bootstrap tests for distributional treatment effects in instrumental variable models this article considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is possibly nonrandomized but there is a binaryinstrument available for the researcher such a scenario is common in observational studies and in randomized experiments with imperfect compliance one possible approach to this problem is to compare the counterfactual cumulative distribution functions of the outcome with and without the treatment this article shows how to estimate these distributions using instrumental variable methods and a simple bootstrap procedure is proposed to test distributional hypotheses such as equality of distributions first order and second order stochastic dominance these tests and estimators are applied to the study of the effects of veteran status on the distribution of civilian earnings the results show a negative effect of military service during the vietnam era that appears to be concentrated on the lower tail of

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

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

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

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

image characterization by fractal descriptors in variational mode decomposition domain application to brain magnetic resonance abstract the main purpose of this work is to explore the usefulness of fractal descriptors estimated in multi resolution domains to characterize biomedical digital image texture in this regard three multi resolution techniques are considered the well known discrete wavelet transform dwt and the empirical mode decomposition emd and the newly introduced variational mode decomposition mode vmd the original image is decomposed by the dwt emd and vmd into different scales then fourier spectrum based fractal descriptors is estimated at specific scales and directions to characterize the image the support vector machine svm was used to perform supervised classification the empirical study was applied to the problem of distinguishing between normal and abnormal brain magnetic resonance images mri affected with alzheimer disease ad our results demonstrate that fractal descriptors estimated in vmd domain outperform those estimated in dwt and emd domains and also those directly estimated from the original image

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

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

multiresolution monogenic signal analysis using the riesz laplace wavelet transform the monogenic signal is the natural 2d counterpart of the 1d analytic signal we propose to transpose the concept to the wavelet domain by considering a complexified version of the riesz transform which has the remarkable property of mapping a real valued primary wavelet basis of l2 r2 into a complex one the riesz operator is also steerable in the sense that it give access to the hilbert transform of the signal along any orientation having set those foundations we specify a primary polyharmonic spline wavelet basis of l2 r2 that involves a single mexican hat like mother wavelet laplacian of a b spline the important point is that our primary wavelets are quasi isotropic they behave like multiscale versions of the fractional laplace operator from which they are derived which ensures steerability we propose to pair these real valued basis functions with their complex riesz counterparts to specify a multiresolution monogenic signal analysis this yields a representation where each wavelet index is associated with a local orientation an amplitude and a phase we give a corresponding wavelet domain method for estimating the underlying instantaneous frequency we also provide a mechanism for improving the shift and rotation invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect reconstruction filterbanks we illustrate the specific feature extraction capabilities of the representation and present novel examples of wavelet domain processing in particular a robust tensor based analysis of directional image patterns the demodulation of interferograms and the reconstruction of digital holograms

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

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

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

rate gains in block coded modulation systems with interblock memory this paper examines the performance gains achievable by adding interblock memory to and altering the mapping of coded bits to symbols in block coded modulation systems the channel noise considered is additive gaussian and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors in the case of the additive white gaussian noise channel these goals translate into the design of block codes of a given weighted or normalized distance whose rate is as high as possible and whose number of codewords at minimum normalized distance is low the effect of designing codes for normalized distance rather than hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest and many such best codes are given

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

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

decomposing a signal into short time narrow banded modes abstract an algorithm for nonparametric decomposition of a signal into the sum of short time narrow banded modes components is introduced specifically the signal data is augmented with its hilbert transform to obtain the analytic signal then the set of constituent amplitude and frequency modulated am fm analytic sinusoids each with slowly varying amplitude and frequency is sought the method for obtaining the short time narrow banded modes is derived by minimizing an objective function comprised of three criteria smoothness of the instantaneous amplitude envelope smoothness of the instantaneous frequency and complete reconstruction of the signal data a minimum of the objective function is approached using a sequence of suboptimal updates of amplitude and phase the updates are intuitive efficient and simple to implement for a given mode the amplitude and phase are extracted from the band pass filtered residual signal after the other modes are removed where the band pass filter is applied about the previous modal instantaneous frequency estimate the method is demonstrated by application to random output only vibration data and order tracking data it is demonstrated that vibration modal responses can be estimated from single channel data and order tracking can be performed without measured tachometer data

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

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

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

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

the boundary of universal discrete quantum groups exactness and factoriality we study the c algebras and von neumann algebras associated with the universal discrete quantum groups they give rise to full prime factors and simple exact c algebras the main tool in our work is the study of an amenable boundary action yielding the akemann ostrand property finally this boundary can be identified with the martin or the poisson boundary of a quantum random walk

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

the inner structure of empirical mode decomposition abstract the empirical mode decomposition emd is a nonlinear method that is truly adaptive with good localization property in the time domain for analyzing non stationary complex data the emd has been proven useful in a wide range of applications however due to the nonlinear and complex nature of the sifting process the most essential step of the emd a firm mathematical foundation or a transparent physical description are still lacked for emd here we embark on constructing a mathematical theory of the sifting operator we first show that the sifting operator can be expressed as the data plus the sum of the responses to the impulses multiplied by the data value at the extrema such an expression of the sifting operator is then used to investigate the adaptive nature and the localizing effect of the emd alternatively the sifting operator can also be represented by a sifting matrix which depends nonlinearly on the extrema distribution based on the eigen decomposition of the sifting matrix the transfer function of the sifting process is analyzed finally we answer what an intrinsic mode function imf is from the wave perspective by exploring the physical basis of the imfs

quantum symmetry groups of finite spaces we determine the quantum automorphism groups of finite spaces these are compact matrix quantum groups in the sense of woronowicz

equivariant poincare duality for quantum group actions we extend the notion of poincare duality in kk theory to the setting of quantum group actions an important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products along the way we discuss general properties of equivariant kk theory for locally compact quantum groups including the construction of exterior products as an example we prove that the standard podle sphere is equivariantly poincare dual to itself

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

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

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

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

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

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

orbit and coset analysis of the golay and related codes let b be a code of length n over a field f with automorphism group g b sub w denotes the subset of codewords of weight w the goal is to classify the vectors of f sup n into orbits under g and to determine their distances from the various subcodes b sub w this is done for the first order reed muller nordstrom robinson and hamming codes of length 16 the golay and shortened golay codes of lengths 22 23 24 and the ternary golay code of length 12

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

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

k amenability for amalgamated free products of amenable discrete quantum groups abstract the basic notions and results of equivariant kk theory concerning crossed products can be extended to the case of locally compact quantum groups we recall these constructions and prove some useful properties of subgroups and amalgamated free products of discrete quantum groups using these properties and a quantum analogue of the bass serre tree we establish the k amenability of amalgamated free products of amenable discrete quantum groups

crude oil price analysis and forecasting based on variational mode decomposition and independent component analysis abstract as one of the most vital energy resources in the world crude oil plays a significant role in international economic market the fluctuation of crude oil price has attracted academic and commercial attention there exist many methods in forecasting the trend of crude oil price however traditional models failed in predicting accurately based on this a hybrid method will be proposed in this paper which combines variational mode decomposition vmd independent component analysis ica and autoregressive integrated moving average arima called vmd ica arima the purpose of this study is to analyze the influence factors of crude oil price and predict the future crude oil price major steps can be concluded as follows firstly applying the vmd model on the original signal crude oil price the modes function can be decomposed adaptively secondly independent components are separated by the ica and how the independent components affect the crude oil price is analyzed finally forecasting the price of crude oil price by the arima model the forecasting trend demonstrates that crude oil price declines periodically comparing with benchmark arima and eemd ica arima vmd ica arima can forecast the crude oil price more accurately

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

multistage decoding of multilevel block m psk modulation codes and its performance analysis multistage decoding of multilevel block multilevel phase shift keying m psk modulation codes for the additive white gaussian noise awgn channel is investigated several types of multistage decoding including a suboptimum soft decision decoding scheme are devised and analyzed upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes error probabilities of some specific multilevel block 8 psk modulation codes are evaluated and simulated the computation and simulation results for these codes show that with multistage decoding significant coding gains can be achieved with large reduction in decoding complexity in one example it is shown that the difference in performance between the proposed suboptimum multistage soft decision decoding and the single stage optimum decoding is small only a fraction of a db loss in snr at the block error probability of 10 sup 6

on block coded modulation with interblock memory block coded modulation with interblock memory bcmim is a variation of block coded modulation bcm which is designed for multilevel coding by providing interblock memory between adjacent blocks the coding rate of a bcmim scheme can be increased without decreasing the minimum squared euclidean distance msed as compared to the original bcm in an early version of bcmim interblock coding is provided only between the first two coding levels of adjacent blocks in this paper we design bcmim with a more general form for which interblock coding can be introduced among many coding levels in this way we can further increase the coding rate of bcmim without decreasing the msed we provide many examples to show the advantages of bcmim with the general form most of the examples are designed based on multidimensional signal sets since a multidimensional signal set can provide more coding levels than a two dimensional 2 d signal set

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

block coded modulation optimized for finite error rate on the white gaussian noise channel this correspondence examines the performance of block coded modulation bcm at finite decoded bit error rates ber we consider the optimum geometric structure to optimize coding gain at finite ber rather than asymptotic coding gain we introduce the concept of the row ber and show that this structure may be implemented by a bcm scheme in which the row bit error rates are equalized we present a design procedure for such schemes and show that significant improvements over conventional schemes are possible

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

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 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

the k theory of free quantum groups in this paper we study the k theory of free quantum groups in the sense of wang and van daele more precisely of free products of free unitary and free orthogonal quantum groups we show that these quantum groups are k amenable and establish an analogue of the pimsner voiculescu exact sequence as a consequence we obtain in particular an explicit computation of the k theory of free quantum groups our approach relies on a generalization of methods from the baum connes conjecture to the framework of discrete quantum groups this is based on the categorical reformulation of the baum connes conjecture developed by meyer and nest as a main result we show that free quantum groups have a gamma element and that gamma 1 as an important ingredient in the proof we adapt the dirac dual dirac method for groups acting on trees to the quantum case we use this to extend some permanence properties of the baum connes conjecture to our setting

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

forecasting exchange rate using variational mode decomposition and entropy theory abstract in this paper we propose a new exchange rate forecasting model using variational mode decomposition vmd with parameter optimization by the combined mean square error mse and error entropy ee criterion exchange rate is decomposed into a series of underlying data components in the transformed multiscale domain using the vmd model a new mse ee criterion is proposed to determine the scale for transient factors among different extracted data components the proposed model extracts the transient factor more accurately and produces more accurate forecasts empirical studies using extensive exchange rates confirmed that the multiscale data structure can be identified more effectively in the decomposed multiscale domain using the proposed methodology the proposed model demonstrates the superior performance compared to the benchmark models

on multilevel block modulation codes the multilevel technique for combining block coding and modulation is investigated a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures a specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed given a multilevel block modulation code c with no interdependency among the binary component codes the proposed method gives a multilevel block modulation code c that has the same rate as c a minimum squared euclidean distance not less than that of c a trellis diagram with the same number of states as that of c and a smaller number of nearest neighbor codewords than that of c finally a technique is presented for analyzing the error performance of block modulation codes for an additive white gaussian noise awgn channel based on soft decision maximum likelihood decoding error probabilities of some specific codes are evaluated by simulation and upper bounds based on their euclidean weight distributions

quantum groups acting on 4 points we classify the compact quantum groups acting on 4 points these are the quantum subgroups of the quantum permutation group q4 our main tool is a new presentation for the algebra c q4 corresponding to an isomorphism of type q4 so 1 3 the quantum subgroups of q4 are subject to a mckay type correspondence that we describe at the level of algebraic invariants

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

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

liberation of orthogonal lie groups abstract we show that under suitable assumptions we have a one to one correspondence between classical groups and free quantum groups in the compact orthogonal case we classify the groups under correspondence with the result that there are exactly 6 of them o n s n h n b n s n b n we investigate the representation theory aspects of the correspondence with the result that for o n s n h n b n this is compatible with the bercovici pata bijection finally we discuss some more general classification problems in the compact orthogonal case notably with the construction of a new quantum group

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

quantum spheres and projective spaces as graph algebras the c algebras of continuous functions on quantum spheres quantum real projective spaces and quantum complex projective spaces are realized as cuntz krieger algebras corresponding to suitable directed graphs structural results about these quantum spaces especially about their ideals and k theory are then derived from the general theory of graph algebras it is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle respectively

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

the baum connes conjecture for free orthogonal quantum groups we prove an analogue of the baum connes conjecture for free orthogonal quantum groups more precisely we show that these quantum groups have a element and that 1 it follows that free orthogonal quantum groups are k amenable we compute explicitly their k theory and deduce in the unimodular case that the corresponding reduced c algebras do not contain nontrivial idempotents our approach is based on the reformulation of the baum connes conjecture by meyer and nest using the language of triangulated categories an important ingredient is the theory of monoidal equivalence of compact quantum groups developed by bichon de rijdt and vaes this allows us to study the problem in terms of the quantum group suq 2 the crucial part of the argument is a detailed analysis of the equivariant kasparov theory of the standard podle

on the structure of quantum automorphism groups we compute the k theory of quantum automorphism groups of finite dimensional c algebras in the sense of wang the results show in particular that the c algebras of functions on the quantum permutation groups s n are pairwise non isomorphic for different values of n along the way we discuss some general facts regarding torsion in discrete quantum groups in fact the duals of quantum automorphism groups are the most basic examples of discrete quantum groups exhibiting genuine quantum torsion phenomena

null space pursuit an operator based approach to adaptive signal separation the operator based signal separation approach uses an adaptive operator to separate a signal into additive subcomponents the approach can be formulated as an optimization problem whose optimal solution can be derived analytically however the following issues must still be resolved estimating the robustness of the operator s parameters and the lagrangian multipliers and determining how much of the information in the null space of the operator should be retained in the residual signal to address these problems we propose a novel optimization formula for operator based signal separation and show that the parameters of the problem can be estimated adaptively we demonstrate the effectiveness of the proposed method by processing several signals including real life signals

ergodic coactions with large multiplicity and monoidal equivalence of quantum groups we construct new examples of ergodic coactions of compact quantum groups in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter these examples are obtained using a bijective correspondence between certain ergodic coactions on c algebras and unitary fiber functors on the representation category of a compact quantum group we classify these unitary fiber functors on the universal orthogonal and unitary quantum groups the associated c algebras and von neumann algebras can be defined by generators and relations but are not yet well understood

a kalman filtering approach to short time fourier analysis the problem of estimating time varying harmonic components of a signal measured in noise is considered the approach used is via state estimation two methods are proposed one involving pole placement of a state observer the other using quadratic optimization techniques the result is the development of a new class of filters akin to recursive frequency sampling filters for inclusion in a parallel bank to produce sliding harmonic estimates kalman filtering theory is applied to effect the good performance in noise and the class of filters is parameterized by the design tradeoff between noise rejection and convergence rate these filters can be seen as generalizing the dft

an algebraic framework for group duality abstract a hopf algebra is a pair a whereais an associative algebra with identity and a homomorphism formatoa asatisfying certain conditions if we drop the assumption thatahas an identity and if we allow to have values in the so called multiplier algebram a a we get a natural extension of the notion of a hopf algebra we call this a multiplier hopf algebra the motivating example is the algebra of complex functions with finite support on a group with the comultiplication defined as dual to the product in the group also for these multiplier hopf algebras there is a natural notion of left and right invariance for linear functionals called integrals in hopf algebra theory we show that if such invariant functionals exist they are unique up to a scalar and faithful for a regular multiplier hopf algebra a i e with invertible antipode with invariant functionals we construct in a canonical way the dual it is again a regular multiplier hopf algebra with invariant functionals it is also shown that the dual of is canonically isomorphic with the original multiplier hopf algebra a it is possible to generalize many aspects of abstract harmonic analysis here one can define the fourier transform one can prove plancherel s formula because any finite dimensional hopf algebra is a regular multiplier hopf algebra and has invariant functionals our duality theorem applies to all finite dimensional hopf algebras then it coincides with the usual duality for such hopf algebras but our category of multiplier hopf algebras also includes in a certain way the discrete quantum groups and the compact quantum groups our duality includes the duality between discrete quantum groups and compact quantum groups in particular it includes the duality between compact abelian groups and discrete abelian groups one of the nice features of our theory is that we have an extension of this duality to the non abelian case but within one category this is shown in the last section of our paper where we introduce the algebras of compact type and the algebras of discrete type we prove that also these are dual to each other we treat an example that is sufficiently general to illustrate most of the different features of our theory it is also possible to construct the quantum double of drinfel d within this category this provides a still wider class of examples so we obtain many more than just the compact and discrete quantum within this setting

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

performance of pll based optical oppm communication systems the power spectral density psd of a direct detected optical signal with overlapping pulse position modulation oppm scheme is derived it is demonstrated that this spectrum contains a strong periodic component at the signal symbol frequency thereby enabling a simple pll device to provide joint symbol and slot synchronization the variance of the timing error for a linearized pll synchronizer is shown to be mainly dominated by and is inversely proportional to the product of the pll closed loop bandwidth and symbol duration of the oppm signal the performance of a shot noise limited pll based optical oppm communication system is then assessed in terms of the overall system symbol error rate

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

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

de finetti theorems for easy quantum groups we study sequences of noncommutative random variables which are invariant under quantum transformations coming from an orthogonal quantum group satisfying the easiness condition axiomatized in our previous paper for 10 easy quantum groups we obtain de finetti type theorems characterizing the joint distribution of any infinite quantum invariant sequence in particular we give a new and unified proof of the classical results of de finetti and freedman for the easy groups sn on which is based on the combinatorial theory of cumulants we also recover the free de finetti theorem of kostler and speicher and the characterization of operator valued free semicircular families due to curran we consider also finite sequences and prove an approximation result in the spirit of diaconis and freedman