bias correction of two state latent markov process parameter estimates under misclassification a discretely observed two state process may misclassify the state of an unobservable continuous time two state markov process we examine the behaviour of maximum likelihood transition probability estimates as functions of known misclassification probabilities since maximum likelihood estimators are not available in closed form we provide two alternatives for bias adjusted estimation in the case of large samples the asymptotic bias is quantified and estimators are constructed iteratively using transition counts and specified misclassification probabilities for finite samples we provide an approximation based on partial derivatives estimators that are bias adjusted to a first approximation are easily constructed and may serve well when misclassification probabilities are known to be small simulation studies reveal the effect of misclassification on estimation repeated diagnostic testing data illustrate the approaches

beyond time frequency analysis energy densities in one and many dimensions given a unitary operator a representing a physical quantity of interest we employ concepts from group representation theory to define two natural signal energy densities for a the first is invariant to a and proves useful when the effect of a is to be ignored the second is covariant to a and measures the a content of signals we also consider joint densities for multiple operators and in the process provide an alternative interpretation of cohen s see englewood cliffs nj prentice hall 1995 general construction for joint distributions of arbitrary variables

a fast refinement for adaptive gaussian chirplet decomposition the chirp function is one of the most fundamental functions in nature many natural events for example most signals encountered in seismology and the signals in radar systems can be modeled as the superposition of short lived chirp functions hence the chirp based signal representation such as the gaussian chirplet decomposition has been an active research area in the field of signal processing a main challenge of the gaussian chirplet decomposition is that gaussian chirplets do not form an orthogonal basis a promising solution is to employ adaptive type signal decomposition schemes such as the matching pursuit the general underlying theory of the matching pursuit method has been well accepted but the numerical implementation in terms of computational speed and accuracy of the adaptive gaussian chirplet decomposition remains an open research topic we present a fast refinement algorithm to search for optimal gaussian chirplets with a coarse dictionary the resulting adaptive gaussian chirplet decomposition is not only fast but is also more accurate than other known adaptive schemes the effectiveness of the algorithm introduced is demonstrated by numerical simulations

brief paper on robust stability of lti fractional order delay systems of retarded and neutral type this paper deals with the analysis of robust bibo stability of lti fractional order delay systems in the presence of real parametric uncertainties two large classes of these systems namely retarded and neutral types are considered two theorems are given to check the robust bibo stability of these two families of fractional order systems one of these theorems provides necessary and sufficient conditions for the case of retarded type and another one presents only sufficient conditions for the case of neutral type furthermore upper and lower bounds cutoff frequencies are provided for drawing the value sets to illustrate the results two numerical examples are presented

discrete time implementation of the cone kernel time frequency representation subtle differences exist between the continuous time and discrete time formulations of the cone kernel time frequency representation that should be taken into account prior to implementation the article derives the discrete formulation from equivalence in the ambiguity domain yielding a kernel different from that obtained by directly sampling the continuous time kernel yet preserving the important properties of the continuous time representation

robust stability test of a class of linear time invariant interval fractional order system using lyapunov inequality this paper provides a new analytical robust stability checking method of fractional order linear time invariant interval uncertain system this paper continues the authors previous work yangquan chen hyo sung ahn i podlubny robust stability check of fractional order linear time invariant systems with interval uncertainties in proceedings of the ieee conference on mechatronics and automation niagara falls canada july 2005 pp 210 215 where matrix perturbation theory was used for the new robust stability checking lyapunov inequality is utilized for finding the maximum eigenvalue of a hermitian matrix through numerical examples the usefulness and the effectiveness of the newly proposed method are verified

video orbits of the projective group a simple approach to featureless estimation of parameters we present direct featureless methods for estimating the eight parameters of an exact projective homographic coordinate transformation to register pairs of images together with the application of seamlessly combining a plurality of images of the same scene resulting in a single image or new image sequence of greater resolution or spatial extent the approach is exact for two cases of static scenes 1 images taken from the same location of an arbitrary three dimensional 3 d scene with a camera that is free to pan tilt rotate about its optical axis and zoom or 2 images of a flat scene taken from arbitrary locations the featureless projective approach generalizes interframe camera motion estimation methods that have previously used a camera model which lacks the degrees of freedom to exactly characterize such phenomena as camera pan and tilt and or which have relied upon finding points of correspondence between the image frames the featureless projective approach which operates directly on the image pixels is shown to be superior in accuracy and the ability to enhance the resolution the proposed methods work well on image data collected from both good quality and poor quality video under a wide variety of conditions sunny cloudy day night these new fully automatic methods are also shown to be robust to deviations from the assumptions of static scene and no parallax

the uncertainty principle global local or both we address the issue of the relation between local quantities and the uncertainty principle we approach the problem by defining local quantities as conditional standard deviations and we relate these to the uncertainty product appearing in the standard uncertainty principle we show that the uncertainty product for the average local standard deviations is always less than or equal to the standard uncertainty product and that it can be arbitrarily small we apply these results to the short time fourier transform spectrogram to explore the commonly held notion that the uncertainty principle somehow limits local quantities we show that indeed for the spectrogram there is a lower bound on the local uncertainty product of the spectrogram due to the windowing operation of this method this limitation is an inherent property of the spectrogram and is not a property of the signal or a fundamental limit we also examine the local uncertainty product for a large class of time frequency distributions that satisfy the usual uncertainty principle including the wigner distribution the choi williams distribution and many other commonly used distributions we obtain an expression for the local uncertainty product in terms of the signal and show that for these distributions the local uncertainty product is less than that of the spectrogram and can be arbitrarily small extension of our approach to an entropy formulation of the uncertainty principle is also considered

wavelets associated with representations of the affine weyl heisenberg group the affine weyl heisenberg group generated by time and frequency translations and time dilations is considered and some associated resolutions of the identity are derived as a result it will be shown that they can all be obtained from those associated with the affine group and the weyl heisenberg group by frequency translations of the analyzed function and the analyzing and reconstructing wavelets

robust asymptotical stability of fractional order linear systems with structured perturbations this paper considers the robust asymptotical stability problem of fractional order linear systems with structured perturbations which are more general than the investigated fractional order interval systems based on the kronecker product and m analysis necessary and sufficient conditions for the robust asymptotical stability are established by transforming such a problem into checking the nonsingularity of a class of uncertain matrices furthermore the robustness bounds with respect to parametric perturbations to preserve the asymptotical stability are given in terms of the structured singular values finally illustrative examples are given to show the effectiveness of the proposed approach

a four parameter atomic decomposition of chirplets a new four parameter atomic decomposition of chirplets is developed for compact and precise representation of signals with chirp components the four parameter chirplet atom is obtained from the unit gaussian function by successive applications of scaling fractional fourier transform frft and time shift and frequency shift operators the application of the frft operator results in a rotation of the wigner distribution of the gaussian in the time frequency plane by a specified angle the decomposition is realized by using the matching pursuit algorithm for this purpose the four parameter space is discretized to obtain a small but complete subset in the hilbert space a time frequency distribution tfd is developed for clear and readable visualization of the signal components it is observed that the chirplet decomposition and the related tfd provide more compact and precise representation of signal inner structures compared with the commonly used time frequency representations

shear madness new orthonormal bases and frames using chirp functions the proportional bandwidth and constant bandwidth time frequency signal decompositions of the wavelet gabor and wilson orthonormal bases have attracted substantial interest for representing nonstationary signals however these representations are limited in that they are based on rectangular tessellations of the time frequency plane while much effort has gone into methods for designing nice wavelet and window functions for these frameworks little consideration has been given to methods for constructing orthonormal bases employing nonrectangular time frequency tilings the authors take a first step in this direction by deriving two new families of orthonormal bases and frames employing elements that shear or chirp in the time frequency plane in addition to translate and scale the new scale shear fan bases and shift shear chevron bases are obtained by operating on an existing wavelet gabor 1946 or wilson basis set with two special unitary warping transformations in addition to the theoretical benefit of broadening the class of valid time frequency plane tilings these new bases could possibly also be useful for representing certain types of signals such as chirping and dispersed signals

robust stabilization criterion of fractional order controllers for interval fractional order plants the robust stabilization criterion of fractional order controllers for interval fractional order plants is proposed in this study for the interval uncertainties existing in the numerator and denominator of a transfer function with respect to a fractional order plant the vertices of the value set corresponding to the characteristic function are offered by the minkowski sum this algorithm for getting the vertices avoids to calculate the redundant vertices reducing the computational complexity an auxiliary function reflecting the position relationship between the origin and the value set is defined to investigate the robust stability conditions the lower and upper limits of the test frequency interval are offered to check the auxiliary function within a finite frequency supposing that the fractional order controller can stabilize the nominal fractional order plant the stabilization criterion of the closed loop system with interval uncertainties is provided based on the auxiliary function and other two conditions finally three illustrative examples with fractional order controllers are given to validate the effectiveness of this robust stabilization criterion

how independent are multiple independent diagnostic classifications multiple performances of diagnostic tests are commonly employed in clinical practice and epidemiologic research to assess test reliability to increase sensitivity or specificity or to correct for misclassification bias an assumption almost universally made in this context is the assumption of independence of test results conditional on the true value for dichotomous diagnostic tests for example disease present or absent this assumption is usually not tenable however since there is typically a continuum of the traits that underly diagnosis and individuals in the vicinity of the implicit or explicit diagnostic cutpoint such as the threshold of clinical detectibility are more likely to be misclassified than other individuals this paper assesses the magnitude of the resulting correlation of diagnostic errors as a function of the distribution of the underlying trait the magnitude of the measurement error and the diagnostic threshold it is concluded that errors of diagnostic tests can be strongly correlated even if errors in perception of the underlying trait are independent it is illustrated by numerical examples that such positive correlation of diagnostic errors can substantially inflate commonly employed indices of reliability such as the kappa coefficient

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

interference suppression in the wigner distribution using fractional fourier transformation and signal synthesis a novel method for the suppression of cross terms in the time frequency domain is introduced first interference is identified using a fractional fourier transform based technique then auto terms are detected synthesized and subtracted from the original signal the process is repeated until all signal components are extracted finally the wigner distributions of pure auto terms are superimposed to yield a high readability representation

quadratic detectors for energy estimation the estimation of signal energy is an important part of physics and signal processing a commonly used energy estimate in signal processing is instantaneous energy that is defined by the square of the signal magnitude at time t i e

robust stability of fractional order system with general interval uncertainties abstract this paper focuses on the analysis of robust stability of fractional order system with general interval uncertainties the concept of general interval uncertainties means that the interval uncertainties exist both in the coefficients and orders of the fractional order system necessary and sufficient conditions are proposed to check the robust stability of general interval fractional order system according to the proposed stability criterion it is interesting to find that the edge theorem which was initially proposed for integer order system cannot be directly extended to test the stability of fractional order system with general interval uncertainties examples are followed to verify the validity of the proposed method

an algorithm for stabilization of fractional order time delay systems using fractional order pid controllers this technical note presents a solution to the problem of stabilizing a given fractional order system with time delay using fractional order pllambdadmu controllers it is based on determining a set of global stability regions in the kp ki kd space corresponding to the fractional orders lambda and mu in the range of 0 2 and then choosing the biggest global stability region in this set this method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements the algorithm is simple and has reliable result which is illustrated by an example and hence is practically useful in the analysis and design of fractional order control systems

cramer rao bounds for wavelet transform based instantaneous frequency estimates we use an asymptotic integral approximation of a wavelet transform as a model for the estimation of instantaneous frequency if our approach allows the calculation of the cramer rao bound for the if variance at each time directly without the need for explicit phase parameterization this is in contrast to other approaches where the cramer rao bounds rely on a preliminary decomposition of the if with respect to a usually polynomial basis attention is confined to the morlet wavelet transform of single component signals corrupted with additive gaussian noise potential computationally and statistically efficient if extraction algorithms suggested by the analysis are also discussed

using association models to analyse agreement data two examples two examples demonstrate how one can use association models to analyse agreement data the first example concerns intra rater variability in the classification of sputum cytology slides and the second deals with variability associated with the reporting of passive smoking histories the paper emphasizes models in which one estimates category scores from the data that is models that are not in the log linear family of models such models have use in assessment of category distinguishability and provide insights not easily obtained with log linear models

lv s distribution principle implementation properties and performance this paper proposes a novel representation known as lv s distribution lvd of linear frequency modulated lfm signals it has been well known that a monocomponent lfm signal can be uniquely determined by two important physical quantities centroid frequency and chirp rate cfcr the basic reason for expressing a lfm signal in the cfcr domain is that these two quantities may not be apparent in the time or time frequency tf domain the goal of the lvd is to naturally and accurately represent a mono or multicomponent lfm in the cfcr domain the proposed lvd is simple and only requires a two dimensional 2 d fourier transform of a parametric scaled symmetric instantaneous autocorrelation function it can be easily implemented by using the complex multiplications and fast fourier transforms fft based on the scaling principle the computational complexity properties detection performance and representation errors are analyzed for this new distribution comparisons with three other popular methods radon wigner transform rwt radon ambiguity transform rat and fractional fourier transform frft are performed with several numerical examples our distribution is demonstrated to be a cfcr representation that is computed without using any searching operation the main significance of the lvd is to convert a 1 d lfm into a 2 d single frequency signal one of the most important applications of the lvd is to generate a new tf representation called inverse lvd ilvd and a new ambiguity function called lv s ambiguity function lvaf both of which may break through the tradeoff between resolution and cross terms

time scale energy distributions a general class extending wavelet transforms the theory of a new general class of signal energy representations depending on time and scale is developed time scale analysis has been introduced recently as a powerful tool through linear representations called continuous wavelet transforms wts a concept for which an exhaustive bilinear generalization is given although time scale is presented as an alternative method to time frequency strong links relating the two are emphasized thus combining both descriptions into a unified perspective the authors provide a full characterization of the new class the result is expressed as an affine smoothing of the wigner ville distribution on which interesting properties may be further imposed through proper choices of the smoothing function parameters not only do specific choices allow recovery of known definitions but they also provide via separable smoothing a continuous transition from wigner ville to either spectrograms or scalograms squared modulus of the wt this property makes time scale representations a very flexible tool for nonstationary signal analysis

on the analytic wavelet transform an exact and general expression for the analytic wavelet transform of a real valued signal is constructed resolving the time dependent effects of nonnegligible amplitude and frequency modulation the analytic signal is first locally represented as a modulated oscillation demodulated by its own instantaneous frequency and then taylor expanded at each point in time the terms in this expansion called the instantaneous modulation functions are time varying functions which quantify at increasingly higher orders the local departures of the signal from a uniform sinusoidal oscillation closed form expressions for these functions are found in terms of bell polynomials and derivatives of the signal s instantaneous frequency and bandwidth the analytic wavelet transform is shown to depend upon the interaction between the signal s instantaneous modulation functions and frequency domain derivatives of the wavelet inducing a hierarchy of departures of the transform away from a perfect representation of the signal the form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal in which case our expressions simplify considerably one may then quantify the time varying bias associated with signal estimation via wavelet ridge analysis and choose wavelets to minimize this bias

minimum variance time frequency distribution kernels when dealing with random processes reduced spectrum estimate variance becomes an important property that augments the list of desirable time frequency t f distribution properties in this correspondence we derive the t f kernel that satisfies the t f constraints and provides the minimum variance for the power spectrum estimate for gaussian white noise processes

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

fast matching pursuit with a multiscale dictionary of gaussian chirps we introduce a modified matching pursuit algorithm called fast ridge pursuit to approximate n dimensional signals with m gaussian chirps at a computational cost o mn instead of the expected o mn sup 2 logn at each iteration of the pursuit the best gabor atom is first selected and then its scale and chirp rate are locally optimized so as to get a good chirp atom i e one for which the correlation with the residual is locally maximized a ridge theorem of the gaussian chirp dictionary is proved from which an estimate of the locally optimal scale and chirp is built the procedure is restricted to a sub dictionary of local maxima of the gaussian gabor dictionary to accelerate the pursuit further the efficiency and speed of the method is demonstrated on a sound signal

time width versus frequency band mapping of energy distributions most of the signal processing operations involve some kind of a transformation or approximation of the signal the transform coefficients or the approximation parameters reveal many hidden characteristics of a signal that can be appropriately processed to extract useful information in recent years adaptive time frequency tf transformations have significantly contributed to this area the tf transformation can be classified into two main categories based on 1 signal decomposition approaches and 2 bilinear tf distributions also known as cohen s class tf distributions are nonparametric in nature and mainly used for visualization purposes on the other hand decomposition approaches are parametric in nature and highly suitable for objective feature extraction this paper focuses on a particular tf decomposition approach adaptive tf transformation based on matching pursuit type algorithm using this decomposition approach a novel time width versus frequency band twfb energy mapping is proposed that possesses both parameterization benefits and meaningful visual patterns with favorable properties for pattern recognition this organized mapping of the tf decomposition parameters allows the application of pruning algorithms such as local discriminant bases ldb to identify application specific tf subspaces the identification of these subspaces enables efficient processing of information and reduces the computational effort considerably the visual patterns of the twfb mappings exhibit high potential of becoming a powerful pattern analysis tool the paper covers in detail the formulation of the twfb mapping and some of its properties experiments performed with speech and synthetic signals produced desirable results demonstrating the benefits of twfb for pattern recognition related applications

estimation of operating characteristics for dependent diagnostic tests based on latent markov models we describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test log linear models are adopted for the classification distributions conditional on the latent state where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests a marginal likelihood is constructed by marginalizing over a latent two state markov process specific latent processes we consider include a first order markov model a second order markov model and a time nonhomogeneous markov model although the method is described in full generality adaptations to handle missing data are described model diagnostics are considered based on the bootstrap distribution of conditional residuals the methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement

the weyl correspondence and time frequency analysis describes the weyl correspondence and its properties showing how it gives a window independent definition of time frequency concentration for use in models in signal detection the definition of concentration is justified by showing that it gives reasonable answers in certain intuitive cases the weyl correspondence expresses a linear transformation as a weighted superposition of time frequency shifts of the signal and then authors explain why this is not the same as transforming a signal into the time frequency domain multiplying by a weight in the transform domain and taking the inverse the investigation into time frequency concentration and the weyl correspondence is justified by a new result the authors show that convolving the wigner distribution with a general smoothing function is equivalent to evaluating a weighted sum of spectrograms this is a new interpretation of the process of smoothing the wigner distribution to reduce cross terms it relates smoothing of the wigner distribution to the multiple window technique pioneered by thomson 1982

an echolocation model for the restoration of an acoustic image from a single emission echo bats can form a fine acoustic image of an object using frequency modulated echolocation sound the acoustic image is an impulse response known as a reflected intensity distribution which is composed of amplitude and phase spectra over a range of frequencies however bats detect only the amplitude spectrum due to the low time resolution of their peripheral auditory system and the frequency range of emission is restricted it is therefore necessary to restore the acoustic image from limited information the amplitude spectrum varies with the changes in the configuration of the reflected intensity distribution while the phase spectrum varies with the changes in its configuration and location here by introducing some reasonable constraints a method is proposed for restoring an acoustic image from the echo the configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition the determination of the location requires extracting the amplitude spectra which vary with its location for this purpose the gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used the location is estimated from the temporal changes of the amplitude spectra

the effect of conditional dependence on the evaluation of diagnostic tests the accuracy of a new diagnostic test is often determined by comparison with a reference test which also has unknown error rates maximum likelihood estimation of the error rates of both tests is possible if they are simultaneously applied to two populations with different disease prevalences the estimation procedure assumes that the two tests are independent conditional on a subject s true diagnostic status if the tests are conditionally dependent error rates for both tests can be substantially underestimated estimators for the prevalence rates in the two populations can be positively or negatively biased depending on the relative magnitude of the two conditional covariances and the value of the prevalence parameter

using latent class models to characterize and assess relative error in discrete measurements whenever a definitive standard is not available to mark accuracy in a classification process discrete measurement error can be discussed only in relative terms if strong assumptions concerning the underlying discrete processes can be made latent class models allow one to characterize patterns of agreement disagreement among raters while simultaneously producing consensus estimates of prevalence a hypothetical definitive standard serves as the latent factor the discrete data are treated as incomplete and log linear models can be used to parameterize latent class models and extensions of latent class models data from the radiographic diagnosis of dental caries by five dentists were explored to estimate prevalence assess relative error and examine the validity of several traditional assumptions concerning diagnostic reliability latent class analysis allowed a more detailed description of diagnostic error than provided by commonly used summary statistics

nonparametric detection of fm signals using time frequency ridge energy in many practical applications signals to be detected are unknown nonlinear frequency modulated fm and are corrupted by strong noise the phase histories of signals are assumed to be unknown smooth functions of time and these functions are poorly modeled or unmodeled by a small number of parameters thus the conventional parametric based detection methods are invalid in these cases this paper proposes a nonparametric detection method using the ridge energy of observations the detection process consists of three steps tf ridge detection ridge energy extraction and decision first the directionally smoothed pseudo wigner ville distribution dspwvd is introduced to highlight the instantaneous frequency if points along a special direction on the if curve of a signal from noise further an angular maximal distribution amad is constructed from a set of dspwvds to highlight the entire if curve as a result the tf ridge of an observation can be estimated well from its amad by the maxima position detector second the ridge energy the total energy along the tf ridge on the pseudo wigner ville distribution pwvd is extracted a noisy signal has larger ridge energy than a pure noise does with a large probability because pure noise energy is randomly distributed throughout the tf plane while the signal energy in a noisy signal is concentrated along the estimated tf ridge third the ridge energy of an observation is used as the test statistic to decide whether or not a signal of interest is present in the observation where the decision threshold is determined by a large number of monte carlo simulations using pure noise finally the simulation experiments to two test signals are made to verify the effectiveness of the proposed method

model based analysis of dispersion curves using chirplets time frequency representations like the spectrogram or the scalogram are widely used to characterize dispersive waves the resulting energy distributions however suffer from the uncertainty principle which complicates the allocation of energy to individual propagation modes especially when the dispersion curves of these modes are close to each other in the time frequency domain this research applies the chirplet as a tool to analyze dispersive wave signals based on a dispersion model the chirplet transform a generalization of both the wavelet and the short time fourier transform enables the extraction of components of a signal with a particular instantaneous frequency and group delay an adaptive algorithm identifies frequency regions for which quantitative statements can be made about an individual mode s energy and employs chirplets locally adapted to a dispersion curve model to extract the proportional energy distribution of that single mode from a multimode dispersive wave signal the

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

on the local frequency group shift and cross terms in some multidimensional time frequency distributions a method for multidimensional time frequency analysis presents an analysis of the representation of local frequency and group shift using multidimensional time frequency distributions in the second part of the correspondence the authors extend the analysis to the multicomponent signals and cross terms effects on the basis of that analysis an efficient method derived from the analysis of the multidimensional wigner distribution defined in the frequency domain is proposed this method provides some substantial advantages over the wigner distribution the well known cross terms effects are reduced or completely removed the oversampling of signals is shown to be unnecessary and the computation time can be significantly reduced as well the theory is illustrated by a two dimensional numerical example

optimum smoothing of the wigner ville distribution a compromise is found between the different requirements that we would like to be fulfilled by a time frequency distribution namely positivity and obtention of a distribution close to the dirac one for the unimodular signal s t exp i phi t the fulfillment of the marginal conditions being of less interest in signal theory starting from the usual wigner ville distribution we define an optimum smoothing by minimizing the width of the different functions approximating the desired dirac distribution the smoothing is obtained by a convolution through a double gaussian of width t and such that t 1 2 two possibilities appear in the first one we do not introduce any correlation between t and in the convolution kernel and obtain a simple result in the second one extrapolating the frequency variation and still using a gaussian we obtain a better result although the smoothing process becomes more complex these results to be physically meaningful impose inequalities on the successive derivatives of which are equivalent to those used for the obtention of the classical limit for the corresponding quantum problem

modeling of multivariate monotone disease processes in the presence of misclassification motivated by a longitudinal oral health study the signal tandmobiel study we propose a multivariate binary inhomogeneous markov model in which unobserved correlated response variables are subject to an unconstrained misclassification process and have a monotone behavior the multivariate baseline distributions and markov transition matrices of the unobserved processes are defined as a function of covariates through the specification of compatible full conditional distributions distinct misclassification models are discussed in all cases the possibility that different examiners were involved in the scoring of the responses of a given subject across time is taken into account a full bayesian implementation of the model is described and its performance is evaluated using simulated data we provide theoretical and empirical evidence that the parameters can be estimated without any external information about the misclassification parameters finally the analyses of the motivating study are presented a

comparison of variance estimation approaches in a two state markov model for longitudinal data with misclassification we examine the behaviour of the variance covariance parameter estimates in an alternating binary markov model with misclassification transition probabilities specify the state transitions for a process that is not directly observable the state of an observable process which may not correctly classify the state of the unobservable process is obtained at discrete time points misclassification probabilities capture the two types of classification errors variance components of the estimated transition parameters are calculated with three estimation procedures observed information jackknife and bootstrap techniques simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation the three approaches generally provide similar variance estimates for large samples and moderate misclassification in these situations the resampling methods are reasonable alternatives when programming partial derivatives is not appealing with smaller chains or higher misclassification probabilities the bootstrap method appears to be the best choice

a generalized wavelet transform for fourier analysis the multiresolution fourier transform and its application to image and audio signal analysis a wavelet transform specifically designed for fourier analysis at multiple scales is described and shown to be capable of providing a local representation which is particularly well suited to segmentation problems it is shown that by an appropriate choice of analysis window and sampling intervals it is possible to obtain a fourier representation which can be computed efficiently and overcomes the limitations of using a fixed scale of window yet by virtue of its symmetry properties allows simple estimation of such fundamental signal parameters as instantaneous frequency and onset time position the transform is applied to the segmentation of both image and audio signals demonstrating its power to deal with signal events which are localized in either time space or frequency feature extraction and segmentation are performed through the introduction of a class of multiresolution markov models whose parameters represent the signal events underlying the segmentation

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

likelihood inference for a class of latent markov models under linear hypotheses on the transition probabilities summary for a class of latent markov models for discrete variables having a longitudinal structure we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process for the maximum likelihood estimation of a latent markov model under hypotheses of this type we outline an em algorithm that is based on well known recursions in the hidden markov literature we also show that under certain assumptions the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent markov model against a less stringent linear hypothesis on the transition probabilities of the same model is of x2 type as a particular case we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent markov version which may be used to test the hypothesis of absence of transition between latent states the approach is illustrated through a series of simulations and two applications the first of which is based on educational testing data that have been collected within the national assessment of educational progress 1996 and the second on data concerning the use of marijuana which have been collected within the national youth survey 19761980

marginal methods for correlated binary data with misclassified responses misclassification is a longstanding concern in medical research although there has been much research concerning error prone covariates relatively little work has been directed to problems with response variables subject to error in this paper we focus on misclassification in clustered or longitudinal outcomes we propose marginal analysis methods to handle binary responses which are subject to misclassification the proposed methods have several appealing features including simultaneous inference for both marginal mean and association parameters and they can handle misclassified responses for a number of practical scenarios such as the case with a validation subsample or replicates furthermore the proposed methods are robust to model misspecification in a sense that no full distributional assumptions are required numerical studies demonstrate satisfactory performance of the proposed methods under a variety of settings copyright 2011 oxford university press

an analytic wavelet transform with a flexible time frequency covering we develop a rational dilation wavelet transform for which the dilation factor the q factor and the redundancy can be easily specified the introduced transform contains hilbert transform pairs of atoms therefore it is also suitable for oscillatory signal processing the transform may be modified to obtain a tight chirplet frame for discrete time signals a fast implementation that makes use of an equivalent filter bank makes the transform suitable for long signals examples on natural signals are provided to demonstrate the utility of the transform

brief analysis of fractional delay systems of retarded and neutral type this paper analyses several properties linked to the robust control of fractional differential systems with delays the bibo stability of both retarded and neutral fractional delay systems is related to the location of their poles in the particular case of retarded systems we give some properties of the poles of the system and the singular values of its hankel operator

a sampling theorem for fractional wavelet transform with error estimates as a generalization of the ordinary wavelet transform the fractional wavelet transform frwt is a very promising tool for signal analysis and processing many of its fundamental properties are already known however little attention has been paid to its sampling theory in this paper we first introduce the concept of multiresolution analysis associated with the frwt and then propose a sampling theorem for signals in frwt based multiresolution subspaces the necessary and sufficient condition for the sampling theorem is derived moreover sampling errors due to truncation and aliasing are discussed the validity of the theoretical derivations is demonstrated via simulations

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

stability and performance analysis for positive fractional order systems with time varying delays this paper addresses the stability and l infty gain analysis problem for continuous time positive fractional order delay systems with incommensurate orders between zero and one a necessary and sufficient condition is firstly given to characterize the positivity of continuous time fractional order systems with bounded time varying delays moreover by exploiting the monotonic and asymptotic property of the constant delay system by virtue of the positivity and comparing the trajectory of the time varying delay system with that of the constant delay system it is proved that the asymptotic stability of positive fractional order systems is not sensitive to the magnitude of delays in addition it is shown that the l infty gain of a positive fractional order system is independent of the magnitude of delays and fully determined by the system matrices finally a numerical example is given to show the validity of the theoretical results

the chirplet transform physical considerations we consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis we propose the use of quadratic chirp functions which we will call q chirps for short giving rise to a parameter space that includes both the time frequency plane and the time scale plane as 2 d subspaces the parameter space contains a time frequency scale volume and thus encompasses both the short time fourier transform as a slice along the time and frequency axes and the wavelet transform as a slice along the time and scale axes in addition to time frequency and scale there are two other coordinate axes within this transform space shear in time obtained through convolution with a q chirp and shear in frequency obtained through multiplication by a q chirp signals in this multidimensional space can be obtained by a new transform which we call the q chirplet transform or simply the chirplet transform the proposed chirplets are generalizations of wavelets related to each other by 2 d affine coordinate transformations translations dilations rotations and shears in the time frequency plane as opposed to wavelets which are related to each other by 1 d affine coordinate transformations translations and dilations in the time domain only

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

dispersion based short time fourier transform applied to dispersive wave analysis although time frequency analysis is effective for characterizing dispersive wave signals the time frequency tilings of most conventional analysis methods do not take into account dispersion phenomena an adaptive time frequency analysis method is introduced whose time frequency tiling is determined with respect to the wave dispersion characteristics in the dispersion based time frequency tiling each time frequency atom is adaptively rotated in the time frequency plane depending on the local wave dispersion although this idea can be useful in various problems its application to the analysis of dispersive wave signals has not been made in this work the adaptive time frequency method was applied to the analysis of dispersive elastic waves measured in waveguide experiments and a theoretical investigation on its time frequency resolution was presented the time frequency resolution of the proposed transform was then compared with that of the standard short time fourier transform to show its effectiveness in dealing with dispersive wave signals in addition to facilitate the adaptive time frequency analysis of experimentally measured signals whose dispersion relations are not known an iterative scheme for determining the relationships was developed the validity of the present approach in dealing with dispersive waves was verified experimentally

correcting for misclassification for a monotone disease process with an application in dental research motivated by a longitudinal oral health study we evaluate the performance of binary markov models in which the response variable is subject to an unconstrained misclassification process and follows a monotone or progressive behavior theoretical and empirical arguments show that the simple version of the model can be used to estimate the prevalence incidences and misclassification parameters without the need of external information and that the incidence estimators associated with the model outperformed approaches previously proposed in the literature we propose an extension of the simple version of the binary markov model to describe the relationship between the covariates and the prevalence and incidence allowing for different classifiers we implemented a bayesian version of the extended model and show that under the settings of our motivating example the parameters can be estimated without any external information finally the analyses of the motivating problem are presented

simultaneously modeling joint and marginal distributions of multivariate categorical responses abstract we discuss model fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses the models are members of a broad class of generalized logit and loglinear models we fit them by improving a maximum likelihood algorithm that uses lagrange s method of undetermined multipliers and a newton raphson iterative scheme we also discuss goodness of fit tests and adjusted residuals and give asymptotic distributions of model parameter estimators for this class of models inferences are equivalent for poisson and multinomial sampling assumptions simultaneous models for joint and marginal distributions may be useful in a variety of applications including studies dealing with longitudinal data multiple indicators in opinion research cross over designs social mobility and inter rater agreement the models are illustrated for one such application using data from a recent general social survey regarding opinions about various types of government s

new approaches for chirplet approximation this correspondence proposes efficient algorithms for approximating complex valued and real valued signals as a weighted sum of multiple chirplet atoms which are characterized by four parameters namely the scale time frequency and chirp rate direct sequential estimation of the parameters of multiple chirplets causes error propagations i e the estimated parameters of the initial chirplets significantly affect the parameter estimation of the subsequent chirplets and may result in large chirplet approximation errors to deal with this problem we further exploit a relaxation relax method for recursive chirplet parameter estimation relax can be used in conjunction with time domain or frequency domain algorithms to improve the parameter estimation accuracy for multiple chirplets unlike previous methods our chirplet approximations require neither any a priori complete dictionary of chirplets nor complicated multidimensional searches to obtain suitable choices of chirplet parameters the effectiveness of the proposed approaches is demonstrated via a number of simulated examples

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

log linear modelling of pairwise interobserver agreement on a categorical scale this article uses log linear models to describe pairwise agreement among several raters who classify a sample on a subjective categorical scale the models describe agreement structure simultaneously for second order marginal tables of a multidimensional cross classification of ratings practical difficulties arise in fitting the models because models refer to pairwise marginal tables of a very large and sparse table a standard analysis that treats the marginal tables as independent yields consistent estimates of model parameters but not of the covariance matrix of the estimates we estimate the covariance matrix using the jackknife we apply the models to describe agreement between evaluations made by seven pathologists of carcinoma in situ of the uterine cervix using a five level ordinal scale previous analyses showed differences among the pathologists in their pairwise levels of agreement but we observe near homogeneity in the dependence structure of their ratings

the scale representation the authors considers scale a physical attribute of a signal and develop its properties he presents an operator which represents scale and study its characteristics and representation this allows one to define the scale transform and the energy scale density spectrum which is an indication of the intensity of scale values in a signal he obtains explicit expressions for the mean scale scale bandwidth instantaneous scale and scale group delay furthermore he derives expressions for mean time mean frequency duration frequency bandwidth in terms of the scale variable the short time transform is defined and used to obtain the conditional value of scale for a given time he shows that as the windows narrows one obtains instantaneous scale convolution and correlation theorems for scale are derived a formulation is devised for studying linear scale invariant systems he derives joint representations of time scale and frequency scale general classes for each are presented using the same methodology as for the time frequency case as special cases the joint distributions of marinovich altes 1978 1986 and bertrand bertrand 1984 are recovered also joint representations of the three quantities time frequency scale are devised a general expression for the local scale autocorrelation function is given uncertainty principles for scale and time and scale and frequency are derived

evolutionary periodogram for nonstationary signals presents a novel estimator for the time dependent spectrum of a nonstationary signal by modeling the signal at any given frequency as having a time varying amplitude accurately represented by an orthonormal basis expansion the authors are able to compute a minimum mean squared error estimate of this time varying amplitude repeating the process over all frequencies they obtain a power distribution as a function of time and frequency that is consistent with the wold cramer evolutionary spectrum based on the model assumptions the authors develop the evolutionary periodogram ep for nonstationary signals an estimator analogous to the periodogram used in the stationary case they also derive the time frequency resolution of the new estimator the approach is free of some of the drawbacks of the bilinear distributions and of the short time fourier transform spectral estimates it is guaranteed to produce nonnegative spectra without the cross term behavior of the bilinear distributions and it does not require windowing of data in the time domain examples illustrating the new estimator are given

wavefield extraction using multi channel chirplet decomposition in acoustical and seismic fields wavefield extraction has always been a crucial issue to solve inverse problem depending on the experimental configuration conventional methods of wavefield decomposition might no longer likely to hold in this paper an original approach is proposed based on a multichannel decomposition of the signal into a weighted sum of elementary functions known as chirplets each chirplet is described by physical parameters and the collection of chirplets makes up a large adaptable dictionary so that a chirplet corresponds unambiguously to one wave component

an echolocation model for range discrimination of multiple closely spaced objects transformation of spectrogram into the reflected intensity distribution using frequency modulated echolocation bats can discriminate the range of objects with an accuracy of less than a millimeter however bats echolocation mechanism is not well understood the delay separation of three or more closely spaced objects can be determined through analysis of the echo spectrum however delay times cannot be properly correlated with objects using only the echo spectrum because the sequence of delay separations cannot be determined without information on temporal changes in the interference pattern of the echoes to illustrate this gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used the delay time for object 1 t1 can be estimated from the echo spectrum around the onset time the delay time for object 2 is obtained by adding t1 to the delay separation between objects 1 and 2 extracted from the first appearance of interference effects further objects can be located in sequence by this same procedure this model can determine delay times for three or more closely spaced objects with an accuracy of about 1 micros when all the objects are located within 30 micros of delay separation this model is applicable for the range discrimination of objects having different reflected intensities and in a noisy environment 0 db signal to noise ratio while the cross correlation method is hard to apply to these problems

general parameterized time frequency transform interest in parameterized time frequency analysis for non stationary signal processing is increasing steadily an important advantage of such analysis is to provide highly concentrated time frequency representation with signal dependent resolution in this paper a general scheme named as general parameterized time frequency transform gptf transform is proposed for carrying out parameterized time frequency analysis the gptf transform is defined by applying generalized kernel based rotation operator and shift operator it provides the availability of a single generalized time frequency transform for applications on signals of different natures furthermore by replacing kernel function it facilitates the implementation of various parameterized time frequency transforms from the same standpoint the desirable properties and the dual definition in the frequency domain of gptf transform are also described in this paper one of the advantages of the gptf transform is that the generalized kernel can be customized to characterize the time frequency signature of non stationary signal as different kernel formulation has bias toward the signal to be analyzed a proper kernel is vital to the gptf thus several potential kernels are provided and discussed in this paper to develop the desired parameterized time frequency transforms in real applications it is desired to identify proper kernel with respect to the considered signal this motivates us to propose an effective method to identify the kernel for the gptf

a constrained weighted least squares approach for time frequency distribution kernel design in most applications of time frequency t f distributions the t f kernel is of finite extent and applied to discrete time signals this paper introduces a matrix based approach for t f distribution kernel design in this new approach the optimum kernel is obtained as the solution of a linearly constrained weighted least squares minimization problem in which the kernel is vectorial and the constraints form a linear subspace similar to fir temporal and spatial constrained least squares ls design methods the passband stopband and transition band of an ideal kernel are first specified the optimum kernel that best approximates the ideal kernel in the ls error sense and simultaneously satisfies the multiple linear constraints is then obtained using closed form expressions this proposed design method embodies a well structured procedure for obtaining fixed and data dependent kernels that are difficult to obtain using other design approaches

coprime factorizations and stability of fractional differential systems we give a frequency domain approach to stabilization for a large class of systems with transfer functions involving fractional powers of s a necessary and sufficient criterion for bibo stability is given and it is shown how to construct coprime factorizations and associated bezout factors in order to parametrize all stabilizing controllers of these systems

wigner based formulation of the chirplet transform using the wigner distribution we derive and analyze a matrix formulation for the chirplet transform a signal analysis tool that generalizes the wavelet and short time fourier transforms the formulation expresses the translations scalings and shears of the chirplet transform in terms of affine matrix transformations on the time frequency plane our approach leads naturally to several new signal transforms which we derive analyze and extend

a numerical algorithm for stability testing of fractional delay systems this paper presents an effective numerical algorithm for testing the bibo stability of fractional delay systems described by fractional order delay differential equations it is based on using cauchy s integral theorem and solving an initial value problem the algorithm has a reliable result which is illustrated by several examples and hence is practically useful in the analysis and design of feedback control for both integer and fractional order systems having time delays

stability of linear time invariant fractional delay systems of retarded type in the space of delay parameters this paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type in the proposed method first by mapping the principal sheet of the riemann surface and a pseudo delay transformation an auxiliary polynomial is generated then this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis the properties of the root path close to these roots are used to identify intervals of delay values in which the system is stable the obtained results are illustrated via some numerical examples

modelling complexity applications of gibbs sampling in medicine summary we review applications of gibbs sampling in medicine involving longitudinal spatial covariate measurement and survival models applications in immunology pharmacology transplantation cancer screening industrial epidemiology and genetic epidemiology are discussed

chirplet approximation of band limited real signals made easy in this paper we present algorithms for approximating real band limited signals by multiple gaussian chirps these algorithms do not rely on matching pursuit ideas they are hierarchical and at each stage the number of terms in a given approximation depends only on the number of positive valued maxima and negative valued minima of a signed amplitude function characterizing part of the signal like the algorithms used in j m greenberg z wang and j li ieee trans signal process 55 2007 pp 734 741 and unlike previous methods our chirplet approximations require neither a complete dictionary of chirps nor complicated multidimensional searches to obtain suitable choices of chirp parameters

conditional inference for predictive agreement we introduce the concept and a measure of predictive agreement tau for two raters classifying items into q categories the measure is based on the linear combination of log odds ratios from 2 x 2 subtables of a q x q cross classification table we show that analysis procedures for this measure and transforms of it can be based on conditional likelihood procedures these procedures are exact which is particularly helpful because of the small tabular cell frequencies which can typically arise with agreement data to illustrate the advantages of the methodology examples of typical agreement data arising from medical studies are considered we demonstrate that the conditional likelihood function portrays the available sample information about tau often more appropriately than the maximum likelihood estimate and an associated standard error we highlight the value of combining information via likelihoods in an example involving 24 2 x 2 tables an example involving three categories is used to illustrate that the methodology for the overall agreement measure can be adapted to examine relative agreement between pairs of categories

technical communique necessary and sufficient stability condition of fractional order interval linear systems this paper establishes a necessary and sufficient stability condition of fractional order interval linear systems it is supposed that the system matrix a is an interval uncertain matrix and fractional commensurate order belongs to email protected email protected 2 using the existence condition of hermitian p p for a complex lyapunov inequality we prove that the fractional order interval linear system is robust stable if and only if there exists hermitian matrix p p such that a certain type of complex lyapunov inequality is satisfied for all vertex matrices the results are directly extended to the robust stability condition of fractional order interval polynomial systems

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

bilinear time frequency representations new insights and properties an analysis of the interference terms of cohen class bilinear time frequency representations tfr of multicomponent signals is presented constraints for achieving new interference properties are derived imposing these interference time and interference frequency concentration constraints on a tfr guarantees that the tfr will be zero everywhere the signal s t is zero and the tfr will contain only those frequencies that occur in the signal thus these new constraints guarantee strong finite support in a tfr when these interference concentration properties are combined with interference attenuation tradeoffs between finite support the marginals and the interference properties are shown to be unavoidable the useful class of product kernels are considered and generalized further to allow tfr with potentially superior interference properties the interference frequency concentration and attenuation properties allow tfr with spectrogram like interference suppression but without the spectrogram s inherent time frequency resolution tradeoff other useful combinations of properties are discussed and analyzed and properties and tradeoffs are illustrated by examples

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

a graphical test for the interval stability of fractional delay systems this paper investigates the bibo bounded input and bounded output interval stability testing of fractional delay systems a problem of justifying the bibo stability of a polytopic family of functions involving fractional order powers as well as exponential powers it proves that the bibo stability of the polytope is governed by the bibo stability of the edges of the polytope and the latter can be tested graphically via frequency response plots the main results generalize some results in the literature

generalized instantaneous parameters and window matching in the time frequency plane the concept of instantaneous parameters which has previously been associated exclusively with 1 d measures like the instantaneous frequency and the group delay are extended to the 2 d time frequency plane such generalized instantaneous parameters are associated with the short time fourier transform they may also be interpreted as local moments of certain time frequency distributions it is shown that these measures enable local signal behavior to be characterized in the time frequency plane for nonstationary deterministic signals the usefulness of the generalized instantaneous parameters is demonstrated in their application to optimal selection of windows for spectrograms this is achieved through window matching in the time frequency plane an algorithm is provided that illustrates the performance of this window matching results based on simulated and real data are presented

implementation of a diffusive differential reassignment method for signal enhancement an application to wolf population counting abstract we investigate the combination of two pde based image processing techniques applied to the image produced by time frequency representations of one dimensional signals such as the spectrogram specifically we consider the energy transport equation associated to the lagrangian coordinates corresponding to the spectrogram differential reassignment proposed by chassandre mottin daubechies auger and flandrin as a spectrogram readability improving method together with the image restoration model proposed by alvarez lions and morel for noise reduction and edge enhancement our aim is to produce a transformation of the spectrogram in which the instantaneous frequency lines are easier to track for using it as an input for a wolves howls counting algorithm after presenting the model derivation we show some analytical properties of it such as the existence of a unique solution and a comparison principle and perform later a discretization to numerically investigate its performance for the cases of synthetic signals and field recorded wolves choruses we finally compare our results with those obtained from well established techniques