multiple correction and continued fraction approximation abstract the main aim of this paper is to further develop a multiple correction method formulated in a previous work 6 as applications we find a kind of hybrid type finite continued fraction approximations in two cases of landau constants and lebesgue constants in addition we refine the previous results of lu 29 and xu and you 48 for the euler mascheroni constant

a globally convergent estimator for n frequencies in this paper we propose a solution to the well known problem of ensuring a simultaneous globally convergent online estimation of the state and the frequencies of a sinusoidal signal composed of n sinusoidal terms we present an estimator which guarantees global boundedness and convergence of both the state estimation and the frequency estimation for all initial conditions and frequency values

improved continued fraction sequence convergent to the somos quadratic recurrence constant abstract in this paper we provide some new continued fraction approximation and inequalities of the somos quadratic recurrence constant using its relation with the generalized euler s constant

group invariant pattern recognition abstract in this paper we develop a group theoretical model for the feature extraction part of pattern recognition systems we argue that the features used should reflect the regularities in the environment in which the system exists we develop first a group theoretical model to describe these regularities and then we show how to construct a feature extraction system that reflects these regularities we show why the so found filter functions often appear as solutions to optimality problems and why they often have some nice properties such as invariance under fourier transformation we will mainly investigate problems connected to the group of rotations in 2 d and 3 d space but we will touch other types of symmetries as well

hybrid observer for global frequency estimation of saturated signals a hybrid observer for the on line global estimation of the frequency and the bias of a saturated sinusoidal signal is proposed robustness of the observer against unknown saturation level is discussed

brief robust adaptive compensation of biased sinusoidal disturbances with unknown frequency asymptotically stable observable linear systems of order n which are not required to be minimum phase and are affected by an additive noisy biased sinusoidal disturbance with unknown bias magnitude phase and frequency are considered the problem of designing an output feedback compensator which regulates the output to zero for any initial condition and for any biased sinusoidal disturbance with no noise is addressed under the assumption that the system parameters are known this problem is solved by a 2n 6 order compensator which generates asymptotically convergent estimates of the biased sinusoidal disturbance and of its parameters including frequency the robustness of the closed loop system with respect to sufficiently small additive unmodelled noise is characterized in terms of input to state stability

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

distortion invariant volterra filters abstract volterra filters are constructed to recognize images independent of changes caused by a linear transformation group e g rotation scaling etc volterra filters are polynomial functions that can model analytic vector functions with arbitrary precision the theory of invariant volterra filters is developed for a general polynomial order however particular emphasis is given to quadratic filters quadratic filters are the lowest order volterra filter that provide a non linear response this suggests a new approach to invariant pattern recognition based upon nearest neighbor classification with respect to an invariant manifold both theoretical and simulation results suggest that quadratic filters can provide invariant pattern recognition with high discrimination and robustness to noise

multiple correction and continued fraction approximation ii the main aim of this paper is to further develop the multiple correction method formulated in our previous works cao et al 2015 cao 2015 as applications we establish a kind of hybrid type finite continued fraction approximations related to bbp type series of the constant and other classical constants such as catalan constant or 2

continued fraction inequalities related to 1 1x x abstract in this paper we provide some new continued fraction inequalities related to 1 1 x x

a globally convergent frequency estimator online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications in this paper the authors provide a solution to the problem of ensuring a globally convergent estimation more specifically they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features 1 all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values 2 the authors obtain a simple tuning procedure for the estimator design parameters which trades off the adaptation tracking capabilities with noise sensitivity ensuring exponential stability of the desired orbit and 3 transient performance is considerably enhanced even for small or large frequencies as witnessed by extensive simulations to reveal some of the stability instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear state dependent time scaling the main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself decomposing the system into a feedback form where the required modifications to ensure stability become apparent even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time varying frequencies preserve local stability in the presence of multiple sinusoids and is robust with respect to noise

asymptotic stability equals exponential stability and iss equals finite energy gain if you twist your eyes in this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables the same is shown for input to state stability and input to state exponential stability and for input to state exponential stability and a nonlinear h estimate

tensor product basis approximations for volterra filters the paper studies approximations for a class of nonlinear filters known as volterra filters although the volterra filter provides a relatively simple and general representation for nonlinear filtering it is often highly overparameterized due to the large number of parameters the utility of the volterra filter is limited the overparameterization problem is addressed in the paper using a tensor product basis approximation tpba in many cases a volterra filter may be well approximated using the tpba with far fewer parameters hence the tpba offers considerable advantages over the original volterra filter in terms of both implementation and estimation complexity furthermore the tpba provides useful insight into the filter response the paper studies the crucial issue of choosing the approximation basis several methods for designing an appropriate approximation basis and error bounds on the resulting mean square output approximation error are derived certain methods are known to be nearly optimal

some new quicker convergences to glaisher kinkelin s and bendersky adamchik s constants in this paper we provide some new sequences to approximate the glaisher kinkelin s constant and bendersky adamchik s constant which are faster than the approximations in literature 1 2

geometric symmetry in the quadratic fisher discriminant operating on image pixels this correspondence examines the design of quadratic fisher discriminants qfds that operate directly on image pixels when image ensembles are taken to comprise all rotated and reflected versions of distinct sample images a procedure based on group theory is devised to identify and discard qfd coefficients made redundant by symmetry for arbitrary sampling lattices this procedure introduces the concept of a degeneracy matrix tensor representations are established for the square lattice point group 8 fold symmetry and hexagonal lattice point group 12 fold symmetry the analysis is largely applicable to the symmetrization of any quadratic filter and generalizes to higher order polynomial volterra filters experiments on square lattice sampled synthetic aperture radar sar imagery verify that symmetrization of qfds can improve their generalization and discrimination ability

on carleman s inequality abstract in this paper the result of p yan and g sun 1999 j math anal appl 240 290 293 is generalized and a conjecture is proposed

quadratic digital filters for image processing a class of nonlinear two dimensional filters is presented a matrix description is developed for such operators and some symmetry conditions are imposed which simplify and render more effective the filter structure a strategy for the design of filters capable of enhancing images having reduced contrast and degraded by noise is proposed

some inequalities involving the constante and an application to carleman s inequality some inequalities involving the constanteare considered a strengthened carleman s inequality is proved

tree structured feature extraction using mutual information one of the most informative measures for feature extraction fe is mutual information mi in terms of mi the optimal fe creates new features that jointly have the largest dependency on the target class however obtaining an accurate estimate of a high dimensional mi as well as optimizing with respect to it is not always easy especially when only small training sets are available in this paper we propose an efficient tree based method for fe in which at each step a new feature is created by selecting and linearly combining two features such that the mi between the new feature and the class is maximized both the selection of the features to be combined and the estimation of the coefficients of the linear transform rely on estimating 2 d mis the estimation of the latter is computationally very efficient and robust the effectiveness of our method is evaluated on several real world data sets the results show that the classification accuracy obtained by the proposed method is higher than that achieved by other fe methods

asymptotic rejection of finite frequency modes of general periodic disturbances in output feedback nonlinear systems this paper deals with asymptotic rejection of individual frequency modes in nonlinear systems under general periodic disturbances an iterative observer design is proposed for disturbance estimation and it is shown that the proposed observer design successfully extracts individual frequency modes from general periodic disturbances the proposed iterative observer design is then applied to asymptotic rejection of nonlinear systems under general periodic disturbances

penalized discriminant analysis fisher s linear discriminant analysis lda is a popular data analytic tool for studying the relationship between a set of predictors and a categorical response in this paper we describe a penalized version of lda it is designed for situations in which there are many highly correlated predictors such as those obtained by discretizing a function or the grey scale values of the pixels in a series of images in cases such as these it is natural efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients both for improved prediction performance and interpretability we cast the classification problem into a regression framework via optimal scoring using this our proposal facilitates the use of any penalized regression technique in the classification setting the technique is illustrated with examples in speech recognition and handwritten character recognition

adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency abstract two algorithms are presented for the rejection of sinusoidal disturbances with unknown frequency the first is an indirect algorithm where the frequency of the disturbance is estimated and the estimate is used in another adaptive algorithm that adjusts the magnitude and phase of the input needed to cancel the effect of the disturbance a direct algorithm that uses the concept of a phase locked loop is also presented in which frequency estimation and disturbance cancellation are performed simultaneously approximate analyses are presented for both schemes and the results are found useful for the selection of the design parameters simulations are given which demonstrate the validity of the analytical results and the ability of the algorithms to reject sinusoidal disturbances with unknown frequency the indirect algorithm is found to have a larger capture region for the parameter estimates whereas the direct algorithm has superior convergence properties locally about the optimum parameter estimates

semi global multi frequency estimation in the presence of deadzone and saturation a hybrid observer to estimate the frequencies of a signal composed of a finite number of sinusoids and measured through saturation and deadzone nonlinearities is proposed the observer design exploits the immersion and invariance technique combined with a cl assic high gain approach yielding semi global exponential convergence to zero of the estimation errors simulation results are provided to illustrate the effectiveness of the observer

an improved lattice based adaptive iir notch filter a novel lattice based adaptive infinite impulse response iir notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth the internal structure is based on planar rotators ensuring reliable numerical behaviour and high processing rates in cordic environments a simple update law allows a simpler implementation than previously proposed designs rather than minimizing an output error cost function the algorithm is designed to achieve a stable associated differential equation resulting in a globally convergent unbiased frequency estimator in the single sinusoid case independent of the notch filter bandwidth using a second order structure in the multiple sinusoid case unbiased estimation of one of the input frequencies is achieved by thinning the notch bandwidth the tracking behavior is superior to conventional output error designs and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures

global frequency estimation using adaptive identifiers online estimation of the frequencies of a signal which is the sum of n sinusoidals with unknown amplitudes frequencies and phases is made through yet another well known and simple system theoretical tool adaptive identifiers convergence of the proposed estimator is proved the new frequency estimator is of 3n order as compared to the order 5n 1 resulting from marino tomei observers results are demonstrated via simulation

global estimation of n unknown frequencies given a signal which is available for measurements and consists of the sum of a bias and n sinusoids with unknown amplitudes frequencies and phases a dynamic algorithm is designed to recover online the unknown values of the frequencies for any initial condition and any value of frequencies amplitudes and phases