wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

the complexity of mean payoff games on graphs abstract we study the complexity of finding the values and optimal strategies of mean payoff games on graphs a family of perfect information games introduced by ehrenfeucht and mycielski and considered by gurvich karzanov and khachiyan we describe a pseudo polynomial time algorithm for the solution of such games the decision problem for which is in np conp finally we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by condon these games are also known to be in np conp but no polynomial or pseudo polynomial time algorithm is known for them

the scattering of sound by two semi infinite parallel staggered plates ii evaluation of the velocity potential for an incident plane wave and an incident duct mode in a recent paper abrahams wickham showed how to exactly solve the diffraction problem for two parallel semi infinite plates that are arranged to form a duct the edges of the plates are misaligned so that the geometry is asymmetric with respect to the central line of the duct in this paper we examine in detail the effect of this asymmetry on the field radiated from the duct when a fundamental travelling mode is excited within it and the scattered field when a plane wave is excited at infinity to evaluate the field in either case it is first necessary to solve the integral equations derived in our paper here we show how this is effected using the expansion theorem also enunciated in that paper this solution is then used to calculate a number of physically interesting quantities such as the variation of the energy capture by the duct when irradiated by an incident plane wave as the stagger is increased and the asymmetric radiation pattern from an incident duct mode the numerical computations are checked using an energy balance argument and finally a simple heuristic approximation is given for the scattering problem that in many situations accurately reproduces the essential physical characteristics of the solution

modular strategies for recursive game graphs many problems in formal verification and program analysis can be formalized as computing winning strategies for two player games on graphs in this paper we focus on solving games in recursive game graphs which can model the control flow in sequential programs with recursive procedure calls while such games can be viewed as the pushdown games studied in the literature the natural notion of winning in our framework requires the strategies to be modular with only local memory that is resolution of choices within a module does not depend on the context in which the module is invoked but only on the history within the current invocation of the module while reachability in global pushdown games is known to be exptime complete we show reachability in modular games to be np complete we present a fixed point computation algorithm for solving modular games such that in the worst case the number of iterations is exponential in the total number of returned values from the modules if the strategy within a module does not depend on the global history but can remember the history of the past invocations of this module that is if memory is local but persistent we show that reachability becomes undecidable

formally reasoning about quality in recent years there has been a growing need and interest in formally reasoning about the quality of software and hardware systems as opposed to traditional verification in which one considers the question of whether a system satisfies a given specification or not reasoning about quality addresses the question of how well the system satisfies the specification we distinguish between two approaches to specifying quality the first propositional quality extends the specification formalism with propositional quality operators which prioritize and weight different satisfaction possibilities the second temporal quality refines the eventually operators of the specification formalism with discounting operators whose semantics takes into an account the delay incurred in their satisfaction in this article we introduce two quantitative extensions of linear temporal logic ltl one by propositional quality operators and one by discounting operators in both logics the satisfaction value of a specification is a number in 0 1 which describes the quality of the satisfaction we demonstrate the usefulness of both extensions and study the decidability and complexity of the decision and search problems for them as well as for extensions of ltl that combine both types of operators

frame theory based analysis and design of oversampled filter banks direct computational method this paper studies the frames corresponding to oversampled filter banks fbs for this class of fb frames we present a state space parameterization of perfect reconstruction fb frames and explicit and numerically efficient formulas to compute the tightest frame bounds to obtain the dual fb frame and to construct a tight paraunitary fb frame from a given untight nonparaunitary fb frame the derivation uses well developed techniques from modern control theory which results in the unified formulas for generic infinite impulse response iir and finite impulse response fir fbs these formulas involve only algebraic manipulations of real matrices and can be computed efficiently reliably and exactly without the approximation required in the existing methods for generic fbs the results provide a unified framework for frame theory based analysis and systematic design of oversampled filter banks

identification of hammerstein systems with quantized observations this work is concerned with identification of hammerstein systems whose outputs are measured by quantized sensors the system consists of a memoryless nonlinearity that is polynomial and possibly noninvertible followed by a linear subsystem the parameters of linear and nonlinear parts are unknown but have known orders input design identification algorithms and their essential properties are presented under the assumptions that the distribution function of the noise is known and the quantization thresholds are known the concept of strongly scaled full rank signals is introduced to capture the essential conditions under which the hammerstein system can be identified with set valued observations under strongly scaled full rank conditions a strongly convergent algorithm is constructed asymptotic consistency and efficiency of the algorithm are investigated

recursive markov chains stochastic grammars and monotone systems of nonlinear equations we define recursive markov chains rmcs a class of finitely presented denumerable markov chains and we study algorithms for their analysis informally an rmc consists of a collection of finite state markov chains with the ability to invoke each other in a potentially recursive manner rmcs offer a natural abstract model for probabilistic programs with procedures they generalize in a precise sense a number of well studied stochastic models including stochastic context free grammars scfg and multi type branching processes mt bp we focus on algorithms for reachability and termination analysis for rmcs what is the probability that an rmc started from a given state reaches another target state or that it terminatesq these probabilities are in general irrational and they arise as least fixed point solutions to certain monotone systems of nonlinear equations associated with rmcs we address both the qualitative problem of determining whether the probabilities are 0 1 or in between and the quantitative problems of comparing the probabilities with a given bound or approximating them to desired precision we show that all these problems can be solved in pspace using a decision procedure for the existential theory of reals we provide a more practical algorithm based on a decomposed version of multi variate newton s method and prove that it always converges monotonically to the desired probabilities we show this method applies more generally to any monotone polynomial system we obtain polynomial time algorithms for various special subclasses of rmcs among these for scfgs and mt bps equivalently for 1 exit rmcs the qualitative problem can be solved in p time for linearly recursive rmcs the probabilities are rational and can be computed exactly in p time we show that our pspace upper bounds cannot be substantially improved without a breakthrough on long standing open problems the square root sum problem and an arithmetic circuit decision problem that captures p time on the unit cost rational arithmetic ram model we show that these problems reduce to the qualitative problem and to the approximation problem to within any nontrivial error for termination probabilities of general rmcs and to the quantitative decision problem for termination extinction of scfgs mt bps

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

asymptotically efficient parameter estimation using quantized output observations this paper studies identification of systems in which only quantized output observations are available an identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations strong convergence of the algorithm is first derived the algorithm is then extended to a scenario of system identification with communication constraints in which the sensor output is transmitted through a noisy communication channel and observed after transmission the main results of this paper demonstrate that these algorithms achieve the cramer rao lower bounds asymptotically and hence are asymptotically efficient algorithms furthermore under some mild regularity conditions these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large these results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank

the complexity of mean payoff pushdown games two player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems in this work we consider solving recursive game graphs or pushdown game graphs that model the control flow of sequential programs with recursion while pushdown games have been studied before with qualitative objectives such as reachability and regular objectives in this work we study for the first time such games with the most well studied quantitative objective the mean payoff objective in pushdown games two types of strategies are relevant 1 global strategies which depend on the entire global history and 2 modular strategies which have only local memory and thus do not depend on the context of invocation but rather only on the history of the current invocation of the module our main results are as follows 1 one player pushdown games with mean payoff objectives under global strategies are decidable in polynomial time 2 two player pushdown games with mean payoff objectives under global strategies are undecidable 3 one player pushdown games with mean payoff objectives under modular strategies are np hard 4 two player pushdown games with mean payoff objectives under modular strategies can be solved in np i e both one player and two player pushdown games with mean payoff objectives under modular strategies are np complete we also establish the optimal strategy complexity by showing that global strategies for mean payoff objectives require infinite memory even in one player pushdown games and memoryless modular strategies are sufficient in two player pushdown games finally we also show that all the problems have the same complexity if the stack boundedness condition is added where along with the mean payoff objective the player must also ensure that the stack height is bounded

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

infinite games on finitely coloured graphs with applications to automata on infinite trees we examine a class of infinite two person games on finitely coloured graphs the main aim is to construct finite memory winning strategies for both players this problem is motivated by applications to finite automata on infinite trees a special attention is given to the exact amount of memory needed by the players for their winning strategies based on a previous work of gurevich and harrington and on subsequent improvements of mcnaughton we propose a unique framework that allows to reestablish and to improve various results concerning memoryless strategies due to emerson and jutla mostowski klarlund

identification of arma models using intermittent and quantized output observations this paper studies system identification of arma models whose outputs are subject to finite level quantization and random packet dropouts using the maximum likelihood criterion we propose a recursive identification algorithm which we show to be strongly consistent and asymptotically normal we also propose a simple adaptive quantization scheme which asymptotically achieves the minimum parameter estimation error covariance the joint effect of finite level quantization and random packet dropouts on identification accuracy are exactly quantified the theoretical results are verified by simulations

qualitative reachability in stochastic bpa games we consider a class of infinite state stochastic games generated by stateless pushdown automata or equivalently 1 exit recursive state machines where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint 0 or 1 the goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied while the other player aims at the opposite we show that the winner in such games can be determined in p for the 0 constraint and in email protected co np for the 1 constraint further we prove that the winning regions for both players are regular and we design algorithms which compute the associated finite state automata finally we show that winning strategies can be synthesized effectively

recursive markov decision processes and recursive stochastic games we introduce recursive markov decision processes rmdps and recursive simple stochastic games rssgs which are classes of finitely presented countable state mdps and zero sum turn based perfect information stochastic games they extend standard finite state mdps and stochastic games with a recursion feature we study the decidability and computational complexity of these games under termination objectives for the two players one player s goal is to maximize the probability of termination at a given exit while the other player s goal is to minimize this probability in the quantitative termination problems given an rmdp or rssg and probability p we wish to decide whether the value of such a termination game is at least p or at most p in the qualitative termination problem we wish to decide whether the value is 1 the important 1 exit subclasses of these models 1 rmdps and 1 rssgs correspond in a precise sense to controlled and game versions of classic stochastic models including multitype branching processes and stochastic context free grammars where the objective of the players is to maximize or minimize the probability of termination extinction we provide a number of upper and lower bounds for qualitative and quantitative termination problems for rmdps and rssgs we show both problems are undecidable for multi exit rmdps but are decidable for 1 rmdps and 1 rssgs specifically the quantitative termination problem is decidable in pspace for both 1 rmdps and 1 rssgs and is at least as hard as the square root sum problem a well known open problem in numerical computation we show that the qualitative termination problem for 1 rmdps i e a controlled version of branching processes can be solved in polynomial time both for maximizing and minimizing 1 rmdps the qualitative problem for 1 rssgs is in np conp and is at least as hard as the quantitative termination problem for condon s finite state simple stochastic games whose complexity remains a well known open problem finally we show that even for 1 rmdps more general qualitative and quantitative model checking problems with respect to linear time temporal properties are undecidable even for a fixed property

vector space framework for unification of one and multidimensional filter bank theory a number of results in filter bank theory can be viewed using vector space notations this simplifies the proofs of many important results in this paper we first introduce the framework of vector space and then use this framework to derive some known and some new filter bank results as well for example the relation among the hermitian image property orthonormality and the perfect reconstruction pr property is well known for the case of one dimensional 1 d analysis synthesis filter banks we can prove the same result in a more general vector space setting this vector space framework has the advantage that even the most general filter banks namely multidimensional nonuniform filter banks with rational decimation matrices become a special case many results in 1 d filter bank theory are hence extended to the multidimensional case with some algebraic manipulations of integer matrices some examples are the equivalence of biorthonormality and the pr property the interchangeability of analysis and synthesis filters the connection between analysis synthesis filter banks and synthesis analysis transmultiplexers etc furthermore we obtain the subband convolution scheme by starting from the generalized parseval s relation in vector space several theoretical results of wavelet transform can also be derived using this framework in particular we derive the wavelet convolution theorem

transient and tracking performance analysis of the quantized lms algorithm for time varying system identification this paper investigates the statistical behavior of the finite precision lms adaptive filter in the identification of an unknown time varying stochastic system nonlinear recursions are derived for the mean and mean square behavior of the adaptive weights transient and tracking algorithm performance curves are generated from the recursions and shown to be in excellent agreement with monte carlo simulations our results demonstrate that linear models are inappropriate for analyzing the transient and the steady state algorithm behavior the performance curves indicate that the transient and tracking capabilities cannot be determined from perturbations about the infinite precision case it is shown that the transient phase of the algorithm increases as the digital wordlength or the speed of variation of the unknown system decrease design examples illustrate how the theory can be used to select the algorithm step size and the number of bits in the quantizer

a new kernel based approach to system identification with quantized output data in this paper we introduce a novel method for linear system identification with quantized output data we model the impulse response as a zero mean gaussian process whose covariance kernel is giv

almost sure convergence rates for system identification using binary quantized and regular sensors abstract this paper presents almost sure convergence rates for system identification under binary quantized and regular sensors to accommodate practical model complexity constraints the system under consideration is represented by a modeled part together with an unknown but bounded unmodeled dynamics under uncorrelated noise sequences identification errors with different sensor types are studied and tight error bounds are obtained without information or constraints on noise moment conditions the results are then extended to correlated noise sequences whose remote past and distant future are asymptotically independent in both cases almost sure error bounds of the laws of iterated logarithms type are derived

parameter estimation in systems with binary valued observations and structural uncertainties this paper studies identification of linear systems with binary valued observations generated via fixed thresholds in addition to stochastic measurement noises the systems are also subject to structural uncertainties including deterministic unmodelled dynamics nonlinear model mismatch and sensor observation bias since binary valued observations can supply only limited information on the signals truncated empirical measures are introduced to extract further information for system identification an effective identification algorithm is constructed based on the proposed empirical measures optimal identification errors time complexity optimal input design and impact of disturbances unmodelled dynamics observation bias and nonlinear model mismatch are thoroughly investigated in a stochastic information framework asymptotic upper and lower bounds are established on identification errors numerical experiments are presented to demonstrate the effectiveness of the algorithms and the main results

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

asymptotically efficient identification of fir systems with quantized observations and general quantized inputs this paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs while asymptotically efficient algorithms for quantized identification under periodic inputs are available their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions under quantized inputs this paper resolves this issue with constructive solutions a two step algorithm is developed which demonstrates desired convergence properties including strong convergence mean square convergence convergence rates asymptotic normality and asymptotical efficiency in terms of the cramer rao lower bound some essential conditions on input excitation are derived that ensure identifiability and convergence it is shown that by a suitable selection of the algorithm s weighting matrix the estimates become asymptotically efficient the strong and mean square convergence rates are obtained optimal input design is given also the joint identification of noise distribution functions and system parameters is investigated numerical examples are included to illustrate the main results of this paper

measuring and synthesizing systems in probabilistic environments the traditional synthesis question given a specification asks for the automatic construction of a system that satisfies the specification whereas often there exists a preference order among the different systems that satisfy the given specification under a probabilistic assumption about the possible inputs such a preference order is naturally expressed by a weighted automaton which assigns to each word a value such that a system is preferred if it generates a higher expected value we solve the following optimal synthesis problem given an omega regular specification a markov chain that describes the distribution of inputs and a weighted automaton that measures how well a system satisfies the given specification under the input assumption synthesize a system that optimizes the measured value for safety specifications and quantitative measures that are defined by mean payoff automata the optimal synthesis problem reduces to finding a strategy in a markov decision process mdp that is optimal for a long run average reward objective which can be achieved in polynomial time for general omega regular specifications along with mean payoff automata the solution rests on a new polynomial time algorithm for computing optimal strategies in mdps with mean payoff parity objectives our algorithm constructs optimal strategies that consist of two memoryless strategies and a counter the counter is in general not bounded to obtain a finite state system we show how to construct an e optimal strategy with a bounded counter for all e 0 furthermore we show how to decide in polynomial time if it is possible to construct an optimal finite state system i e a system without a counter for a given specification we have implemented our approach and the underlying algorithms in a tool that takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification if such a system exists we present some experimental results showing optimal systems that were automatically generated in this way

pushdown processes a pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton a winning condition in such a game is defined in terms of states appearing infinitely often in the play it is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton an exptime procedure for finding a winner in a pushdown game is presented the procedure is then used to solve the model checking problem for the pushdown processes and the propositional calculus the problem is shown to be dexptime complete

general solution for a class of diffraction problems using a special mathematical technique previously developed by malyuzhinets the general solution of two dimensional plane wave diffraction problems in an angular region of any angle with boundary conditions containing spatial derivatives of arbitrary orders is constructed

recursive identification of fir systems with binary valued outputs and communication channels this paper investigates the recursive identification of the finite impulse response systems whose outputs are subject to both the binary valued quantization and the communication unreliability the discrete memoryless channel with packet losses and the additive white gaussian noise channel with time delay are considered a stochastic gradient type algorithm and a stochastic approximation type algorithm are respectively proposed to estimate the unknown system parameters under some mild conditions the algorithms can be proved to be convergent in the almost sure and mean square senses also the convergence rates are given numerical examples are included to illustrate the performance of the algorithms

framing pyramids burt and adelson 1983 introduced the laplacian pyramid lp as a multiresolution representation for images we study the lp using the frame theory and this reveals that the usual reconstruction is suboptimal we show that the lp with orthogonal filters is a tight frame and thus the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric with the forward transform in more general cases we propose an efficient filterbank fb for the reconstruction of the lp using projection that leads to a proved improvement over the usual method in the presence of noise setting up the lp as an oversampled fb we offer a complete parameterization of all synthesis fbs that provide perfect reconstruction for the lp finally we consider the situation where the lp scheme is iterated and derive the continuous domain frames associated with the lp

quantized feedback fuzzy sliding mode control design via memory based strategy this paper is concerned with the sliding mode control smc design for a class of takagi sugeno t s fuzzy nonlinear systems subject to model uncertainties and input quantization mismatch a novel memory based sliding surface is presented which includes not only the current states but also the past state information of the systems sufficient conditions for the design of the switching gains are given via linear matrix inequality lmi technique and then the reaching conditions of the sliding surface is constructed to ensure the reachability of the sliding manifold furthermore an adaptive neuro fuzzy inference system anfis is introduced for reducing the high frequency chattering induced by the signum function term in the sliding mode control the effectiveness of the proposed methodology is illustrated by matlab simulations

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

oversampled sigma delta modulation oversampled sigma delta modulation has been proposed as a practical implementation for high rate analog to digital conversion because of its simplicity and its robustness against circuit imperfections to date mathematical developments of the basic properties of such systems have been based either on simplified continuous time approximate models or on linearized discrete time models where the quantizer is replaced by an additive white uniform noise source in this paper we rigorously derive several basic properties of a simple discrete time single integrator loop sigma delta modulator with an accumulate and dump demodulator the derivation does not require any assumptions on the correlation or distribution of the quantizer error and hence involves no linearization of the nonlinear system but it does show that when the input is constant the state sequence of the integrator in the encoder loop can be modeled exactly as a linear system in an appropriate space two basic properties are developed 1 the behavior of the sigma delta quantizer when driven by a constant input and its relation to uniform quantization and 2 the rate distortion tradeoffs between the oversampling ratio and the average mean squared quantization error

quantized identification with dependent noise and fisher information ratio of communication channels system identification is studied in which the system output is quantized transmitted through a digital communication channel and observed afterwards this paper explores strong convergence efficiency and complexity of identification algorithms under colored noise and dependent communication channels it first presents algorithms for certain core identification problems using quantized observations on the basis of empirical measures and nonlinear mappings strong consistency with probability one convergence is established under mixing noises furthermore with pre quantization signal processing it is shown that certain modified algorithms can achieve asymptotic efficiency under correlated noises to improve convergence speeds quantization threshold adaptation algorithms are introduced these results are then used to study the impact of communication channels on system identification under dependent channels the concept of fisher information ratio is introduced to characterize such impact it is shown that the fisher information ratio can be calculated from certain channel characteristic matrices the relationship between the fisher information ratio and shannon s channel capacity is discussed from the angle of time and space information the methods of identification input designs that link general system parameters to core identification problems are reviewed

time domain oversampled lapped transforms theory structure and application in image coding this paper generalizes time domain lapped transforms tdlts proposed by tran et al to oversampled systems thus leading to time domain oversampled lapped transforms tdolts these new transforms correspond to a subclass of oversampled linear phase perfect reconstruction filterbanks olpprfbs which can be implemented by adding a prefilter before the discrete cosine transform dct and a post filter after the inverse discrete cosine transform idct structures of the pre and post filters are developed and the frame theoretic properties of tdolts are analyzed a new parameterization of lattice matrices through the givens qr factorization is proposed for unconstrained optimization comparisons with other parameterization methods are also included several design examples along with some image coding results are presented to demonstrate the validity of the theory and the potential of tdolts in image coding especially in error resilient coding

bandwidth constrained distributed estimation for wireless sensor networks part i gaussian case we study deterministic mean location parameter estimation when only quantized versions of the original observations are available due to bandwidth constraints when the dynamic range of the parameter is small or comparable with the noise variance we introduce a class of maximum likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the clairvoyant sample mean estimator when the dynamic range is comparable or larger than the noise standard deviation we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint we will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons we finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave

identification of sparse fir systems using a general quantisation scheme this paper presents an identification scheme for sparse fir systems with quantised data we consider a general quantisation scheme which includes the commonly deployed static quantiser as a special case to tackle the sparsity issue we utilise a bayesian approach where an l1 a priori distribution for the parameters is used as a mechanism to promote sparsity the general framework used to solve the problem is maximum likelihood ml the ml problem is solved by using a generalised expectation maximisation algorithm

fixed order fir approximation of linear systems from quantized input and output data the problem of identifying a fixed order fir approximation of linear systems with unknown structure assuming that both input and output measurements are subjected to quantization is dealt with in this paper a fixed order fir model providing the best approximation of the input output relationship is sought by minimizing the worst case distance between the output of the true system and the modeled output for all possible values of the input and output data consistent with their quantized measurements the considered problem is firstly formulated in terms of robust optimization then two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented the effectiveness of the proposed approach is illustrated by means of a simulation example

identification of fir systems based on quantized output measurements a quadratic programming based method this technical note proposes a quadratic programming qp based method for identification of finite impulse response fir dynamic systems from quantized or binary data the main idea of the proposed method is to reformulate this identification problem usually viewed as a nonlinear estimation problem with discontinuous nonlinearities in the form of a standard qp problem which is a convex optimization problem and can be solved efficiently the so called complete input conditions to ensure the unique solution of the qp problem are developed and the consistency of the estimated parameters is established under the complete input conditions numerical examples demonstrate the effectiveness of the proposed method

deterministic analysis of oversampled a d conversion and decoding improvement based on consistent estimates discusses the deterministic analysis of oversampled a d conversion adc the properties derivable from such an analysis and the consequences on reconstruction using nonlinear decoding given a band limited input x producing a quantized version c the authors consider the set of all input signals that are band limited and produce c they call any element of this set a consistent estimate of x regardless of the type of encoder simple predictive or noise shaping they show that this set is convex and as a consequence any nonconsistent estimate can be improved they also show that the classical linear decoding estimates are not necessarily consistent numerical tests performed on simple adc single loop and multiloop spl sigma spl delta modulation show that consistent estimates yield a mean square error mse that decreases asymptotically with the oversampling ratio faster than the linear decoding mse by approximately 3 db octave this implies an asymptotic mse of the order of spl oscr r sup spl minus 2n 2 instead of spl oscr r sup spl minus 2n 1 in linear decoding where r is the oversampling ratio and n the order of the modulator methods of improvement of nonconsistent estimates based on the deterministic knowledge of the quantized signal are proposed for simple adc predictive adc single loop and multiloop spl sigma spl delta modulation

distributed adaptive quantization for wireless sensor networks from delta modulation to maximum likelihood we consider distributed parameter estimation using quantized observations in wireless sensor networks wsns where due to bandwidth constraint each sensor quantizes its local observation into one bit of information a conventional fixed quantization fq approach which employs a fixed threshold for all sensors incurs an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated to address this difficulty we propose a distributed adaptive quantization aq approach which with sensors sequentially broadcasting their quantized data allows each sensor to adaptively adjust its quantization threshold three aq schemes are presented 1 aq fs that involves distributed delta modulation dm with a fixed stepsize 2 aq vs that employs dm with a variable stepsize and 3 aq ml that adjusts the threshold through a maximum likelihood ml estimation process the ml estimators associated with the three aq schemes are developed and their corresponding cramer rao bounds crbs are analyzed we show that our 1 bit aq approach is asymptotically optimum yielding an asymptotic crb that is only pi 2 times that of the clairvoyant sample mean estimator using unquantized observations

instantaneous erasures in oversampled filter banks conditions for output perfect reconstruction in this paper we aim at finding the conditions that an oversampled filter bank ofb should satisfy in order to maintain its perfect reconstruction property when erasures happen in the subband domain this problem has been addressed before mainly from frame theoretic point of view and only for the case of what we call in this paper classic erasure in the frame theoretic approach the stable filter banks are associated with frames in l2 bbz and a subband erasure is defined as the deletion of the frame expansion coefficients corresponding to the frame vectors resulting from each filter and all its translated versions this is equivalent to assuming that all the samples of a subband have been completely lost classic erasure and this is why in this approach it is always assumed that each channel is either working perfectly or not at all in this paper we extend this notion of erasure to a situation where subband channels are allowed to be on or off arbitrarily in each time instance and we define a new type of erasure called instantaneous erasure using an approach based on the time domain analysis of perfect reconstruction property we introduce general conditions for perfect reconstruction of the output and also the sufficient conditions for two classes of filter banks causal ofbs with causal inverse and ofbs with maximum robustness against classic erasure

asymptotically optimal parameter estimation with scheduled measurements to reduce the communication cost of a sensor node this paper is concerned with an estimation framework with scheduled measurements for a linear system a scheduler is designed to control the transmission of measurements from sensor to estimator which results in that only a subset of measurements is transmitted to the estimator we propose an innovation based scheduler and derive an analytical expression for the cramer rao lower bound crlb for the given scheduling strategy under a communication constraint an adaptive scheduler and a corresponding recursive estimator are jointly designed to asymptotically attain the crlb the structure of the estimator bears close resemblance to the standard least square estimator lse with the full set of sensor measurements moreover we prove that the estimation performance in terms of mean square estimation error is comparable to the standard lse even under a moderate communication cost the theoretical results are verified by simulations

mode conversion corner singularities and matrix wiener hopf factorization in diffraction theory the diffraction of acoustic electromagnetic and elastic waves by an edge is a subject of continuing mathematical and physical importance the physical motivation for research is the vast number of technological and geophysical applications of the fundamental models of linear wave propagation in continuous media while the mathematical drive is to understand and devise new analytical and numerical techniques for their quantification this paper is concerned with certain physical aspects of diffraction which have proven to give the most troublesome of mathematical difficulties these are mode conversion that is when the incident wave is scattered among different modes supported by the propagating medium and edge or corner singularities when the diffracting obstacle creates a stress singularity it is shown by way of a particular example that the exact solution of diffraction problems involving these phenomena will in general give rise to a vector wiener hopf equation with a matrix kernel whose factorization is non commutative the main result of this paper is a new procedure motivated by a precise treatment of both the corner singularity and mode conversion for determining the factors in this case

recursive algorithms for parameter estimation with adaptive quantizer this paper studies a parameter estimation problem of networked linear systems with fixed rate quantization under the minimum mean square error criterion we propose a recursive estimator of stochastic approximation type and derive a necessary and sufficient condition for its asymptotic unbiasedness this motivates to design an adaptive quantizer for the estimator whose strong consistency asymptotic unbiasedness and asymptotic normality are rigorously proved using the newton based and averaging techniques we obtain two accelerated recursive estimators with the fastest convergence speed of o 1 k and exactly evaluate the quantization effect on the estimation accuracy if the observation noise is gaussian an optimal quantizer and the accelerated estimators are co designed to asymptotically approach the minimum cramer rao lower bound all the estimators share almost the same computational complexity as the gradient algorithms with un quantized observations and can be easily implemented finally the theoretical results are validated by simulations

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

reachability in recursive markov decision processes we consider a class of infinite state markov decision processes generated by stateless pushdown automata this class corresponds to 112 player games over graphs generated by bpa systems or equivalently 1 exit recursive state machines an extended reachability objective is specified by two sets s and t of safe and terminal stack configurations where the membership to s and t depends just on the top of the stack symbol the question is whether there is a suitable strategy such that the probability of hitting a terminal configuration by a path leading only through safe configurations is equal to or different from a given email protected 0 1 we show that the qualitative extended reachability problem is decidable in polynomial time and that the set of all configurations for which there is a winning strategy is effectively regular more precisely this set can be represented by a deterministic finite state automaton with a fixed number of control states this result is a generalization of a recent theorem by etessami and yannakakis which says that the qualitative termination for 1 exit rmdps which exactly correspond to our 112 player bpa games is decidable in polynomial time interestingly the properties of winning strategies for the extended reachability objectives are quite different from the ones for termination and new observations are needed to obtain the result as an application we derive the exptime completeness of the model checking problem for 112 player bpa games and qualitative pctl formulae

robust distributed maximum likelihood estimation with dependent quantized data in this paper we consider the distributed maximum likelihood estimation mle with dependent quantized data under the assumption that the structure of the joint probability density function pdf is known but it contains unknown deterministic parameters the parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe the dependence of observations across sensors since mle with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf we concentrate on mle with multiple groups of quantizers which can be determined by the use of prior information or some heuristic approaches to fend off against the risk of a poor outlier quantizer the asymptotic efficiency of the mle scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach as an illustrative example we consider an estimation problem with a bivariate non gaussian pdf that has applications in distributed constant false alarm rate cfar detection systems simulations show the robustness of the proposed mle scheme especially when the number of quantized measurements is small

recursive projection algorithm on fir system identification with binary valued observations this paper studies the identification of finite impulse response fir systems with binary valued observations combining with the stochastic gradient algorithm and statistical property of the system noise a recursive projection algorithm is proposed to estimate the unknown system parameters under some mild conditions on the a priori knowledge of the unknown parameters and inputs the algorithm is proved to be convergent in the almost sure and mean square sense furthermore the almost sure and mean square convergence rates of estimation errors are also obtained a numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained

alternating time temporal logic temporal logic comes in two varieties linear time temporal logic assumes implicit universal quantification over all paths that are generated by the execution of a system branching time temporal logic allows explicit existential and universal quantification over all paths we introduce a third more general variety of temporal logic alternating time temporal logic offers selective quantification over those paths that are possible outcomes of games such as the game in which the system and the environment alternate moves while linear time and branching time logics are natural specification languages for closed systems alternating time logics are natural specification languages for open systems for example by preceding the temporal operator eventually with a selective path quantifier we can specify that in the game between the system and the environment the system has a strategy to reach a certain state the problems of receptiveness realizability and controllability can be formulated as model checking problems for alternating time formulas depending on whether or not we admit arbitrary nesting of selective path quantifiers and temporal operators we obtain the two alternating time temporal logics atl and atl atl and atl are interpreted over concurrent game structures every state transition of a concurrent game structure results from a choice of moves one for each player the players represent individual components and the environment of an open system concurrent game structures can capture various forms of synchronous composition for open systems and if augmented with fairness constraints also asynchronous composition over structures without fairness constraints the model checking complexity of atl is linear in the size of the game structure and length of the formula and the symbolic model checking algorithm for ctl extends with few modifications to atl over structures with weak fairness constraints atl model checking requires the solution of 1 pair rabin games and can be done in polynomial time over structures with strong fairness constraints atl model checking requires the solution of games with boolean combinations of buchi conditions and can be done in pspace in the case of atl the model checking problem is closely related to the synthesis problem for linear time formulas and requires doubly exponential time

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

quantized identification of arma systems with colored measurement noise this paper studies the identification of arma systems with colored measurement noises using finite level quantized observations compared with the case under colorless noises this problem is more challenging our approach is to jointly design an adaptive quantizer and a recursive estimator to identify system parameters specifically the quantizer uses the latest estimate to adjust its thresholds and the estimator is updated by using quantized observations to accommodate the temporal correlations of quantization errors and measurement noises we construct a second order statistics equivalent system from which the original arma system is identified the associated identifiability problem and convergence are analyzed as well finally numerical simulations are performed to demonstrate the effectiveness of the proposed algorithm

vector quantization analysis of spl sigma spl delta modulation when considering a class of finite dimensional input signals such as bandlimited signals in the discrete fourier sense within a finite time window o t of observation we show that a single loop spl sigma spl delta modulator behaves like the encoder of a vector quantizer the intrinsic behavior of the modulator can be studied by analyzing the partition it generates in the input space we show that this partition yields a particular structure that we call the hyperplane wave structure as one consequence to this analysis it can be proved for the considered class of bandlimited signals that the mean squared error mse of reconstruction cannot asymptotically decrease with the oversampling ratio r faster than o r sup 4 regardless of the type of reconstruction used we then generalize this analysis to n loop spl sigma spl delta modulators and show that the mse cannot decrease faster than o r sup 2n 2

bound ratio minimization of filter bank frames this paper investigates and solves the problem of frame bound ratio minimization for oversampled perfect reconstruction pr filter banks fbs for a given analysis prfb a finite dimensional convex optimization algorithm is derived to redesign the subband gain of each channel the redesign minimizes the frame bound ratio of the fb while maintaining its original properties and performance the obtained solution is precise without involving frequency domain approximation and can be applied to many practical problems in signal processing the optimal solution is applied to subband noise suppression and tree structured fb gain optimization resulting in deeper insights and novel solutions to these two general classes of problems and considerable performance improvement effectiveness of the optimal solution is demonstrated by extensive numerical 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

parametric identification of transfer functions in the frequency domain a survey this paper gives a survey of frequency domain identification methods for rational transfer functions in the laplace s or z domain the interrelations between the different approaches are highlighted through a study of the equivalent cost functions the properties of the various estimators are discussed and illustrated by several examples

sigma delta spl sigma spl delta quantization and finite frames the k level sigma delta spl sigma spl delta scheme with step size spl delta is introduced as a technique for quantizing finite frame expansions for spl ropf sup d error estimates for various quantized frame expansions are derived and in particular it is shown that spl sigma spl delta quantization of a unit norm finite frame expansion in spl ropf sup d achieves approximation error where n is the frame size and the frame variation spl sigma f p is a quantity which reflects the dependence of the spl sigma spl delta scheme on the frame here spl par spl middot spl par is the d dimensional euclidean 2 norm lower bounds and refined upper bounds are derived for certain specific cases as a direct consequence of these error bounds one is able to bound the mean squared error mse by an order of 1 n sup 2 when dealing with sufficiently redundant frame expansions this represents a significant improvement over classical pulse code modulation pcm quantization which only has mse of order 1 n under certain nonrigorous statistical assumptions spl sigma spl delta also achieves the optimal mse order for pcm with consistent reconstruction

conditions for optimality of naive quantized finite horizon control this paper presents properties of a control law which quantizes the unconstrained solution to a unitary horizon quadratic programme this naive quantized control law underlies many popular algorithms such as converters and decision feedback equalities and is easily shown to be globally optimal for horizon one however the question arises as to whether it is also globally optimal for horizons greater than one i e whether it solves a finite horizon quadratic programme where decision variables are restricted to belonging to a quantized set by using dynamic programming we develop sufficient conditions for this to hold the present analysis is restricted to first order plants however this case already raises a number of highly non trivial issues the results can be applied to arbitrary horizons and quantized sets which may contain a finite or an infinite though countable number of elements

an improved uniform approximation for diffraction integrals a saddle point formula for integrals whose integrands possess a multi valued exponent and one or more poles is derived the result includes a number of error or fresnel functions which is equal to the product of the number of poles and the number of sheets possessed by the exponent s riemann surface such formulae have previously been suggested on the basis of known exact results and transformations both of which are specific to a particular exponent in general the multi valuedness can be taken into account by a straightforward modification to a standard procedure which would ordinarily yield only a single error function for each pole in the context of diffraction theory this type of approximation remains valid in the vicinity of an optical boundary even in some cases where a wavefield is incident in a direction almost or exactly parallel to a sharp obstacle grazing incidence

lower bound on the mean squared error in oversampled quantization of periodic signals using vector quantization analysis oversampled analog to digital conversion is a technique which permits high conversion resolution using coarse quantization classically by lowpass filtering the quantized oversampled signal it is possible to reduce the quantization error power in proportion to the oversampling ratio r in other words the reconstruction mean squared error mse is in spl oscr r sup 1 it was recently found that this error reduction is not optimal under certain conditions it was shown on periodic bandlimited signals that an upper bound on the mse of optimal reconstruction is in spl oscr r sup 2 instead of spl oscr r sup 1 in the present paper we prove on the same type of signals that the order spl oscr r sup 2 is the theoretical limit of reconstruction as an mse lower bound the proof is based on a vector quantization approach with an analysis of partition cell density

joint identification of plant rational models and noise distribution functions using binary valued observations system identification of plants with binary valued output observations is of importance in understanding modeling capability and limitations for systems with limited sensor information establishing relationships between communication resource limitations and identification complexity and studying sensor networks this paper resolves two issues arising in such system identification problems first regression structures for identifying a rational model contain non smooth nonlinearities leading to a difficult nonlinear filtering problem by introducing a two step identification procedure that employs periodic signals empirical measures and identifiability features rational models can be identified without resorting to complicated nonlinear searching algorithms second by formulating a joint identification problem we are able to accommodate scenarios in which noise distribution functions are unknown convergence of parameter estimates is established recursive algorithms for joint identification and their key properties are further developed

asymptotic analysis of an algorithm for parameter estimation and identification of 1 b quantized ar time series krishnamurthy and mareels 1995 presented a parameter estimation algorithm called the binary series estimation algorithm bsea for gaussian autoregressive ar time series given 1 b quantized noisy measurements of particular interest were the rather surprising computer simulation results that showed that for certain ar series in multiplicative noise the bsea based on 1 b quantized measurements yielded significantly better parameter estimates than yule walker methods that are based on the unquantized measurements the present paper carries out an asymptotic analysis of the bsea for gaussian ar models in particular from a central limit theorem the authors obtain expressions for the asymptotic covariances of the parameter estimates from this they 1 present an algorithm for estimating the order of an ar series from 1 b quantized measurements and 2 theoretically justify why bsea can yield better estimates than the yule walker methods in some cases computer simulations show that the theoretically predicted parameter estimate covariances are extremely accurate in addition the authors present examples of their order estimation algorithm

recursive identification of systems with binary valued outputs and with arma noises abstract this paper considers the identification problem of the arma system followed by a binary sensor in which the internal variables are corrupted by additive arma noises recursive estimates for the parameters of the linear system and for the threshold of the binary sensor are given by the stochastic approximation algorithms with expanding truncations saawet under reasonable conditions all the estimates are proved to be convergent to the true values with probability one the almost surely convergence rates are also investigated a simulation example is included to justify the theoretical results

optimal noise reduction in oversampled pr filter banks this paper studies the optimal noise reduction problem for oversampled filter banks fbs with perfect reconstruction pr constraint both the optimal design and worst case design are considered where the former caters for the noise with known power spectral density psd and the latter for the noise with unknown psd state space based explicit formulae involving only algebraic riccati equation and matrix manipulations are provided for the general iir or fir oversampled pr fbs and the relations between different cases are analyzed and revealed extensive numerical examples are provided to illustrate the proposed design methods and to show their effectiveness

rate distortion performance in coding bandlimited sources by sampling and dithered quantization the rate distortion characteristics of a scheme for encoding continuous time band limited stationary sources with a prescribed band is considered in this coding procedure the input is sampled at nyquist s rate or faster the samples undergo dithered uniform or lattice quantization using subtractive dither and the quantizer output is entropy coded the rate distortion performance and the tradeoff between the sampling rate and the quantization accuracy is investigated utilizing the observation that the coding scheme is equivalent to an additive noise channel it is shown that the mean square error of the scheme is fixed as long as the product of the sampling period and the quantizer second moment is kept constant while for a fixed distortion the coding rate generally increases when the sampling rate exceeds the nyquist rate finally as the lattice quantizer dimension becomes large the equivalent additive noise channel of the scheme tends to be white gaussian and both the rate and the distortion performance become invariant to the sampling rate

noise reduction in oversampled filter banks using predictive quantization we introduce two methods for quantization noise reduction in oversampled filter banks these methods are based on predictive quantization noise shaping or linear prediction it is demonstrated that oversampled noise shaping or linear predictive subband coders are well suited for subband coding applications where for technological or other reasons low resolution quantizers have to be used in this case oversampling combined with noise shaping or linear prediction improves the effective resolution of the subband coder at the expense of increased rate simulation results are provided to assess the achievable quantization noise reduction and resolution enhancement and to investigate the rate distortion properties of the proposed methods

identification of wiener systems with binary valued output observations this work is concerned with identification of wiener systems whose outputs are measured by binary valued sensors the system consists of a linear fir finite impulse response subsystem of known order followed by a nonlinear function with a known parametrization structure the parameters of both linear and nonlinear parts are unknown input design identification algorithms and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible it is shown that under scaled periodic inputs identification of wiener systems can be decomposed into a finite number of core identification problems the concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the wiener system can be identified with binary valued observations under scaled full rank conditions and joint identifiability a strongly convergent algorithm is constructed the algorithm is shown to be asymptotically efficient for the core identification problem hence achieving asymptotic optimality in its convergence rate for computational simplicity recursive algorithms are also developed

noise reduction in tight weyl heisenberg frames the functions g that give rise to tight weyl heisenberg frames based on time and frequency discretization steps q sub 0 and p sub 0 with p sub 0 q sub 0 2 pi k k in n are characterized and the noise reducing properties of such frames are examined it is shown that when the frame coefficients c sub m n f of a function f are subject to stationary noise n the average squared l sup 2 norm of the corresponding noise contribution to the reconstruction of f is down by a factor proportional to k sup 2 for a fixed number of sample points also a measure of local error of the reconstruction is introduced as opposed to the global l sup 2 error for a given noise n formulae are derived for the optimal choice or choices of the basis function g in the sense of minimizing this local error