numerical stability of circular hilbert transform and its application to signal decomposition abstract in this paper we propose a novel method of computing hilbert transform based on the mechanical quadrature method experiments show that the method outperforms the library function hilbert in matlab when the values of functions being handled are very large or approach to infinity that is a problem we have to deal with when we compute for instance outer functions as an application we use the method to obtain the unwinding series of signals which is a positive frequency decomposition of signals and is dependent of extraction of outer functions involving computation of hilbert transform the experimental results show better stability then we give the transient time frequency distribution of the unwinding series of signals finally experiments of noisy signals are given and the results show that the introduced method can well resist some disturbance

a group theoretic consequence of the donald flanigan conjecture abstract the donald flanigan conjecture asserts that for any finite group g and prime p dividing its order g the group algebra f pg can be deformed into a semisimple and hence rigid algebra we show that this implies that there is some element g g whose centralizer cg g has a normal subgroup of index p the method is to observe that the donald flanigan deformation must be a jump whence from the deformation theory h1 f pg f pg 0 using a standard result linking hochschild and group cohomology one sees that some h1 cg g f p must be non zero giving the result our corollary to the d f conjecture has recently been verified by fleischmann janiszczak and lempken using the classification of finite simple groups

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

pointed brauer trees abstract in this paper we establish a one to one correspondence between brauer trees with an additional structure that we call pointing and equivalence classes of tilting complexes of the corresponding brauer star algebra which are of a special combinatorial nature under the correspondence the identification of the indecomposable summands of the tilting complex with edges of the brauer tree is completely natural the procedure gives an algorithm for producing large numbers of distinct tilting complexes for the same brauer tree

value iteration algorithm for mean field games abstract in the literature existence of mean field equilibria has been established for discrete time mean field games under both the discounted cost and the average cost optimality criteria in this paper we provide a value iteration algorithm to compute stationary mean field equilibrium for both the discounted cost and the average cost criteria whose existence proved previously we establish that the value iteration algorithm converges to the fixed point of a mean field equilibrium operator then using this fixed point we construct a stationary mean field equilibrium in our value iteration algorithm we use q functions instead of value functions

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

estimating group delay and phase delay via discrete time analytic cross correlation starting with two finite n point real valued discrete time signals frequency domain algorithm procedures are provided for estimating the group delay and phase delay between the signals these delays are extracted from the complex valued discrete time analytic cross correlation sequence computed using the two signals special adjustments of the cross correlation transform end points are shown to be necessary in order to generate a proper analytic cross correlation sequence two cases are considered for delay estimation 1 to sample interval resolution and 2 to subsample interval resolution by interpolation

on the variation of interaural time differences with frequency interaural time difference itd is a major cue to sound localization in humans and animals for a given subject and position in space itd depends on frequency this variation is analyzed here using a head related transfer functions hrtfs database collected from the literature and comprising human hrtfs from 130 subjects and animal hrtfs from six specimens of different species for humans the itd is found to vary with frequency in a way that shows consistent differences with respect to a spherical head model maximal itd values were found to be about 800 s in low frequencies and 600 s in high frequencies the itd variation with frequency up to 200 s for some positions occurs within the frequency range where itd is used to judge the lateral position of a sound source in addition itd varies substantially within the bandwidth of a single auditory filter leading to systematic differences between envelope and fine structure itds because the frequency dependent pattern of itd does not display spherical symmetries it potentially provides cues to elevation and resolves front back confusion the fact that the relation between position and itds strongly depends on the sound s spectrum in turn suggests that humans and animals make use of this relationship for the localization of sounds

rigid monomial algebras in this paper we obtain a classification of rigid monomial algebras with directed quiver by a monomial algebra will be meant a finite dimensional algebra over a field k of the form kq z where kq is the quiver algebra for a finite quiver q and z is a two sided ideal generated by a minimal set of paths z of length at least 2 these algebras have also been called zero relations algebras the problem of classifying rigid finite dimensional algebras was raised by gerstenhaber in 11 in that paper he shows that if the hochschild cohomology in degree two h2 a 4 of a k algebra a vanishes then a is rigid the converse of this statement is false at least if the field is of positive characteristic see 12 however for monomial algebras with directed quiver the converse of gerstenhaber s result holds as a consequence of our classification in 10 p 141 gabriel wrote that it should be one of the main tasks of associative algebra to determine for every n the number of irreducible components of the variety of algebras of dimension n also kraft 17 p 140 points out that the generic structures should be understood moreover the classification of rigid algebras can give lower bounds for the number of irreducible components as for example mazzola did in 18 some of the techniques developed to study the representation theory of finite dimensional algebras have been proven to be useful to treat rigidity problems in particular quivers with relations are at the origin of the definition of combinatorial invariants closely related to the hochschild cohomology homology and cyclic homology see 14 9 4 19 5 7 moreover happel and schaps have highlighted recently the connections between deformation and tilting theories in 15 in this paper we compute the dimension of h2 a a for a kq z a monomial algebra using a new quiver associated to q and z some of the connected components of this parallel quiver are relevant and we call them

a unified approach to closed loop time delay estimation systems two generalized configurations for a closed loop delay estimation system cldes are discussed the indirect correlation ic configuration is compared to the conventional cldes the direct correlation dc configuration it is shown that the baseband equivalents of the two configurations differ only by the input noise however the noise power in the ic configuration is far less than that of the dc configuration using the known procedure for calculation of the variance of the time delay estimator it is shown that the two configurations result in the same variance however this procedure is known to be incorrect since for the direct correlation configuration which is known to have an intrinsic noise that persists even when the input signals are ideal the variance is nonzero for zero input signal to noise ratio snr thus another procedure is suggested for variance calculation that overcomes this problem it is shown using this expression that the variance of the time delay estimator is smaller for the ic configuration provided the input snr is not less than 0 db

interpolation by the fft revisited an experimental investigation a numerical investigation into the accuracy of interpolation by fast fourier transform fft using a sinusoidal test signal is described the method is precisely defined including a previously unnoticed detail which makes a significant difference to the accuracy of the result the experiments show that with no input windowing the accuracy of interpolation is almost independent of sinusoidal wavelength very close to the nyquist limit the resulting rms error is inversely proportional to input sequence length and is very low for sequence lengths likely to be encountered in practice as wavelength passes through the nyquist limit there is a sudden increase in error as is expected from sampling theory if the sequence ends are windowed by short cosine half bells accuracy is further improved at longer wavelengths in comparison small kernal convolution methods such as linear interpolation and cubic convolution perform badly at wavelengths anywhere near the nyquist limit

2d partial unwinding a novel non linear phase decomposition of images this paper aims at proposing a novel 2d non linear phase decomposition of images which performs the image processing tasks better than the traditional fourier transformation linear phase decomposition but further it has additional mathematical properties allowing more effective image analysis including adaptive decomposition components and positive instantaneous phase derivatives 1d unwinding blaschke decomposition has recently been proposed and studied through factorization it expresses arbitrary 1d signal into an infinite linear combination of blaschke products it offers fast converging positive frequency decomposition in the form of rational approximation however in the multi dimensional cases the usual factorization mechanism does not work as a consequence there is no genuine unwinding decomposition for multi dimensions in this paper a 2d partial unwinding decomposition based on algebraic transforms reducing multi dimensions to the 1d case is proposed and analyzed the result shows that the fast convergence offers efficient image reconstruction the tensor type decomposing terms are mutually orthogonal giving rise to 2d positive frequency decomposition the comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the fourier category an application in watermarking is presented to demonstrate its potential in applications

analytic signal generation tips and traps in this correspondence we discuss methods to produce the discrete analytic signal from a discrete real valued signal such an analytic signal is complex and contains only positive frequencies its projection onto the real axis is the same as the original signal our use stems from instantaneous frequency estimation and time frequency signal analysis problems for these problems the negative frequency component of real signals causes unwanted interference the task of designing a filter to produce an approximation to the ideal analytic signal is not as simple as its formulation might suggest our result is that the direct methods of zeroing the negative frequencies or using hilbert transform filters have undesirable defects we present an alternative which is similar to the quadrature filters used in modem designs

on the determination of the position of extrema of sampled correlators the problem of determination of the position of the extremum of a continuous correlator function from its samples if the spectrum of the correlator is not bandlimited is discussed searching for the position of the extremum by fitting a parabola through three samples around that extremum leads to clustering of the estimates around values corresponding with the sampling moments

waveform information from quantum mechanical entropy although the entropy of a given signal type waveform is technically zero it is nonetheless desirable to use entropic measures to quantify the associated information several such prescriptions have been advanced in the literature but none are generally successful here we report that the fourier conjugated total entropy associated with quantum mechanical probabilistic amplitude functions pafs is a meaningful measure of information in non probabilistic real waveforms with either the waveform itself or its normalized analytic representation acting in the role of the paf detailed numerical calculations are presented for both adaptations showing the expected informatic behaviours in a variety of rudimentary scenarios particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals

asymmetric pulse modeling for fri sampling we consider sampling and reconstruction of finite rate of innovation fri signals such as a train of pulses where the pulses have varying degrees of asymmetry we address the problem of asymmetry modeling starting from a given symmetric prototype we show that among the class of unitary operators that are linear and invariant to translation and scale the fractional hilbert frh operator is unique for parametrically modeling pulse asymmetry the frh operator is obtained by a trigonometric interpolation between the standard hilbert and identity operators where the interpolation weights are determined by the degree of asymmetry the frh operators are also steerable which allows for estimation of the asymmetry factors in addition to the delays and amplitudes using the high resolution spectral estimation techniques that are used for solving standard fri problems we also develop the discrete counterpart using discrete frh operators and show that all the desirable properties carry over smoothly to the discrete setting as well we derive closed form expressions for the cramer rao bounds and hammersley chapman robbins bound on the variances of the estimators for continuous and discrete parameters respectively experimental results show that the proposed estimators have variances that meet the lower bounds we demonstrate an application of the proposed discrete frh methodology on real electrocardiogram ecg signals in the presence of noise specifically we show how the asymmetry of qrs complexes in various channels of an ecg signal could be modeled accurately

cross correlation of instantaneous phase increments in pressure flow fluctuations applications to cerebral autoregulation we investigate the relationship between the blood flow velocities bfv in the middle cerebral arteries and beat to beat blood pressure bp recorded from a finger in healthy and post stroke subjects during the quasisteady state after perturbation for four different physiologic conditions supine rest head up tilt hyperventilation and co2 rebreathing in upright position to evaluate whether instantaneous bp changes in the steady state are coupled with instantaneous changes in the bfv we compare dynamical patterns in the instantaneous phases of these signals obtained from the hilbert transform as a function of time we find that in post stroke subjects the instantaneous phase increments of bp and bfv exhibit well pronounced patterns that remain stable in time for all four physiologic conditions while in healthy subjects these patterns are different less pronounced and more variable we propose an approach based on the cross correlation of the instantaneous phase increments to quantify the coupling between bp and bfv signals we find that the maximum correlation strength is different for the two groups and for the different conditions for healthy subjects the amplitude of the cross correlation between the instantaneous phase increments of bp and bfv is small and attenuates within 3 5 heartbeats in contrast for post stroke subjects this amplitude is significantly larger and cross correlations persist up to 20 heartbeats further we show that the instantaneous phase increments of bp and bfv are cross correlated even within a single heartbeat cycle we compare the results of our approach with three complementary methods direct bp bfv cross correlation transfer function analysis and phase synchronization analysis our findings provide insight into the mechanism of cerebral vascular control in healthy subjects suggesting that this control mechanism may involve rapid adjustments within a heartbeat of the cerebral vessels so that bfv remains steady in response to changes in peripheral bp

computing the discrete time analytic signal via fft starting with a real valued n point discrete time signal frequency domain algorithms are provided for computing 1 the complex valued standard n point discrete time analytic signal of the same sample rate 2 the complex valued decimated n 2 point discrete time analytic signal of half the original sample rate and 3 the complex valued interpolated nm point discrete time analytic signal of m times the original sample rate special adjustment of the transform end points are shown to be necessary in order to generate proper discrete time analytic signals

time delay estimation by combining efficient algorithms and generalized cross correlation methods this paper analyzes the performance of the two efficient algorithms presented by stein and cabot for time delay of arrival estimation tde between two signals it is shown that these estimators are unbiased and explicit expressions for the tde mean square error mse are presented it is also shown how to improve the performance of these algorithms by combining them with generalized cross correlation gcc methods in the analysis we only assume stationary signals which are not necessarily gaussian the first algorithm stein is indirect and uses the symmetry of the cross correlation function between the two signals it is shown here that the tde mse depends on the unknown delay the performance of this algorithm can be improved by combining it with the gcc method and the pertinent tde mse expressions are presented the second algorithm cabot is based on finding the zero of the cross correlation function between one signal and the hilbert transform of the other signal here too the pertinent tde mse expressions are presented this algorithm is also combined with the gcc method and the optimal weight function for which the tde mse expression coincides with the cramer rao lower bound is found

a note on the application of the hilbert transform to time delay estimation it is shown that the hilbert transform may be employed to convert the maximum finding task of a delay estimator to one of finding a zero crossing the basic theory of the technique is shown and a few applications are described its primary application is in servo tracking and servo velocity measurement systems which employ correlation techniques a review of prior work in this field is given

mean field games convergence of a finite difference method mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to infty have been recently introduced by lasry and lions numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works here convergence theorems for these methods are proved under various assumptions on the coupling operator

mean field games numerical methods for the planning problem mean field games describe the asymptotic behavior of differential games in which the number of players tends to infty here we focus on the optimal planning problem i e the problem in which the positions of a very large number of identical rational agents with a common value function evolve from a given initial spatial density to a desired target density at the final horizon time we propose a finite difference semi implicit scheme for the optimal planning problem which has an optimal control formulation the latter leads to existence and uniqueness of the discrete control problem we also study a penalized version of the semi implicit scheme for solving the resulting system of equations we propose a strategy based on newton iterations we describe some numerical experiments

moments of click evoked otoacoustic emissions in human ears group delay and spread instantaneous frequency and bandwidth a click evoked otoacoustic emission ceoae has group delay and spread as first and second order temporal moments varying over frequency and instantaneous frequency and bandwidth as first and second order spectral moments varying over time energy smoothed moments were calculated from a ceoae database over 0 5 15 khz bandwidth and 0 25 20 ms duration group delay and instantaneous frequency were calculated without phase unwrapping using a coherence synchrony measure that accurately classified ears with hearing loss ceoae moment measurements were repeatable in individual ears group delays were similar for ceoaes and stimulus frequency oaes group spread is a frequency specific measure of temporal spread in an emission related to spatial spread across tonotopic generation sites along the cochlea in normal ears group delay and spread increased with frequency and decreased with level a direct measure of cochlear tuning above 4 khz was analyzed using instantaneous frequency and bandwidth synchronized spontaneous oaes were present in most ears below 4 khz and confounded interpretation of moments in ears with sensorineural hearing loss group delay and spread varied with audiometric classification and amount of hearing loss group delay differed between older males and females ceoae moments reveal clinically relevant information on cochlear tuning in ears with normal and impaired hearing

fft pruning applied to time domain interpolation and peak localization the efficiency of the fast fourier transform may be increased by removing operations on input values which are zero and on output values which are not required this is applied to interpolation of complex and real valued time domain functions for real functions analytic signal concepts may be used to get the hilbert transform as a byproduct and applied to the cross correlation function this gives an efficient and accurate method for peak localization

autoregressive modeling of temporal spectral envelopes with finite length discrete trigonometric transforms the theory of autoregressive ar modeling also known as linear prediction has been established by the fourier analysis of infinite discrete time sequences or continuous time signals nevertheless for various finite length discrete trigonometric transforms dtts including the discrete cosine and sine transforms of different types the theory is not well established several dtts have been used in current audio coding and the ar modeling method can be applied to reduce coding artifacts or exploit data redundancies this paper systematically develops the ar modeling fundamentals of temporal and spectral envelopes for the sixteen members of the dtts this paper first considers the ar modeling in the generalized discrete fourier transforms gdfts then we derive the modeling to all the dtts by introducing the analytic transforms which convert the real valued vectors into complex valued ones through the process we build the compact matrix representations for the ar modeling of the dtts in both time domain and dtt domain these compact forms also illustrate that the ar modeling for the envelopes can be performed through the hilbert envelope and the power envelope these compact forms can be used to develop new coding technologies or examine the possible defects in the existing ar modeling methods for dtts we apply the forms to analyze the current temporal noise shaping tns tool in mpeg 2 4 advanced audio coding aac

mean field games numerical methods mean field type models describing the limiting behavior as the number of players tends to infty of stochastic differential game problems have been recently introduced by j m lasry and p l lions c r math acad sci paris 343 2006 pp 619 625 c r math acad sci paris 343 2006 pp 679 684 jpn j math 2 2007 pp 229 260 numerical methods for the approximation of the stationary and evolutive versions of such models are proposed here in particular existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated numerical experiments are carried out

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques