algorithm for multicomponent signals analysis based on synchrosqueezing with an application to signal sampling and denoising in this paper we address the problem of the retrieval of the components from a multicomponent signal using ideas from the synchrosqueezing framework the emphasis is on the wavelet choice and we propose a novel algorithm based first on the detection of components followed by their reconstruction simulations illustrate how the proposed procedure compares with the empirical mode decomposition and other related methods in terms of mode mixing we conclude the paper by studying the sensitivity of the proposed technique to sampling and an application to signal denoising

second order synchrosqueezing transform or invertible reassignment towards ideal time frequency representations this paper considers the analysis of multicomponent signals defined as superpositions of real or complex modulated waves it introduces two new post transformations for the short time fourier transform that achieve a compact time frequency representation while allowing for the separation and the reconstruction of the modes these two new transformations thus benefit from both the synchrosqueezing transform which allows for reconstruction and the reassignment method which achieves a compact time frequency representation numerical experiments on real and synthetic signals demonstrate the efficiency of these new transformations and illustrate their differences

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

integral representation of the density matrix of the xxz chain at finite temperatures we present an integral formula for the density matrix of a finite segment of the infinitely long spin xxz chain this formula is valid for any temperature and any longitudinal magnetic field