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

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

emd based refined composite multiscale entropy analysis of complex signals abstract multiscale entropy mse is an effective method to measure the complexity of signals from complex systems which has been applied to various fields successfully however mse may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse graining procedure reduces the length of data considerably at large scales refined composite multiscale entropy rcmse is then developed to solve this problem however trends superimposed in signals may significantly affect the complexity measurement thus we introduce an empirical mode decomposition based rcmse called emd rcmse to first eliminate such effects of trends and then measure the complexity of signals it is validated from simulated signals and has good estimation in addition this method is also applied to study the complexity of traffic signals and we obtain some interesting results 1 traffic signals are more complex than the results showing from rcmse mse 2 weekday and weekend patterns different combination of trends greatly affect the results 3 complexity indices change with time at each day due to the degree of human activities

nonextensive random matrix theory approach to mixed regular chaotic dynamics we apply tsallis q indexed entropy to formulate a nonextensive random matrix theory which may be suitable for systems with mixed regular chaotic dynamics the joint distribution of the matrix elements is given by folding the corresponding quantity in the conventional random matrix theory by a distribution of the inverse matrix element variance it keeps the basis invariance of the standard theory but violates the independence of the matrix elements we consider the subextensive regime of q more than unity in which the transition from the wigner to the poisson statistics is expected to start we calculate the level density for different values of the entropic index our results are consistent with an analogous calculation by tsallis and collaborators we calculate the spacing distribution for mixed systems with and without time reversal symmetry comparing the result of calculation to a numerical experiment shows that the proposed nonextensive model provides a satisfactory description for the initial stage of the transition from chaos towards the poisson statistics

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

nonlinear stochastic exclusion financial dynamics modeling and time dependent intrinsic detrended cross correlation abstract in attempt to reproduce price dynamics of financial markets a stochastic agent based financial price model is proposed and investigated by stochastic exclusion process the exclusion process one of interacting particle systems is usually thought of as modeling particle motion with the conserved number of particles in a continuous time markov process in this work the process is utilized to imitate the trading interactions among the investing agents in order to explain some stylized facts found in financial time series dynamics to better understand the correlation behaviors of the proposed model a new time dependent intrinsic detrended cross correlation tdi dcc is introduced and performed also the autocorrelation analyses are applied in the empirical research furthermore to verify the rationality of the financial price model the actual return series are also considered to be comparatively studied with the simulation ones the comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets

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

analysis of economic growth fluctuations based on eemd and causal decomposition abstract in this paper we first apply ensemble empirical mode decomposition eemd to analyze the change rate of gdp time series for ten major countries each signal is decomposed into four modes with different scales and a residual trend the variance contribution and averaged period cycle for each mode is then calculated results show that economic growth fluctuations for most of the countries mainly fluctuate at a short period between 3 5 years then the causal decomposition proposed by yang et al is utilized to detect the mutual causation among different countries the novelty of this method is that the causal interaction is identified in instantaneous phase coherence at a specific time scale the strengths and directions of causal relationship for each mode among countries differ from each other which mirrors the fact that the world economic activities are fluctuated and changeable over varying periods however no visible causation for the fourth mode long term cycle among countries is characterized meaning that the development of economy over a long period for most countries depends on its own conditions

scaling analysis of phase fluctuations in experimental three phase flows abstract the characterization of complex patterns arising from three phase e g oil gas water flows is an important problem with significant engineering and industrial applications based solely on measured conductance fluctuation signals from experimental three phase flows we propose a method to characterize and distinguish three commonly observed flow patterns using the phase characterization method we first calculate the instantaneous phase from the signals then through performing a scaling analysis detrended fluctuation analysis dfa we extract scaling behaviors associated with the phase fluctuations and find that the dfa scaling exponent is sensitive to the transition among different flow patterns which can be used to characterize nonlinear dynamics of the three phase flow from a novel perspective we investigate the three phase flow in terms of phase characterization and scaling analysis the results indicate that our method can provide new insights into the exploration of complex mechanism in flow pattern transition the effectiveness of the method is demonstrated and its broader applicability is articulated

dynamic correlations at different time scales with empirical mode decomposition abstract we introduce a simple approach which combines empirical mode decomposition emd and pearson s cross correlations over rolling windows to quantify dynamic dependency at different time scales the emd is a tool to separate time series into implicit components which oscillate at different time scales we apply this decomposition to intraday time series of the following three financial indices the s p 500 usa the ipc mexico and the vix volatility index usa obtaining time varying multidimensional cross correlations at different time scales the correlations computed over a rolling window are compared across the three indices across the components at different time scales and across different time lags we uncover a rich heterogeneity of interactions which depends on the time scale and has important lead lag relations that could have practical use for portfolio management risk estimation and investment decisions

symplectic geometry spectrum analysis of nonlinear time series various time series decomposition techniques including wavelet transform singular spectrum analysis empirical mode decomposition and independent component analysis have been developed for non linear dynamic system analysis in this paper we describe a symplectic geometry spectrum analysis sgsa method to decompose a time series into a set of independent additive components sgsa is performed in four steps embedding symplectic qr decomposition grouping and diagonal averaging the obtained components can be used for de noising prediction control and synchronization we demonstrate the effectiveness of sgsa in reconstructing and predicting two noisy benchmark nonlinear dynamic systems the lorenz and mackey glass attractors examples of prediction of a decadal average sunspot number time series and a mechanomyographic signal recorded from human skeletal muscle further demonstrate the applicability of the sgsa method in real life applications

empirical mode decomposition using rational splines an application to rainfall time series empirical mode decomposition emd a relatively new form of time series decomposition has the feature of not assuming that a time series is linear or stationary as is implicitly done in fourier analysis in natural time series such as records of rainfall streamflow temperature etc where most variables exhibit nonlinear and non stationary behaviour this feature is particularly useful allowing more meaningful quantification of the proportion of variance in a time series due to fluctuations at different time scales than previous spectral analysis techniques however in its original form the emd algorithm relies on cubic spline interpolation of the extrema which often inflate the variance of the resultant components intrinsic mode functions and residual in this paper a suggested improvement to the emd algorithm using rational splines and flexible treatment of the end conditions is outlined and the consequent effect on three exemplary annual rainfall time series is assessed as a proof of concept it is recognized that many more examples are needed for the fine tuning of the ideas before it can be widely recommended and this work is currently underway

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

analytical signal analysis of strange nonchaotic dynamics we apply an analytical signal analysis to strange nonchaotic dynamics through this technique it is possible to obtain the spectrum of instantaneous intrinsic mode frequencies that are present in a given signal we find that the second mode frequency and its variance are good order parameters for dynamical transitions from quasiperiodic tori to strange nonchaotic attractors snas and from snas to chaotic attractors phase fluctuation analysis shows that snas and chaotic attractors behave identically within short time windows as a consequence of local instabilities in the dynamics in longer time windows however the globally stable character of snas becomes apparent this methodology can be of great utility in the analysis of experimental time series and representative applications are made to signals obtained from rossler and duffing oscillators

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

identification of short term and long term time scales in stock markets and effect of structural break abstract the paper presents the comparative study of the nature of stock markets in short term and long term time scales with and without structural break in the stock data structural break point has been identified by applying zivot and andrews structural trend break model to break the original time series t s o into two time series time series before structural break t s b and time series after structural break t s a in order to identify the of short term and long term market the hurst exponent h technique has been applied on the intrinsic mode functions i m f obtained from the t s o t s b and t s a by using empirical mode decomposition method h 0 5 for all the imfs of t s o t s b and t s a having in the range of few days d to 3 months m and h 0 75 for all the imfs of t s o t s b and t s a having 5 m based on the value of h the market has been divided into two time horizons short term market having 3 d 3 m and h 0 5 and long term market having 5 m and h 0 75 as h 0 5 in short term and h 0 75 in long term the market is random in short term and has long range correlation in long term robustness of the results has also been verified by using detrended fluctuation exponent analysis and normalised variance n v techniques we obtained 0 5 for reconstructed short term time series and 1 68 for long term reconstructed time series separation of short term and long term market are also identified using n v technique the time scales for short term and long term markets are independent of structural break happened due to extreme event the obtained using the proposed method for short term and long term market may be useful for investors to identify the investment time horizon and hence to design the investment and trading strategies

fault identification of rotor bearing system based on ensemble empirical mode decomposition and self zero space projection analysis abstract accurately identifying faults in rotor bearing systems by analyzing vibration signals which are nonlinear and nonstationary is challenging to address this issue a new approach based on ensemble empirical mode decomposition eemd and self zero space projection analysis is proposed in this paper this method seeks to identify faults appearing in a rotor bearing system using simple algebraic calculations and projection analyses first eemd is applied to decompose the collected vibration signals into a set of intrinsic mode functions imfs for features second these extracted features under various mechanical health conditions are used to design a self zero space matrix according to space projection analysis finally the so called projection indicators are calculated to identify the rotor bearing system s faults with simple decision logic experiments are implemented to test the reliability and effectiveness of the proposed approach the results show that this approach can accurately identify faults in rotor bearing systems

the structure of bandlimited bmo functions and applications abstract in this paper we analyze the structure of bandlimited bmo functions using a recently found equation for the calculation of the hilbert transform of bounded bandlimited functions we derive a decomposition result for bandlimited bmo functions which is similar to the well known fefferman stein decomposition based on this decomposition we characterize the range of the hilbert transform moreover we present interesting applications of this result we characterize the peak value behavior of bandlimited bmo functions show that the derivative of bandlimited bmo functions is bounded and prove a sampling theorem for bandlimited bmo functions

joint probability densities of level spacing ratios in random matrices we calculate analytically for finite size matrices joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential we focus on the ratios of two spacings between three consecutive real eigenvalues as well as certain generalizations such as the overlapping ratios the resulting formulas are further analyzed in detail in two specific cases the hermite and the laguerre cases for which we offer explicit calculations for small n the analytical results are in excellent agreement with numerical simulations of usual random matrix ensembles and with the level statistics of a quantum many body lattice model and zeros of the riemann zeta function

cross correlation analysis of stock markets using emd and eemd abstract empirical mode decomposition emd is a data driven signal analysis method for nonlinear and nonstationary data since it is intuitive direct posterior and adaptive emd is widely applied to various fields of study in this paper emd and ensemble empirical mode decomposition eemd a modified method of emd are applied to financial time series through analyzing the intrinsic mode functions imfs of emd and eemd we find eemd method performs better on the orthogonality of imfs than emd with clustering the ordered frequencies of imfs the imfs obtained from eemd method are grouped into high medium and low frequency components representing the short medium and long term volatilities of the index sequences respectively with the cross correlation analysis of dcca cross correlation coefficient our findings allow us to gain further and detailed insight into the cross correlations of stock markets

singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation abstract a short time existence theorem is proven for the initial boundary value problem for a class of quasilinear symmetric hyperbolic systems containing a constant coefficient spatial operator multiplied by a large parameter solutions u are shown to remain bounded independently of for a time independent of provided that u 0 and u l 0 are bounded independently of and certain structural conditions are satisfied this result is applied to the quasigeostrophic approximation of the shallow water equations and the constant pressure approximation in combustion and solutions for these cases are shown to converge to solutions of limiting equations as

asymmetric multiscale detrended fluctuation analysis of california electricity spot price abstract in this paper we develop a new method called asymmetric multiscale detrended fluctuation analysis which is an extension of asymmetric detrended fluctuation analysis a dfa and can assess the asymmetry correlation properties of series with a variable scale range we investigate the asymmetric correlations in california 1999 2000 power market after filtering some periodic trends by empirical mode decomposition emd our findings show the coexistence of symmetric and asymmetric correlations in the price series of 1999 and strong asymmetric correlations in 2000 what is more we detect subtle correlation properties of the upward and downward price series for most larger scale intervals in 2000 meanwhile the fluctuations of s asymmetry and s absolute asymmetry are more significant in 2000 than that in 1999 for larger scale intervals and they have similar characteristics for smaller scale intervals we conclude that the strong asymmetry property and different correlation properties of upward and downward price series for larger scale intervals in 2000 have important implications on the collapse of california power market and our findings shed a new light on the underlying mechanisms of power price

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

empirical mode decomposition and synchrogram approach to cardiorespiratory synchronization we use the empirical mode decomposition method to decompose experimental respiratory signals into a set of intrinsic mode functions imfs and consider one of these imfs as a respiratory rhythm we then use the hilbert spectral analysis to calculate the instantaneous phase of the imf heartbeat data are finally incorporated to construct the cardiorespiratory synchrogram which is a visual tool for inspecting synchronization we perform analysis on 20 data sets collected by the harvard medical school from ten young 21 34 years old and ten elderly 68 81 years old rigorously screened healthy subjects our results support the existence of cardiorespiratory synchronization we also investigate the origin of the cardiorespiratory synchronization by addressing the problem of correlations between regularities of respiratory and cardiac signals our analysis shows that regularity of respiratory signals plays a dominant role in the cardiorespiratory synchronization

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

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

analytic signals and the transition to chaos in deterministic flows the transition from regular to chaotic motions in deterministic flows is characterized by a change from a discrete fourier spectrum to a broadband one the onset of chaos is thus associated with the creation of an infinite number of new fourier modes given a system that generates a time series x t we study the transition to chaos from the perspective of analytic signals which are defined via the hilbert transform in order to identify distinct analytic signals we decompose the original time series x t into a finite number of modes that correspond to proper rotations in the complex plane of their analytic signals we provide numerical evidence that at the transition there is no substantial change in the number of analytic signals characterizing x t furthermore the distributions of the instantaneous frequencies of the analytic signals in the chaotic regime are well localized and exhibit no broadband feature these results suggest a simple organization of chaos in terms of analytic signals

dissipative quasi geostrophic dynamics under random forcing the quasi geostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small rossby number we consider the quasi geostrophic equation with dissipation under random forcing in bounded domains we show that global unique solutions exist for appropriate initial data unlike the deterministic quasi geostrophic equation whose well posedness is well known there seems to be no rigorous result on global existence and uniqueness of the randomly forced quasi geostrophic equation our work provides such a rigorous result on global existence and uniqueness under very mild conditions

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

an improved hilbert huang transform and its application in vibration signal analysis abstract the vibration generated by industrial machines always contains nonlinear and non stationary signals recently a number of new methods have been proposed to analyse these signals one of the promising methods is the hilbert huang transform hht the hht is derived from the principals of empirical mode decomposition emd and the hilbert transform when applying the hht first the emd will decompose the acquired signal into a collection of intrinsic mode functions imf the imf is a kind of complete adaptive and almost orthogonal representation for the analysed signal since the imf is almost monocomponent it can determine all the instantaneous frequencies from the nonlinear or non stationary signal second the local energy of each instantaneous frequency can be derived through the hilbert transform hence the result is an energy frequency time distribution of the signal since applying the process of hht is not computational intensive the hht becomes a promising method to extract the properties of nonlinear and non stationary signal however after the completion of a thorough experiment the result generated by the hht has its deficiency first the emd will generate undesirable imfs at the low frequency region that may cause misinterpretation to the result second depends on the analysed signal the first obtained imf may cover too wide a frequency range such that the property of monocomponent cannot be achieved third the emd operation cannot separate signals that contain low energy components in this study new techniques have been applied to improve the result of hht in the improved version of hht the wavelet packet transform wpt is used as preprocessing to decompose the signal into a set of narrow band signals prior to the application of emd with the help from wpt each imf derived from the emd can truly become monocomponent then a screening process is conducted to remove unrelated imfs from the result both simulated and experimental vibration signals of having a rotary system with the fault of rubbing occurred have proven that the improved hht does show the rubbing symptoms more clear and accurate than the original hht hence the improved hht is a precise method for nonlinear and non stationary signal analysis

multiscale image fusion using complex extensions of emd empirical mode decomposition emd is a fully data driven technique for decomposing signals into their natural scale components however the problem of uniqueness caused by the empirical nature of the algorithm and its sensitivity to changes in parameters makes it difficult to perform fusion of data from multiple and heterogeneous sources a solution to this problem is proposed using recent complex extensions of emd which guarantees the same number of decomposition levels that is the uniqueness of the scales the methodology is used to address multifocus image fusion whereby two or more partially defocused images are combined in automatic fashion so as to create an all in focus image

a new approach to sparse decomposition of nonstationary signals with multiple scale structures using self consistent nonlinear waves abstract a new method for signal decomposition is proposed and tested based on self consistent nonlinear wave equations with self sustaining physical mechanisms in mind the new method is adaptive and particularly effective for dealing with synthetic signals consisting of components of multiple time scales by formulating the method into an optimization problem and developing the corresponding algorithm and tool we have proved its usefulness not only for analyzing simulated signals but more importantly also for real clinical data

a biased look at phase locking brief critical review and proposed remedy a number of popular measures of dependence between pairs of bandlimited signals rely on analytic phase a common misconception is that the dependence revealed by these measures must be specific to the spectral range of the filtered input signals implicitly or explicitly obtaining analytic phase involves normalizing the signal by its own envelope which is a nonlinear operation that introduces broad spectral leakage we review how this generates bias and complicates the interpretation of commonly used measures of phase locking a specific example of this effect may create spurious phase locking as a consequence of nonzero circular mean in the phase of input signals which can be viewed as spectral leakage to 0 hz corrections for this problem which recenter or uniformize the distribution of phase may fail when the amplitudes of the compared signals are correlated to address the more general problem of spectral bias a novel measure of phase locking is proposed the amplitude weighted phase locking value this measure is closely related to coherence but it removes ambiguities of interpretation that detract from the latter

turning tangent empirical mode decomposition a framework for mono and multivariate signals a novel empirical mode decomposition emd algorithm called 2t emd for both mono and multivariate signals is proposed in this correspondence it differs from the other approaches by its computational lightness and its algorithmic simplicity the method is essentially based on a redefinition of the signal mean envelope computed thanks to new characteristic points which offers the possibility to decompose multivariate signals without any projection the scope of application of the novel algorithm is specified and a comparison of the 2t emd technique with classical methods is performed on various simulated mono and multivariate signals the monovariate behaviour of the proposed method on noisy signals is then validated by decomposing a fractional gaussian noise and an application to real life eeg data is finally presented

superstatistical generalizations of wishart laguerre ensembles of random matrices using beck and cohen s superstatistics we introduce in a systematic way a family of generalised wishart laguerre ensembles of random matrices with dyson index 1 2 and 4 the entries of the data matrix are gaussian random variables whose variancesfluctuate from one sample to another according to a certain probability density f and a single deformation parameter three superstatistical classes for f are usually considered 2 inverse 2 and log normal distributions while the first class already considered by two of the authors leads to a power law decay of the spectral density we here introduce and solve exactly a superposition of wishart laguerre ensembles with inverse 2 distribution the corresponding macroscopic spectral density is given by a deformation of the semi circle and marcenko pastur laws on a non compact support with exponential tails after discussing in detail the validity of wigner s surmise in the wishart laguerre class we introduce a generalised dependent surmise with stretched exponential tails which well approximates the individual level spacing distribution in the bulk the analytical results are in excellent agreement with numerical simulations to illustrate our findings we compare the 2 and inverse 2 class to empirical data from financial covariance matrices

an improved empirical mode decomposition method based on the cubic trigonometric b spline interpolation algorithm abstract empirical mode decomposition emd is a new method presented recently for analyzing nonlinear and non stationary signals its basic idea is to decompose the signal into a series of complete orthogonal intrinsic mode functions imfs based on the local characteristics of the signal in time domain the key step of emd is to use the cubic spline interpolation to connect the maximum and minimum values of the signals into upper and lower envelopes respectively and then calculate the mean values of upper and lower envelopes based on the cubic trigonometric b spline interpolation algorithm a new improved method for emd is proposed named ctb emd in this paper in this method the interpolation curve is more flexible because of the adjustability of shape of the cubic trigonometric b splines curve thus the overshoot and undershoot problems in the cubic spline interpolation curve can be avoided and then the decomposition of the signal is more accurate and effect through numerical experiments we compare the effect of this method with other methods on decomposing simulation signals and real signals experimental results show that this method can decompose signals more effectively and accurately

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

an optimization based empirical mode decomposition scheme the empirical mode decomposition emd has been developed by n e huang et al in 1998 as an iterative method to decompose a nonlinear and nonstationary univariate function additively into multiscale components these components called intrinsic mode functions imfs are constructed such that they are approximately orthogonal to each other with respect to the l 2 inner product moreover the components allow for a definition of instantaneous frequencies through complexifying each component by means of the application of the hilbert transform this approach via analytic signals however does not guarantee that the resulting frequencies of the components are always non negative and thus physically meaningful and that the amplitudes can be interpreted as envelopes in this paper we formulate an optimization problem which takes into account important features desired of the resulting emd specifically we propose a data adapted iterative method which minimizes in each iteration step a smoothness functional subject to inequality constraints involving the extrema in this way our method constructs a sparse data adapted basis for the input function as well as a mathematically stringent envelope for the function moreover we present an optimization based normalization to extract instantaneous frequencies from the analytic function approach we present corresponding algorithms together with several examples

on the stochastic kuramoto sivanshinsky equation in this article we study the solution of the kuramoto sivashinsky equation on a bounded interval subject to a random forcing term we show that a unique solution to the equation exists for all time and depends continuously on the initial data

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

spectral and convergence analysis of the discrete alif method abstract the adaptive local iterative filtering alif method is a recently proposed iterative procedure to decompose a signal into a finite number of simple components called intrinsic mode functions it is an alternative to the well known and widely used empirical mode decomposition method and it has proved to be a powerful and promising algorithm however so far no convergence analysis is available for the alif algorithm both in the continuous and discrete settings in the present paper we focus on the discrete version of the alif method and we tackle the problem of studying its convergence properties using recent results about sampling matrices and the theory of generalized locally toeplitz sequences which we extend in this paper we perform a spectral analysis of the alif iteration matrices with a special attention to the eigenvalue clustering and the eigenvalue distribution based on the eigenvalue distribution we formulate a necessary condition for the convergence of the discrete alif method moreover we provide a simple criterion to construct appropriate filters satisfying this condition we also present several numerical examples in support of the theoretical study our contribution represents a first significant step toward a complete convergence analysis of the alif method an analysis which appears to be rather difficult from a mathematical viewpoint as the alif iteration matrices possess a peculiar structure that to the best of the authors knowledge has never been investigated in the literature

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

speech enhancement using empirical mode decomposition and the teager kaiser energy operator in this paper a speech denoising strategy based on time adaptive thresholding of intrinsic modes functions imfs of the signal extracted by empirical mode decomposition emd is introduced the denoised signal is reconstructed by the superposition of its adaptive thresholded imfs adaptive thresholds are estimated using the teager kaiser energy operator tkeo of signal imfs more precisely tkeo identifies the type of frame by expanding differences between speech and non speech frames in each imf based on the emd the proposed speech denoising scheme is a fully data driven approach the method is tested on speech signals with different noise levels and the results are compared to emd shrinkage and wavelet transform wt coupled with tkeo speech enhancement performance is evaluated using output signal to noise ratio snr and perceptual evaluation of speech quality pesq measure based on the analyzed speech signals the proposed enhancement scheme performs better than wt tkeo and emd shrinkage approaches in terms of output snr and pesq the noise is greatly reduced using time adaptive thresholding than universal thresholding the study is limited to signals corrupted by additive white gaussian noise v c 2014 acoustical society of america http dx doi org 10 1121 1 4837835

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

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

one or two frequencies the empirical mode decomposition answers this paper investigates how the empirical mode decomposition emd a fully data driven technique recently introduced for decomposing any oscillatory waveform into zero mean components behaves in the case of a composite two tones signal essentially two regimes are shown to exist depending on whether the amplitude ratio of the tones is greater or smaller than unity and the corresponding resolution properties of the emd turn out to be in good agreement with intuition and physical interpretation a refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments the analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the emd are assessed

dissipative quasi geostrophic motion under temporally almost periodic forcing the full nonlinear dissipative quasi geostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square integral of the wind forcing and the parameter ekman number viscosity and the domain size the proof involves the pullback attractor for the associated nonautonomous dynamical system

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

on invariant 2 2 β ensembles of random matrices abstract we introduce and solve exactly a family of invariant 2 2 random matrices depending on one parameter and we show that rotational invariance and real dyson index are not incompatible properties the probability density for the entries contains a weight function and a multiple trace trace interaction term which corresponds to the representation of the vandermonde squared coupling on the basis of power sums as a result the effective dyson index eff of the ensemble can take any real value in an interval two weight functions gaussian and non gaussian are explored in detail and the connections with ensembles of dumitriu edelman and the so called poisson wigner crossover for the level spacing are respectively highlighted a curious spectral twinning between ensembles of different symmetry classes is unveiled as a consequence the identification between symmetry group orthogonal unitary or symplectic and the exponent of the vandermonde 1 2 4 is shown to be potentially deceptive the proposed technical tool more generically allows for designing actual matrix models which i are rotationally invariant ii have a real dyson index eff iii have a pre assigned confining potential or alternatively level spacing profile the analytical results have been checked through numerical simulations with an excellent agreement eventually we discuss possible generalizations and further directions of research

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

nonlinear vibration characterization by signal decomposition abstract methods for nonlinear vibration characterization by decomposing dynamic responses using the hilbert huang transform and a sliding window fitting technique are presented numerical results show that hilbert huang transform can be used for decomposing nonlinear non stationary signals in order to reveal and estimate nonlinear effects major nonlinear phenomena that can be extracted from transient and or steady state dynamic responses include different nonlinearities softening and hardening effects intrawave amplitude and phase modulation distorted harmonic responses under a single frequency harmonic excitation interwave amplitude and phase modulation and multiple mode vibrations caused by internal external resonances however the discontinuity induced gibbs phenomenon makes hilbert huang transform analysis inaccurate around the two data ends on the other hand the sliding window fitting analysis has no gibbs phenomenon at the two data ends but it cannot extract accurate modulation frequencies due to the use of non orthogonal basis functions in the sliding window least squares curve fitting process

instantaneous frequency time analysis of physiology signals the application of pregnant women s radial artery pulse signals abstract this study used the hilbert huang transform a recently developed instantaneous frequency time analysis to analyze radial artery pulse signals taken from women in their 36th week of pregnancy and after pregnancy the acquired instantaneous frequency time spectrum hilbert spectrum is further compared with the morlet wavelet spectrum results indicate that the hilbert spectrum is especially suitable for analyzing the time series of non stationary radial artery pulse signals since in the hilbert huang transform signals are decomposed into different mode functions in accordance with signal s local time scale therefore the hilbert spectrum contains more detailed information than the morlet wavelet spectrum from the hilbert spectrum we can see that radial artery pulse signals taken from women in their 36th week of pregnancy and after pregnancy have different patterns this approach could be applied to facilitate non invasive diagnosis of fetus physiological signals in the future

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

a generalized demodulation approach to time frequency projections for multicomponent signals in this paper we introduce a flexible approach for the time frequency analysis of multicomponent signals involving the use of analytic vectors and demodulation the demodulated analytic signal is projected onto the time frequency plane so that as closely as possible each component contributes exclusively to a different tile in a wavelet packet tiling of the time frequency plane and at each time instant the contribution to each tile definitely comes from no more than one component a single reverse demodulation is then applied to all projected components the resulting instantaneous frequency of each component in each tile is not constrained to a set polynomial form in time and is readily calculated as is the corresponding hilbert energy spectrum two examples illustrate the method in order better to understand the effect of additive noise the approximate variance of the estimated instantaneous frequency in any tile has been formulated by starting with pure noise and studying its evolving covariance structure through each step of the algorithm the validity and practical utility of the resulting expression for the variance of the estimated instantaneous frequency is demonstrated via a simulation experiment

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 approach to phase and phase synchrony estimation time varying phase synchrony is an important bivariate measure that quantifies the dynamics between nonstationary signals and has been widely used in many applications including chaotic oscillators in physics and multichannel electroencephalography recordings in neuroscience current state of the art in time varying phase estimation uses either the hilbert transform or the complex wavelet transform of the signals both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the hilbert transform and the nonuniform time frequency resolution inherent to the wavelet analysis in this paper a new phase estimation method based on the rihaczek distribution and reduced interference rihaczek distribution belonging to cohen s class is proposed these distributions offer phase estimates with uniformly high time frequency resolution which can be used for defining time and frequency dependent phase synchrony properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing methods

evidence of multifractality from cee exchange rates against euro abstract the multifractal spectrum of a time series can be ascertained with a number of techniques some based on wavelets others based on the much newer multifractal detrended fluctuation analysis mf dfa we test for the presence of multifractality in daily data on selected exchange rates from central and eastern european economies against euro the approach is based on a slight modification of the mf dfa analysis in that local trends are not allowed to be polynomially fitted but rather are estimated through a sifting process which is established through a so called empirical mode decomposition emd algorithm we assess the drivers of the multifractal spectrum strength like temporal correlations or distributions based on surrogate data another topic discussed is whether the entrance in the exchange rate mechanism erm ii influenced the multifractality of the exchange rates

a study of the characteristics of white noise using the empirical mode decomposition method based on numerical experiments on white noise using the empirical mode decomposition emd method we find empirically that the emd is effectively a dyadic filter the intrinsic mode function imf components are all normally distributed and the fourier spectra of the imf components are all identical and cover the same area on a semi logarithmic period scale expanding from these empirical findings we further deduce that the product of the energy density of imf and its corresponding averaged period is a constant and that the energy density function is chi squared distributed furthermore we derive the energy density spread function of the imf components through these results we establish a method of assigning statistical significance of information content for imf components from any noisy data southern oscillation index data are used to illustrate the methodology developed here

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

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

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

derivative optimized empirical mode decomposition for the hilbert huang transform in the empirical mode decomposition emd for the hilbert huang transform hht a nonlinear and non stationary signal is adaptively decomposed by an hht into a series of intrinsic mode functions imfs with the lowest one as the trend at each step of the emd the low frequency component is mainly determined by the average of the upper envelope consisting of local maxima and the lower envelope consisting of local minima the high frequency component is the deviation of the signal relative to the low frequency component the fact that no local maximum and minimum can be determined at the two end points leads to detrend uncertainty and in turn causes uncertainty in the hht to reduce such uncertainty hermitian polynomials are used to obtain the upper and lower envelopes with the first derivatives at the two end points q l q r as parameters which are optimally determined on the base of minimum temporal variability of the low frequency component in the each step of the decomposition this well posed mathematical system is called the derivative optimized emd demd with the demd the end effect and detrend uncertainty are drastically reduced and scales are separated naturally without any a priori subjective selection criterion

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

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

multiscale multifractal detrended fluctuation analysis of earthquake magnitude series of southern california abstract the multifractal characteristics of magnitude time series of earthquakes that occurred in southern california from 1990 to 2010 are studied in this work a method for the scale division of the magnitude of these earthquakes based on empirical mode decomposition emd and multifractal analysis is proposed this method gains a new insight into measuring multifractal properties of the magnitude time series at multiple scales and it reveals further information about the dynamic seismic behavior by using emd a time series can be decomposed into mode time series that represent different time frequency components we find that time frequency components show long range correlation with different hurst exponents by using r s analysis based on the different fractal structures of components we consider three different scale series micro mid and macro scale subsequences which are superposed and reconstructed by the components the multifractal properties of the three scale subsequences are analyzed by using multifractal detrended fluctuation analysis mf dfa the results show that the three different scale subsequences have various shapes of multifractal spectra and corresponding distinct properties the micro scale subsequence singularity spectrum shows left skewed indicating a relative dominance of the lower hurst exponent the mid scale subsequence has a right skewed singularity spectrum the macro scale subsequence exhibits the most significant persistence and shows the strongest multifractality

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

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

measurement of linear dependence and feedback between multiple time series abstract measures of linear dependence and feedback for multiple time series are defined the measure of linear dependence is the sum of the measure of linear feedback from the first series to the second linear feedback from the second to the first and instantaneous linear feedback the measures are nonnegative and zero only when feedback causality of the relevant type is absent the measures of linear feedback from one series to another can be additively decomposed by frequency a readily usable theory of inference for all of these measures and their decompositions is described the computations involved are modest

decomposition of one dimensional waveform using iterative gaussian diffusive filtering methods the gaussian smoothing method is shown to have a wide transition zone around the cutoff frequency selected to filter a given dataset we proposed two iterative gaussian smoothing methods to tighten the transition zone one being approximately diffusive and the other being strictly diffusive the first version smoothes repeatedly the remaining high frequency parts and the second version requires an additional step to further smooth the resulting smoothed response in each of the smoothing operation based on the choice of the criterion for accuracy the smoothing factor and the number of iterations are derived for an infinite data length in both methods by contrast for a finite length data string results of the interior points sufficiently away from the two endpoints obtained by both methods can be shown to exhibit an approximate diffusive property the upper bound of the distance affected by the error propagation inward due to the lack of data beyond the two ends is numerically estimated numerical experiments also show that results of employing the iterative gaussian smoothing method are almost the same as those obtained by the strict diffusive version except that the error propagation distance induced by the latter is slightly deeper than that of the former the proposed method has been successfully applied to decompose the wave formation of a number of test cases including two sets of real experimental data

dynamic fluctuations of cross correlations in multi time scale abstract with the empirical mode decomposition we investigate the dynamic fluctuations of cross correlations in multi time scale in this approach the time series of price returns in financial markets is decomposed into a small number of intrinsic mode functions and the corresponding time series of phases can be obtained with the hilbert transform through the empirical mode decomposition we uncover that the cross correlations between stocks change significantly for different time scales and exhibit singular behaviors during a financial crisis with the phase correlation analysis we observe that the cross correlations between market indices vary also for different time scales dividing the total time interval into two sub intervals by the year 2007 we detect that the market indices are much more correlated after 2007

hilbert huang transform stability spectral analysis applied to flutter flight test data a new method the hilbert huang transform hht has been applied to analyze the aerostructures test wing atw flight flutter data from nasa dryden flight research center the analysis shows the yielding of the wing after the onset of flutter but just before breaking off of the wingtip based on hht a new stability spectral analysis is also proposed that shows both positive stable and negative unstable damping the stability spectral analysis further shows that the flutter of atw bending occurs at 2 5 hz in addition to 18 hz as determined by modal analysis and identification both hht and the teager energy operator based nonlinearity indicator show that the vibrations of the atw are nonlinear throughout the flight test flutter maneuver

robust image watermarking based on multiband wavelets and empirical mode decomposition in this paper we propose a blind image watermarking algorithm based on the multiband wavelet transformation and the empirical mode decomposition unlike the watermark algorithms based on the traditional two band wavelet transform where the watermark bits are embedded directly on the wavelet coefficients in the proposed scheme we embed the watermark bits in the mean trend of some middle frequency subimages in the wavelet domain we further select appropriate dilation factor and filters in the multiband wavelet transform to achieve better performance in terms of perceptually invisibility and the robustness of the watermark the experimental results show that the proposed blind watermarking scheme is robust against jpeg compression gaussian noise salt and pepper noise median filtering and con vfilter attacks the comparison analysis demonstrate that our scheme has better performance than the watermarking schemes reported recently

on the computational complexity of the empirical mode decomposition algorithm abstract it has been claimed that the empirical mode decomposition emd and its improved version the ensemble emd eemd are computation intensive in this study we will prove that the time complexity of the emd eemd which has never been analyzed before is actually equivalent to that of the fourier transform numerical examples are presented to verify that emd eemd is in fact a computationally efficient method

2d prony huang transform a new tool for 2d spectral analysis this paper provides an extension of the 1d hilbert huang transform for the analysis of images using recent optimization techniques the proposed method consists of 1 adaptively decomposing an image into oscillating parts called intrinsic mode functions imfs using a mode decomposition procedure and 2 providing a local spectral analysis of the obtained imfs in order to get the local amplitudes frequencies and orientations for the decomposition step we propose two robust 2d mode decompositions based on nonsmooth convex optimization 1 a genuine 2d approach which constrains the local extrema of the imfs and 2 a pseudo 2d approach which separately constrains the extrema of lines columns and diagonals the spectral analysis step is an optimization strategy based on prony annihilation property and applied on small square patches of the imfs the resulting 2d prony huang transform is validated on simulated and real data

large deviations for the stochastic quasigeostrophic equation with multiplicative noise this paper proves a large deviation principle for the stochastic quasigeostrophic equation with multiplicative noise the proof is based on the laplace principle and on weak convergence methods we also give a rigorous mathematical result on the existence of a strong solution and uniqueness of mild solutions to the stochastic quasigeostrophic equation in the dimension d 2 3 finally large deviations for short time are considered