measuring time frequency information content using the renyi entropies the generalized entropies of renyi inspire new measures for estimating signal information and complexity in the time frequency plane when applied to a time frequency representation tfr from cohen s class or the affine class the renyi entropies conform closely to the notion of complexity that we use when visually inspecting time frequency images these measures possess several additional interesting and useful properties such as accounting and cross component and transformation invariances that make them natural for time frequency analysis this paper comprises a detailed study of the properties and several potential applications of the renyi entropies with emphasis on the mathematical foundations for quadratic tfrs in particular for the wigner distribution we establish that there exist signals for which the measures are not well defined

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

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

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

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

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

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

construction of conformally invariant higher spin operators using transvector algebras this paper deals with a systematic construction of higher spin operators defined as conformally invariant differential operators acting on functions on flat space rm with values in an arbitrary half integer irreducible representation for the spin group to be more precise the higher spin version of the dirac operator and associated twistor operators will be constructed as generators of a transvector algebra hereby generalising the well known fact that the classical dirac operator on rm and its symbol generate the orthosymplectic lie superalgebra osp 1 2 to do so we will use the extremal projection operator and its relation to transvector algebras in the second part of the article the conformal invariance of the constructed higher spin operators will be proven explicitly

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

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

symmetric pairs and gorelik elements abstract the second author gave a formula for the elements of the enveloping algebra of a lie superalgebra defined by gorelik under an appropriate unimodularity assumption we show that this formula is a particular case of a formula for the jacobian of the exponential map of a symmetric superspace

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

the minimal primitive spectrum of the enveloping algebra of the lie superalgebra osp 1 2l abstract a well known theorem of duflo the annihilation theorem claims that the annihilator of a verma module in the enveloping algebra of a complex semisimple lie algebra is centrally generated for the lie superalgebra osp 1 2 l this result does not hold in this article we introduce a correct analogue of the centre for which the annihilation theorem does hold in the case osp 1 2 l this substitute of the centre is the centralizer of the even part of the enveloping algebra this algebra shares some nice properties with the centre as a consequence of the annihilation theorem we obtain the description of the minimal primitive spectrum of the enveloping algebra of the lie superalgebra osp 1 2 l we also deduce a criterium for a osp 1 2 l verma module to be a direct sum of sp 2 l verma modules

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

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

spinor valued l2 spaces on sm 1 and representations of spin 1 m abstract we show that the l 2 spaces of spinor valued functions on s m 1 provide models for the unitary principal series representations of spin 1 m which are characterized by the feature that they contain the fundamental spinor representation s of spin m the novelty of our approach is that we use tools characteristic of hypercomplex analysis the group spin 1 m is realized as a group of vahlen matrices and the harish chandra modules of such representations are expressed in terms of spherical monogenics which generalize the classical spherical harmonics by switching to the framework of hypercomplex analysis on the sphere we are able to extend part of the well known results for the scalar spherical principal series representations of so 1 m to the spinor setting in the process we introduce a clifford algebra valued riesz transform on the sphere

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

on casimir s ghost we define on the universal enveloping superalgebra of a nonstandard adjoint action endowing it with a module structure this allows in particular to construct a bosonic operator which anticommutes with all the fermionic generators and which appears to be the square root of a certain casimir operator

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

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

improving the readability of time frequency and time scale representations by the reassignment method in this paper the use of the reassignment method first applied by kodera gendrin and de villedary 1976 to the spectrogram is generalized to any bilinear time frequency or time scale distribution this method creates a modified version of a representation by moving its values away from where they are computed so as to produce a better localization of the signal components we first propose a new formulation of this method followed by a thorough theoretical study of its characteristics its practical use for a large variety of known time frequency and time scale distributions is then addressed finally some experimental results are reported to demonstrate the performance of this method

on the ideal structure of some banach algebras related to convolution operators on lp g keywords generalized fourier algebras p convolution operators maximal regular ideals minimal ideals amenability reference cahru article 2004 002doi 10 1016 j jfa 2004 02 011 record created on 2008 12 10 modified on 2016 08 08

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

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

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

characterization of signals by the ridges of their wavelet transforms the characterization and the separation of amplitude and frequency modulated signals is a classical problem of signal analysis and signal processing we present a couple of new algorithmic procedures for the detection of ridges in the modulus of the continuous wavelet transform of one dimensional 1 d signals these detection procedures are shown to be robust to additive white noise we also derive and test a new reconstruction procedure the latter uses only information from the restriction of the wavelet transform to a sample of points from the ridge this provides a very efficient way to code the information contained in the signal

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

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

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

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

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

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

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

a high resolution quadratic time frequency distribution for multicomponent signals analysis the paper introduces a new kernel for the design of a high resolution time frequency distribution tfd we show that this distribution can solve problems that the wigner ville distribution wvd or the spectrogram cannot in particular the proposed distribution can resolve two close signals in the time frequency domain that the two other distributions cannot moreover we show that the proposed distribution is more accurate than the wvd and the spectrogram in the estimation of the instantaneous frequency of a stepped fm signal embedded in additive gaussian noise synthetic and real data collected from real world applications are shown to validate the proposed distribution

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

asymptotic wavelet and gabor analysis extraction of instantaneous frequencies the behavior of the continuous wavelet and gabor coefficients in the asymptotic limit using stationary phase approximations are investigated in particular it is shown how under some additional assumptions these coefficients allow the extraction of some characteristics of the analyzed signal such as frequency and amplitude modulation laws applications to spectral line estimations and matched filtering are briefly discussed

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

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

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

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

a remark on the casimir elements of lie superalgebras and quantized lie superalgebras it is shown that the second order casimir operators c and cq of the lie superalgebra osp 1 2 and the quantized lie superalgebra ospq 1 2 respectively possess natural square roots

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

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

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

relaxed highest weight modules i rank 1 cases relaxed highest weight modules play a central role in the study of many important vertex operator super algebras and their associated logarithmic conformal field theories including the admissible level affine models indeed their structure and their super characters together form the crucial input data for the standard module formalism that describes the modular transformations and grothendieck fusion rules of such theories in this article character formulae are proved for relaxed highest weight modules over the simple admissible level affine vertex operator superalgebras associated to mathfrak s mathfrak l 2 and mathfrak osp 1 vert 2 moreover the structures of these modules are specified completely this proves several conjectural statements in the literature for mathfrak s mathfrak l 2 at arbitrary admissible levels and for mathfrak osp 1 vert 2 at level frac 5 4 for other admissible levels the mathfrak osp 1 vert 2 results are believed to be new

representations of banach algebras subordinate to topologically introverted spaces let a be a banach algebra x a closed subspace of a y a dual banach space with predual y and a continuous representation of a on y we call subordinate to x if each coordinate function y x for all y y y if x is topologically left right introverted and y is reflexive we show the existence of a natural bijection between continuous representations of a on y subordinate to x and normal representations of x on y we show that if a has a bounded approximate identity then every weakly almost periodic functional on a is a coordinate function of a continuous representation of a subordinate to wap a we show that a function f on a locally compact group g is left uniformly continuous if and only if it is the coordinate function of the conjugate representation of l1 g associated to some unitary representation of g we generalize the latter result to an arbitrary banach algebra with bounded right approximate identity we prove the functionals in luc a are all coordinate functions of some norm continuous representation of a on a dual banach space

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

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

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

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 remarkable connection between the representations of the lie superalgebras osp 1 2n and the lie algebras o 2n 1 we show that there is a one to one correspondence between the graded representations of osp 1 2n and the non spinorial representations of o 2n 1 the clebsch gordan series for osp 1 2n reduce to the corresponding series for o 2n 1 and the properly defined casimir operators of order at least up to four have the same eigenvalues

fourier stieltjes algebra of a topological group abstract this paper is an invitation to the study of the fourier stieltjes algebra b g the linear span of the continuous positive definite complex valued functions on a topological group g we study b g when g has a host algebra or a group c algebra the analogue of the group c algebra of a locally compact group our main challenge is that a topological group g cannot have a positive regular borel measure which is left translation invariant unless g is locally compact

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