a nonlinear optimum detection problem i theory an approximate log likelihood ratio for detecting a deterministic signal in linear and nonlinear gaussian noise is derived the new aspect of this detection problem is the inclusion of a nonlinear form of gaussian noise and a certain interaction between the signal and the linear noise such as modulation of the signal by the noise the derived log likelihood ratio consists of a modified version of the classical correlation detector and a new processor where the latter is an order of magnitude smaller than the former in the absence of the signal noise interaction the modification consists of subtracting the estimate of the nonlinear noise from the input to the correlation detector the nonlinear processor is a quadratic correlation processor where the correlation is not against the transformed signal but against the difference of two estimates of the nonlinear noise under the two hypotheses signal presence and signal absence presence of the signal noise interaction introduces further modification and complication on both processors

signal detection in nearly gaussian skewed noise the problem of detecting a constant signal in nearly gaussian skewed noise is studied in this paper sensitivity of both the linear detector and the sign detector are examined it is shown that the performance of the linear detector deteriorates when the noise distribution becomes skewed on the other hand the sign detector appears to be less sensitive to the noise skewness furthermore a modification of the linear detector is proposed this modified scheme when the noise skewness measure is small will behave almost like the linear detector in gaussian noise

chaos synchronization of different chaotic systems subjected to input nonlinearity abstract in this paper a unified mathematical expression describing a class of synchronization systems is presented for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied based on lyapunov stability theory a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the lyapunov sense in spite of the input nonlinearity this technique is applied to achieve chaos synchronization of three pairs of different chaotic systems lorenz chen chen liu and liu lorenz in drive response structure the numerical simulation results demonstrate the validity and feasibility of the proposed controller

robust matched filters the problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered two general aspects of this problem are treated first maximin robust designs are characterized for a general hilbert space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty these results are seen to generalize earlier results for specific matched filtering problems the second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion channel distortion is modeled by considering an unknown received signal which may differ in l 2 norm from the transmitted or nominal signal by no more than a fixed amount the effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion general expressions are developed for the determination of the robust filter and its performance and numerical results are presented for the case of baseband detection in gauss markov noise

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

regular problem for solutions of a retarded semilinear differential nonlocal equation abstract this paper deals with the regularity and existence of solutions of a retarded semilinear differential equation with nonlocal condition by using the fundamental solution in the case where the principal operators are unbounded operators

a new approach for secure communication using constrained hyperchaotic systems a new constrained hyperchaotic system is presented a secure communication scheme using the generated chaotic signals is proposed the crls estimator for nonlinear systems is used for chaos synchronization the crls estimator and the convergence of its nonlinear update phase are analyzed simulation results demonstrate the proposed secure scheme effectiveness in this paper a new technique is developed for a typical secure communication scheme in this approach we introduce the concept of constrained hyperchaotic systems to encrypt the carrier of the data signal to be transmitted at the transmitter end two different chaotic oscillators are coupled constrained and used as a new hyperchaotic system one of the outputs of the constrained hyperchaotic system is used as a carrier for the encrypted data then the outputs of the system including the modulated carrier are encrypted using a set of pre defined encryption rules at the receiving end and after decrypting the received outputs the discrete time constrained regularized least square crls estimator is used to reconstruct the constrained hyperchaotic signals and hence retrieve the transmitted data simulation results are presented to illustrate the capability of the crls estimator in reconstructing the states of the constrained hyperchaotic system moreover the proposed secure communication scheme is applied to transmit discrete images for which the quality of the transmission process is measured by the bit error rate ber

on minimax robustness a general approach and applications the minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary the existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications in particular it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust the efficacy of the methods proposed for a general game is tested in the problems of matched filtering wiener filtering quadratic detection and output energy filtering in which uncertainties in their respective signal and noise models are assumed to exist these problems are analyzed in a common hilbert space framework and they serve to point out the advantages and limitations of the proposed techniques

chaotic sliding mode controllers for uncertain time delay chaotic systems with input nonlinearity this paper presents a novel robust chaotic controller for stabilizing uncertain time delay chaotic systems with input nonlinearity based on dynamic output sliding mode control smc lyapunov theory and linear matrix inequality lmi technique the stability of overall uncertain time delay chaotic system with input nonlinearity under the proposed control scheme is guaranteed without the state predictor the selection of sliding surface and the design of control law are two important issues which have been addressed a priori knowledge of upper bounds of uncertainties is not required furthermore the proposed scheme ensures robustness against input nonlinearity time delays nonlinear real valued functions parameter uncertainties and disturbances simultaneously finally simulation results demonstrate the validity of the proposed control methodology

sequential cfar detectors using a dead zone limiter the performances of some proposed sequential constant false alarm rate cfar detectors are evaluated the observations are passed through a dead zone limiter the output of which is 1 0 or 1 depending on whether the input is less than c between c and c or greater than c where c is a constant the test statistic is the sum of the outputs the test is performed on a reduced set of data those with absolute value larger than c with the test statistic being the sum of the signs of the reduced set of data both constant and linear boundaries are considered numerical results show a significant reduction of the average number of observations needed to achieve the same false alarm and detection probabilities as compared to a fixed sample size cfar detector using the same kind of test statistic

signal interception in non gaussian noise the interception of weak signals in nongaussian noise is discussed the spectral correlation property exhibited by all cyclostationary signals is exploited to synthesize multi cycle and single cycle detectors which assure a superior tolerance as compared to radiometric techniques to one of the most challenging problems in interception namely accommodating unknown and changing noise level and interference activity the proposed detectors perform a maximum likelihood estimate of the noise level and use the estimate to form the detection statistic to obtain some analytical information about the performance of the multi cycle and single cycle detectors the deflection which is a useful measure of the output signal to noise ratio especially appropriate for weak signal snr interception has been evaluated the receiver operating characteristics carried out via computer simulation confirm the superiority of the proposed cycle detector with respect to the traditional radiometer

module phase synchronization in complex dynamic system the concept of module phase synchronization was proposed the chaos synchronization between drive system and response system was achieved in module space and phase space respectively module phase synchronization different from the evolutions in real space there is no pseudorandom behavior in phase space when module phase synchronization achieve all the phases of complex state variables switched between two fixed values which are determined by initial values of drive system and the modules varied within a bounded field the theoretical analysis and the simulations were also given

non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity abstract the problem of non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity is investigated by using sliding mode control a novel control law is established such that the sliding surface in the state estimation space can be reached in a finite time and chattering reduction is obtained a sufficient condition for passivity and asymptotic stability of the combined system is derived via linear matrix inequality lmi finally a simulation example is presented to show the validity and advantages of the proposed method

detection in multivariate non gaussian noise the applications of multivariate edgeworth series and higher order statistics to the discrete time detection of a known constant signal in multivariate non gaussian noise are considered a technique to derive suboptimum detectors from the neyman pearson optimum and locally optimum detectors is described a numerical algorithm based on knowledge of the noise cumulants is presented in order to analyze the finite sample size performance of the suboptimum detectors as an example the performance of the detectors as compared with the linear detector in multivariate gaussian gaussian mixture noise is presented via receiver operating characteristic curves numerical results indicate that the suboptimum detectors when exploiting knowledge of the dependence structure of the noise can have very good performance with respect to the linear detector

optimal and robust memoryless discrimination from dependent observations discrimination is considered between two possible sources based on dependent observations of their output the discrimination problem is modeled by means of a general binary hypothesis test the main emphasis being on situations that cannot be modeled as signals in additive noise the observations are modeled as stationary m dependent or rho mixing processes the structure of the discriminator is such that the observations are passed through a memoryless nonlinearity summed up to form a test statistic which is then compared to a threshold only fixed sample size tests are considered four different performance measures which resemble the signal to noise ratios encountered in the signal in additive noise problems are derived under different problem formulations the optimal nonlinearities for each of the performance measures are derived as solutions to various integral equations for three of the four performance measures the authors have successfully obtained robust nonlinearities for uncertainty in the marginal and the joint probability density functions of the observations computer simulation results that demonstrate the advantage of using these nonlinearities over the i i d nonlinearity under the probability of error criterion are presented

a new hyperchaotic system from the lu system and its control this paper presents a 4d new hyperchaotic system which is constructed by a linear controller to a 3d lu system some complex dynamical behaviors such as hopf bifurcation chaos and hyperchaos of the simple 4d autonomous system are investigated and analyzed the corresponding hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories lyapunove exponents bifurcation path analysis of power spectrum and poincare projections furthermore the design is illustrated with both simulations and experiments finally the control problem of a new hyperchaotic system is investigated using negative feedback control ordinary feedback control dislocated feedback control and speed feedback control are used to suppress hyperchaos to an unstable equilibrium numerical simulations are presented to demonstrate the effectiveness of the proposed controllers

optimal probability of error thresholds and performance for two versions of the sign detector expressions are obtained for specifying the optimal error probability minimum p sub e thresholds lambda sub 01 and lambda sub 02 for the traditional and modified sign detectors respectively these thresholds are shown to depend on the parameters p p sub 1 and m where m is the number of observations z sub i used in the test statistic p sub 1 p h sub 1 is the prior probability for hypothesis h sub 1 that signal s sub 1 is present and 1 p sub 1 p h sub 0 corresponds to the hypothesis h sub 0 that signal s sub 0 is present and p pr z sub i or 0 mod h sub 1 with s sub 0 0 for the traditional sign detector and p pr z sub i or lambda mod h sub 1 pr z sub i

chaos synchronization of a new hyperchaotic system abstract in this paper two kinds of synchronization schemes for a new hyperchaotic system are presented firstly on the basis of stability criterion of linear system synchronization is achieved with the help of the active control theory secondly a nonlinear controller is designed according to lyapunov stability theory to assure that synchronization can be achieved furthermore an adaptive control approach for synchronization of uncertain hyperchaotic systems is proposed finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods

chaos synchronization and parameter identification for gyroscope system synchronization of chaos for a two degree of freedom heavy symmetric gyroscope system are studied in this paper because of the nonlinear terms of the system the system exhibits both regular and chaotic motions by lyapunov stability theory with control terms by adaptive control and by random optimization method the synchronization of two identical systems and tracking of the parameter of the systems are studied

complex linear quadratic systems for detection and array processing linear quadratic lq filters for detection and estimation are widely used in the real case we investigate their extension in the complex case which introduces various new questions in particular we calculate the optimum lq array receiver in a non gaussian environment by using the deflection criterion and evaluate some of its performance

stability property and essential spectrum of linear retarded functional differential equations in this work we shall study stability and stabilization of a class of retarded functional differential equations in banach spaces we present sufficient and necessary sometimes conditions for weak asymptotic and exponential stability properties it is shown that retarded growth bounds are totally determined by retarded non isolated spectra isolated eigenvalues with infinite algebraic multiplicity and spectral bounds stabilization problem via compact perturbations a topic which is practically useful in the context of control theory of dynamical systems is considered as well

expansions of the likelihood ratio and applications the likelihood ratio receiver although optimal is oftentimes difficult to realize to overcome this difficulty suboptimal approximations have been studied in the past one of the simplest approaches is to expand the likelihood ratio and truncate this expansion under the weak signal assumption in this paper we first study the relations between the taylor expansion and the volterra expansion under a weak signal assumption we emphasize the links between the taylor expansion with respect to the snr and the detection criteria on one hand and with robustness on the other in particular using two criteria derived from deflection we show that the minimax robust filter is the matched filter finally an application to underwater signal detection is studied showing that the degradation resulting from the use of the locally optimal receiver is small

robust stability ofc0 semigroups and an application to stability of delay equations abstract let a be a closed linear operator on a complex banach space x and let a be a fixed element of the resolvent set of a let u and y be banach spaces and let d l u x and e l x y be bounded linear operators we define r a d e by formula and prove that formula we give two applications of this result the first is an exact formula for the so called stability radius of the generator of a c 0 semigroup of linear operators on a hilbert space it is derived from a precise result about robustness under perturbations of uniform boundedness in the right half plane of the resolvent of an arbitrary semigroup generator the second application gives sufficient conditions on the norm of the operators b j l x such that the classical solutions of the delay equation formula are exponentially stable in l p h 0 x

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

optimal control of linear retarded systems in banach spaces this paper deals with standard optimal control problems namely the fixed time integral convex cost problem and the time optimal control problem for linear retarded systems in banach spaces for the basis of optimal control theory the fundamental solution is constructed and a variation of constant formula of mild solutions is established after the controlled system description and the formulation of optimal control problems are given the retarded adjoint system is introduced for the integral convex cost problem two existence theorems of optimal controls and necessary conditions of optimality are given these conditions are precisely characterized by the solution of retarded adjoint system the pointwise maximum principle for time varying control domain is derived from the optimality conditions the bang bang principle is also established for the terminal value cost problem under some regularity condition of the adjoint system for the time optimal control problem to a target set an existence theorem is shown in the case where the target set has interior the maximum principle and the bang bang principle are established for the time optimal control finally a convergence theorem of time optimal controls to a point target set is given this paper also contains illustrative examples which give technologically important control problems

linear quadratic optimal control of hereditary differential systems infinite dimensional riccati equations and numerical approximations recent theory of infinite dimensional riccati equations is applied to the linear quadratic optimal control problem for hereditary differential systems and it is shown that for most such problems the operator solutions of the riccati equations are of trace class i e nuclear with special attention to trace norm convergence an abstract approximation theory is developed and applied to a particular approximation scheme numerical examples are given problems on both finite and infinite time intervals are studied for both the hereditary system and the approximating systems in the infinite time problem characteristic equations are derived for the closed loop eigenvalues and formulas for the corresponding eigenvectors are given

a reduced complexity quadratic structure for the detection of stochastic signals quadratic detection of discrete time stochastic signals in additive stationary gaussian noise is considered a banded quadratic detector structure is introduced to reduce the multiplicative complexity and data storage requirements of the optimum full quadratic detector and the optimization of this reduced complexity structure is studied the issue of performance versus complexity is explored for the specific problems of detecting wide sense markov and triangularly correlated signals in white noise with the conclusion that performance of the reduced complexity detector can be very close to optimum if an adequate quadratic form bandwidth is chosen

adaptive stabilization of uncertain unified chaotic systems with nonlinear input abstract this paper addresses the problem of adaptive stabilization of uncertain unified chaotic systems with nonlinear input in the sector form a novel representation of nonlinear input function that is a linear input with bounded time varying coefficient is firstly established then an adaptive control scheme is proposed based on the new nonlinear input model by using barbalat s lemma the asymptotic stability of the closed loop system is proved in spite of system uncertainties external disturbance and input nonlinearity one of the advantages of the proposed design method is that the prior knowledge on the plant parameter the bound parameters of the uncertainties and the slope parameters inside the sector nonlinearity is not required finally numerical simulations are performed to verify the analytical results

feedback stabilization of linear retarded systems in banach spaces feedback stabilizability is studied for linear retarded systems in banach spaces under the assumptions that the control is finite dimensional and the corresponding instantaneous free system generates a compact semigroup the rank condition for exponential stabilizability is established based on the stabilizability result due to bhat and wonham the condition is expressed in terms of eigenvectors and controllers and the equivalent spectral mode controllability and observability conditions are given an application is given to a class of parabolic partial functional differential equations with mixed boundary conditions

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

global synchronization of chaotic systems via linear balanced feedback control global synchronization of two identical chaotic systems by the linear balanced feedback control and the gerschgorin theorem is studied in this paper linear feedback control method based on lyapunov stability theory and extreme approach is introduced to design controller to synchronize two identical chaotic systems two techniques are applied to four scroll chaotic systems for determining the balanced feedback gains a numerical example is given to illuminate the design procedure and advantage of the results derived

detection of weak signals in non gaussian noise a locally optimum detector structure is derived for the detection of weak signals in non gaussian environments optimum performance is obtained by employing a zero memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise gaussian the asymptotic detection performance of the locally optimum detector under non gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in gaussian noise numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest

linear quadratic noise smoothing filters for quantum limited images we consider the use of nonlinear estimators for the noise smoothing of images obtained under quantum limited imaging conditions a volterra expansion is investigated from which a set of linear quadratic filters is derived using higher order statistics the filters are applicable for single frame and multiple frames of a single scene imaged under low light levels

optimal linear quadratic systems for detection and estimation the problem of linear quadratic systems for detection has long been solved by assuming the deflection criterion and gaussian noise it is shown here that the gaussian assumption can be removed and a complete solution is presented for an arbitrary probability distribution with finite fourth order moments the optimal solution can always be obtained by solving a linear system of equations some properties of the optimal systems are developed for particular examples of nongaussian noise it is shown that there is a strong relationship between linear quadratic optimal detection and optimal estimation which extends results known for the purely linear case

lipschitzian semigroups and abstract functional differential equations abstract the paper is devoted to studying an abstract functional differential equation by a nonlinear semigroup approach we first prove in details the equivalence of the well posedness of an abstract functional differential equation and an associated abstract cauchy problem in the sense of strong solutions secondly a sufficient condition is derived for well posedness of the abstract functional differential equation thirdly we present principles of linearized stability for the abstract functional differential equation finally the results obtained are applied to a reaction diffusion equation with delays

the maximum principle for relaxed hereditary differential systems with function space end condition this paper contains a proof of the global pointwise maximum principle for relaxed hereditary differential systems with general function space end condition first a multiplier theorem establishes the existence of lagrange multipliers l 0 l where to l 0 in mathbb r and l is in the dual of the sobolev space w n infty r 0 then l can be identified with an element of w n infty r 0 provided that the optimal trajectory satisfies a certain regularity condition this yields two equivalent forms of the maximum principle using the results on regular reachability obtained in a companion paper the maximum principle is shown to be in a certain sense generically valid

pragmatical adaptive chaos control from a new double van der pol system to a new double duffing system a new pragmatical adaptive control method for different chaotic systems is proposed traditional chaos control is limited to decrease chaos of one chaotic system this method enlarges the effective scope of chaos control we can control a chaotic system e g a new chaotic double van der pol system to a given chaotic or regular system e g a new chaotic double duffing system or to a damped simple harmonic system by a pragmatical theorem of asymptotical stability based on an assumption of equal probability of initial point an adaptive control law is derived such that it can be proved strictly that the common zero solution of error dynamics and of parameter dynamics is asymptotically stable numerical simulations are given to show the effectiveness of the proposed scheme

asymptotic expansions and rate of convergence in signal detection the number of samples required for signal detection is considered as a function of the error probabilities this problem is treated in the context of detecting a constant signal in additive independent and identically distributed noise detectors that base their decisions on the comparison with a threshold of accumulated nonlinearly transformed observations are treated asymptotic expressions are derived for the relationship between sample size and error probabilities for this model in two situations that in which the nonlinearity has a partially absolutely continuous output distribution and that in which it has a lattice output distribution traditional analyses of such problems have involved only the lowest order terms of such relationships i e central limit theorem results leading to performance indices such as the pitman asymptotic relative efficiency are such indices are known to be of limited accuracy in predicting performance for more moderate sample sizes here the behavior of sample size as a function of error probabilities is considered in more detail leading to more accurate indices of relative efficiencies for such detection problems several specific examples are examined in detail and numerical results are included to illustrate the significantly improved performance estimation afforded thereby for even small sample sizes

adaptive control and synchronization of a modified chua s circuit system this study addresses the adaptive control and synchronization of the modified chua s circuit system with unknown system parameters adaptive control law is applied to suppress chaos to one of the three steady states adaptive control law is applied to achieve synchronization of two identical modified chua s circuit systems routh hurwitz criteria and lyapunov direct method are used to study the asymptotic stability of the steady states numerical simulations are included to show the effectiveness of the proposed control method

threshold detection in narrow band non gaussian noise the middleton class a narrow band non gaussian noise model 9 12 is examined it is shown that this noise model which is known to fit closely a variety of non gaussian noises can itself be closely approximated by a computationally much simpler noise model it is then shown by numerical examples that for the problem of locally optimum detection the simplest form of this approximation yields nearly optimal asymptotic performance the performance of other simple suboptimal threshold detectors in class a noise is also examined finally a useful relationship between the class a model and the e mixture model is developed

approximate analysis of the convergence of relative efficiency to are for known signal detection the limitations of the asymptotic relative efficiency are in predicting finite sample size detector performance have been noted in several previous studies it has been observed that the finite sample size relative efficiency re may converge very slowly to its asymptotic limit in addition in some cases the re approaches the are from below while in other cases the re either starts above or overshoots the are and approaches it from above results indicate that both of these effects can be predicted for a useful class of detectors for known signals in additive noise the prediction formula is developed for the generalized correlation detector structure the result is then used to analyze some specific detectors among these are the sign detector the dead zone detector the soft limiter and the noise blanker calculations and simulations giving the relative efficiency as a function of sample size have been used to verify predictions

adaptive variable structure control for chaos suppression of unified chaotic systems this paper investigates the chaos suppression problem for a class of unified chaotic systems subject to uncertainties and control input with dead zone nonlinearity using the variable structure control technique a robust adaptive control law is established to suppress chaos in a class of unified chaotic systems even with unknown uncertainties and dead zone nonlinearity in input in particular a switching surface is newly proposed to simplify the task of ensuring the stability of the closed loop system in the sliding mode numerical results validate the effectiveness of the proposed adaptive control scheme

geometrical properties of optimal volterra filters for signal detection linear quadratic filters are a special example of volterra filters that are limited to the second order it is shown that all the results recently published which are valid in the linear quadratic case can be extended with the appropriate notations to volterra filters of arbitrary order particularly the optimum volterra filter giving the maximum of the deflection for detecting a signal in noise is wholly calculated in addition several geometrical properties of optimal volterra filters are investigated by introducing appropriate scalar products in particular the concept of space orthogonal to the signal and the noise alone reference nar property are introduced allowing a decomposition of the optimal filter that exhibits a relation between detection and estimation extensions to the infinite case and relations with the likelihood ratio are also investigated

application of the volterra functional expansion in the detection of nonlinear functions of gaussian processes detection of a memoryless nonlinear functional of a gaussian process in additive gaussian white noise is considered the volterra functional expansion for the likelihood ratio and two examples of calculating the kernels are presented it is shown that kernels up to third order can be obtained for a hard limited gaussian process and for the absolute value of a gaussian process for the case of hard limiting the kernels are nonlinear functions of the autocorrelation of the gaussian process for the absolute value case the kernels are nonlinear functions of the kernel derived for the linear problem a monte carlo simulation of receiver performance is presented for the case of detection of the absolute value of a first order butterworth process in additive gaussian white noise the suboptimal detector is obtained by truncating the log likelihood ratio to second order

comment on anomalous behavior of receiver output snr as a predictor of signal detection performance exemplified for quadratic receivers and incoherent fading gaussian channels by gardner w a a previously published derivation of an optimal quadratic receiver with respect to a generalized signal to noise ratio is corrected and a different performance measure is proposed for which a general analytical solution exists

a fast algorithm for general volterra filtering volterra filters are a classical instrument for nonlinear channels and systems modeling noise and echo cancellation signal estimation and detection and various other applications as is well known the computational weight of volterra filters exponentially grows with the nonlinearity degree this work presents a contribution to the efficient computation of volterra filters with generic order nonlinearity found in many telecommunication applications our technique rests on the interpretation of the mth order one dimensional volterra filters in terms of m dimensional linear convolution and it adopts a multidimensional fast convolution scheme this makes the method applicable to any m interestingly enough fast convolution based on the standard multidimensional fast fourier transform md fft in the case of volterra filters is outperformed by direct computation our method is efficient due to the use of a special md fft which can exploit the symmetries of the signals entering the computation of volterra filters and which makes it superior to direct computation the points of interests of the results presented are both the generality and the fact that they show that the well known nonlinearity multidimensionality tradeoff of volterra filters can have computational implications

pointwise completeness and degeneracy of functional differential equations in banach spaces i general time delays abstract a general theory for pointwise completeness and degeneracy of functional differential equations in infinite dimensional spaces is presented for the basis of the theory a fundamental solution and a retarded resolvent are introduced and the fact that the laplace transform of the fundamental solution is the retarded resolvent is proved the concepts of exact and approximate pointwise completeness are defined by the attainable sets of all possible mild solutions of the equations and are investigated in the framework of linear operator theory a necessary and sufficient condition and a negative result for exact pointwise completeness are given the degenerate space is defined by the orthogonal complement of the attainable set and various characterizations of the space in terms of fundamental solution and or coefficient operators are established with some examples interesting characterizations of the full degenerate set in terms of retarded resolvent and generalized eigenfunctions which extend the well known finite dimensional degeneracy conditions are also established

two mode indirect adaptive control approach for the synchronization of uncertain chaotic systems by the use of a hierarchical interval type 2 fuzzy neural network two mode adaptive controllers have two phases of operation a learning phase and an operation phase this paper presents a two mode indirect adaptive control approach for the synchronization of chaotic systems using a hierarchical interval type 2 fuzzy neural network ht2fnn its contribution to the existing literature is the adaptation laws derived for the parameters of the membership functions based on lyapunov stability analysis since in hierarchical case each t2fnn has only two inputs the computing of the derivatives is much simpler than the case in classical interval type 2 fnn moreover a novel approach is presented for the compensation of the approximation error the tuning of the parameters of the membership functions mf and the use of an interval type 2 fnn ensures that the estimation error is very small so that it can be negligible furthermore the number of mf required is seen to be less than that needed with type 1 fuzzy sets the simulation results confirm the efficacy of the proposed scheme in the synchronization of a uncertain nonidentical chaotic systems

semigroups and linear partial differential equations with delay abstract we prove the equivalence of the well posedness of a partial differential equation with delay and an associated abstract cauchy problem this is used to derive sufficient conditions for well posedness exponential stability and norm continuity of the solutions applications to a reaction diffusion equation with delay are given

optimal linear detectors for additive noise channels in an attempt to gain insight into the design of linear detectors for additive white noise channels discrete time case we describe several procedures both optimal and suboptimal using the wiener representation for nonlinear systems we derive an ad hoc suboptimal design procedure exact designs are found when the noise amplitude s probability distribution is stable and when the noise is laplacian considering all the linear detectors thus derived no general form for the optimal linear detector s unit sample response becomes apparent performance analyses and simulations indicate substantial performance losses occur when linear detectors are used instead of optimal likelihood ratio ones

detection of lines and boundaries in speckle images application to medical ultrasound describes an approach to boundary detection in ultrasound speckle based on an image enhancement technique the enhancement algorithm works by filtering the image with sticks short line segments which are varied in orientation to achieve the maximum projected value at each point in this paper we present three significant extensions to improve the performance of the basic method first we investigate the effect of varying the size and shape of the sticks we show that these variations affect the performance of the algorithm in very fundamental ways for example by making it more or less sensitive to thinner or more tightly curving boundaries second we present a means of improving the performance of this technique by estimating the distribution function of the orientation of the line passing through each point finally we show that images can be stained for easier visual interpretation by applying to each pixel a false color whose hue is related to the orientation of the most prominent line segment at that point examples are given to illustrate the performance of the different settings on a single image