Willsky, Alan S.
Overview
Works:  249 works in 534 publications in 4 languages and 2,240 library holdings 

Roles:  Author 
Classifications:  QA402, 003 
Publication Timeline
.
Most widely held works by
Alan S Willsky
Signals and systems
by
Alan V Oppenheim(
Book
)
74 editions published between 1983 and 2014 in 5 languages and held by 1,214 WorldCat member libraries worldwide
"More than half of the 600+ problems in the second edition of Signals & Systems are new, while the remainder are the same as in the first edition. This manual contains solutions to the new problems, as well as updated solutions for the problems from the first edition."Pref
74 editions published between 1983 and 2014 in 5 languages and held by 1,214 WorldCat member libraries worldwide
"More than half of the 600+ problems in the second edition of Signals & Systems are new, while the remainder are the same as in the first edition. This manual contains solutions to the new problems, as well as updated solutions for the problems from the first edition."Pref
Digital signal processing and control and estimation theory : points of tangency, areas of intersection, and parallel directions
by
Alan S Willsky(
Book
)
14 editions published between 1977 and 1979 in English and held by 344 WorldCat member libraries worldwide
14 editions published between 1977 and 1979 in English and held by 344 WorldCat member libraries worldwide
Detection of abrupt changes in dynamic systems
by
Alan S Willsky(
Book
)
1 edition published in 1984 in English and held by 78 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 78 WorldCat member libraries worldwide
Signale und Systeme
by
Alan V Oppenheim(
Book
)
2 editions published between 1989 and 1992 in German and held by 25 WorldCat member libraries worldwide
2 editions published between 1989 and 1992 in German and held by 25 WorldCat member libraries worldwide
Signale und Systeme
by
Alan V Oppenheim(
Book
)
5 editions published between 1989 and 1992 in German and Undetermined and held by 24 WorldCat member libraries worldwide
5 editions published between 1989 and 1992 in German and Undetermined and held by 24 WorldCat member libraries worldwide
Signale und Systeme
by
Alan V Oppenheim(
Book
)
1 edition published in 1989 in German and held by 20 WorldCat member libraries worldwide
1 edition published in 1989 in German and held by 20 WorldCat member libraries worldwide
Kalman filtering and Riccati equations for descriptor systems
by
Ramine Nikoukhah(
Book
)
10 editions published between 1990 and 1991 in English and held by 14 WorldCat member libraries worldwide
In this paper we consider a general formulation of a discretetime filtering problem for descriptor systems. It is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems. Using a "dual approach" to estimation we derive a socalled "3block" form for the optimal filter and a corresponding 3block Riccati equation for a general class of timevarying descriptor models which need not represent a wellposed system in that the dynamics may be either over or underconstrained. Specializing to the timeinvariant case we examine the asymptotic properties of the 3block filter, and in particular analyze in detail the resulting 3block algebraic Riccati equation, generalizing significantly the results in [23, 28, 33]. Finally, the noncausal nature of discretetime descriptor dynamics implies that future dynamics may provide some information about the present state. We present a modified form for the descriptor Kalman filter that takes this information into account
10 editions published between 1990 and 1991 in English and held by 14 WorldCat member libraries worldwide
In this paper we consider a general formulation of a discretetime filtering problem for descriptor systems. It is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems. Using a "dual approach" to estimation we derive a socalled "3block" form for the optimal filter and a corresponding 3block Riccati equation for a general class of timevarying descriptor models which need not represent a wellposed system in that the dynamics may be either over or underconstrained. Specializing to the timeinvariant case we examine the asymptotic properties of the 3block filter, and in particular analyze in detail the resulting 3block algebraic Riccati equation, generalizing significantly the results in [23, 28, 33]. Finally, the noncausal nature of discretetime descriptor dynamics implies that future dynamics may provide some information about the present state. We present a modified form for the descriptor Kalman filter that takes this information into account
Multiscale system theory
by
Albert Benveniste(
Book
)
9 editions published between 1990 and 1991 in English and held by 11 WorldCat member libraries worldwide
In many applications, it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a timeandscale decomposition of signals that offers the possibility of such an analysis. Until recently, however, there has been no corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms. A recent work of some of the present authors and coauthors proposed such a framework via models of "stochastic fractals" on the dyadic tree. In this paper we investigate some of the fundamental issues that are relevant to system theories on the dyadic tree, both for systems and signals
9 editions published between 1990 and 1991 in English and held by 11 WorldCat member libraries worldwide
In many applications, it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a timeandscale decomposition of signals that offers the possibility of such an analysis. Until recently, however, there has been no corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms. A recent work of some of the present authors and coauthors proposed such a framework via models of "stochastic fractals" on the dyadic tree. In this paper we investigate some of the fundamental issues that are relevant to system theories on the dyadic tree, both for systems and signals
Xin hao yu xi tong(jing jian ben)
by Ao ben hai(
Book
)
1 edition published in 1999 in Chinese and held by 11 WorldCat member libraries worldwide
1 edition published in 1999 in Chinese and held by 11 WorldCat member libraries worldwide
An estimationbased approach to the reconstruction of optical flow
by
Anne Rougée(
Book
)
5 editions published in 1987 in English and held by 9 WorldCat member libraries worldwide
5 editions published in 1987 in English and held by 9 WorldCat member libraries worldwide
Aggregation and multilevel control in discrete event dynamic systems
by Cüneyt M Özveren(
Book
)
7 editions published between 1989 and 1990 in English and held by 9 WorldCat member libraries worldwide
In this paper we consider the problem of higherlevel aggregate modelling and control of discreteevent dynamic systems (DEDS) modelled as finite state automata in which some events are controllable, some are observed, and some represent events to be tracked. The higherlevel models considered correspond to associating specified sequences of events in the original system to single macroscopic events in the higher level model. We also consider the problem of designing a compensator that can be used to restrict microscopic behavior so that the system will only produce strings of these primitive sequences or tasks. With this lower level control in place we can construct higherlevel models which typically have many fewer states and events than the original system. Also, motivated by applications such as flexible manufacturing, we address the problem of constructing and controlling higherlevel models of interconnections of DEDS. This allows us to "slow down" the combinatorial explosion typically present in computations involving interacting automata
7 editions published between 1989 and 1990 in English and held by 9 WorldCat member libraries worldwide
In this paper we consider the problem of higherlevel aggregate modelling and control of discreteevent dynamic systems (DEDS) modelled as finite state automata in which some events are controllable, some are observed, and some represent events to be tracked. The higherlevel models considered correspond to associating specified sequences of events in the original system to single macroscopic events in the higher level model. We also consider the problem of designing a compensator that can be used to restrict microscopic behavior so that the system will only produce strings of these primitive sequences or tasks. With this lower level control in place we can construct higherlevel models which typically have many fewer states and events than the original system. Also, motivated by applications such as flexible manufacturing, we address the problem of constructing and controlling higherlevel models of interconnections of DEDS. This allows us to "slow down" the combinatorial explosion typically present in computations involving interacting automata
Multiscale autoregressive processes
by
M Basseville(
Book
)
7 editions published between 1989 and 1990 in English and held by 9 WorldCat member libraries worldwide
In many applications (e.g. recognition of geophysical and biomedical signals and multiscale analysis of images), it is of interest to analyze and recognize phenomena occuring at different scales The recently introduced wavelet trans forms provide a timeandscale decomposition of signals that offers the possibil ity of such analysis. At present, however, there is no corresponding statistical framework to support the development of optimal, multiscale statistical sig nal processing algorithms. In this paper we describe such a framework. The theory of multiscale signal representations leads naturally to models of signals on trees, and this provides the framework for our investigation. In particular, in this paper we describe the class of isotropic processes on homogenous trees and develop a theory of autoregressive models in this context. This leads to generalizations of Schur and Levinson recursions, associated properties of the resulting reflection coefficients, and the initial pieces in a system theory for multiscale modeling
7 editions published between 1989 and 1990 in English and held by 9 WorldCat member libraries worldwide
In many applications (e.g. recognition of geophysical and biomedical signals and multiscale analysis of images), it is of interest to analyze and recognize phenomena occuring at different scales The recently introduced wavelet trans forms provide a timeandscale decomposition of signals that offers the possibil ity of such analysis. At present, however, there is no corresponding statistical framework to support the development of optimal, multiscale statistical sig nal processing algorithms. In this paper we describe such a framework. The theory of multiscale signal representations leads naturally to models of signals on trees, and this provides the framework for our investigation. In particular, in this paper we describe the class of isotropic processes on homogenous trees and develop a theory of autoregressive models in this context. This leads to generalizations of Schur and Levinson recursions, associated properties of the resulting reflection coefficients, and the initial pieces in a system theory for multiscale modeling
Asymptotic Orders of Reachability in Perturbed Linear Systems
by Cüneyt M Özveren(
Book
)
7 editions published between 1987 and 1988 in English and held by 8 WorldCat member libraries worldwide
A framework for studying asymptotic orders of reachability in perturbed linear, timeinvariant systems is developed. The systems of interest are defined by matrices that have Taylor or Laurent expansions in the perturbation parameter e about the point 0. The reachability structure is exposed via the Smith form of the reachability matrix. This approach is used to provide insight into the kinds of inputs needed to reach weakly reachable target states, into the structure of highgain feedback for pole placement, and into the types of inputs that steer trajectories arbitrarily close to almost (A, B)invariant subspaces and almost (A, B)controllability subspaces
7 editions published between 1987 and 1988 in English and held by 8 WorldCat member libraries worldwide
A framework for studying asymptotic orders of reachability in perturbed linear, timeinvariant systems is developed. The systems of interest are defined by matrices that have Taylor or Laurent expansions in the perturbation parameter e about the point 0. The reachability structure is exposed via the Smith form of the reachability matrix. This approach is used to provide insight into the kinds of inputs needed to reach weakly reachable target states, into the structure of highgain feedback for pole placement, and into the types of inputs that steer trajectories arbitrarily close to almost (A, B)invariant subspaces and almost (A, B)controllability subspaces
Output stabilizability of discrete event dynamic systems
by Cüneyt M Özveren(
Book
)
5 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
In this paper, we investigate the problem of designing stabilizing feedback compensators for Discrete Event Dynamic Systems (DEDS). The DEDS model used is a finitestate automaton in which some transition events are controllable and some events are observed. The problem of output stabilization is defined as the construction of a compensator such that the closed loop system is stable, in the sense that all state trajectories go through a given set E infinitely often. We define a stronger notion of output stabilizability which requires that we also have perfect knowledge of the state in E through which the trajectory passes on each of its visits to E. Necessary and sufficient conditions are presented for both notions. The complexity of these tests is polynomial in the cardinality of the state space of the observer. A number of sufficient conditions for the weaker notion are also presented. Corresponding tests for these sufficient conditions are shown to be polynomial in the cardinality of the state space of the system. Finally, a problem of resilient output stabilizability is addressed
5 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
In this paper, we investigate the problem of designing stabilizing feedback compensators for Discrete Event Dynamic Systems (DEDS). The DEDS model used is a finitestate automaton in which some transition events are controllable and some events are observed. The problem of output stabilization is defined as the construction of a compensator such that the closed loop system is stable, in the sense that all state trajectories go through a given set E infinitely often. We define a stronger notion of output stabilizability which requires that we also have perfect knowledge of the state in E through which the trajectory passes on each of its visits to E. Necessary and sufficient conditions are presented for both notions. The complexity of these tests is polynomial in the cardinality of the state space of the observer. A number of sufficient conditions for the weaker notion are also presented. Corresponding tests for these sufficient conditions are shown to be polynomial in the cardinality of the state space of the system. Finally, a problem of resilient output stabilizability is addressed
Optical flow computation via multiscale regularization
by Mark R Luettgen(
Book
)
4 editions published in 1992 in English and held by 6 WorldCat member libraries worldwide
The apparent motion of brightness patterns in an image is referred to as the optical flow. In computational vision, optical flow is an important input into higher level vision algorithms performing tasks such as segmentation, tracking, object detection, robot guidance and recovery of shape information. In addition, methods for computing optical flow are an essential part of motion compensated coding schemes. In this paper, we present a new approach to the problem of computing optical flow. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation which arises from the often used "smoothness constraint" regularization term. We utilize the interpretation of the smoothness constraint as a "fractal prior" to motivate regularization based on a recently introduced class of multiscale stochastic models. These models are associated with efficient multiscale smoothing algorithms, and experiments on several image sequences demonstrate the substantial computational savings that can be achieved through their use
4 editions published in 1992 in English and held by 6 WorldCat member libraries worldwide
The apparent motion of brightness patterns in an image is referred to as the optical flow. In computational vision, optical flow is an important input into higher level vision algorithms performing tasks such as segmentation, tracking, object detection, robot guidance and recovery of shape information. In addition, methods for computing optical flow are an essential part of motion compensated coding schemes. In this paper, we present a new approach to the problem of computing optical flow. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation which arises from the often used "smoothness constraint" regularization term. We utilize the interpretation of the smoothness constraint as a "fractal prior" to motivate regularization based on a recently introduced class of multiscale stochastic models. These models are associated with efficient multiscale smoothing algorithms, and experiments on several image sequences demonstrate the substantial computational savings that can be achieved through their use
Analysis, Estimation, and Control for Perturbed and Singular Systems and for Systems Subject to Discrete Events
by
Alan S Willsky(
Book
)
6 editions published between 1987 and 1991 in English and held by 6 WorldCat member libraries worldwide
In this report, we summarize our accomplishments in the research program presently supported by Grant AFOSR880032 over the period from October 1, 1987 to September 30, 1988. The basic scope of this program is the analysis, estimation, and control of complex systems with particular emphasis on (a) the development of asymptotic methods and theories for nearly singular systems; (b) the investigation of theoretical questions related to singular systems; and (c) the analysis of complex systems subject to or characterized by sequences of discrete events. These three topics are described in the next three sections of this report. A full list of publications supported by Grant AFOSR880032 is also included. The principal investigator for this effort is Professor Alan S. Willsky, and Professor George C. Verghese is coprincipal investigator. Professors Willsky and Verghese were assisted by several graduate research assistants as well as additional thesis students not requiring stipend or tuition support from this grant
6 editions published between 1987 and 1991 in English and held by 6 WorldCat member libraries worldwide
In this report, we summarize our accomplishments in the research program presently supported by Grant AFOSR880032 over the period from October 1, 1987 to September 30, 1988. The basic scope of this program is the analysis, estimation, and control of complex systems with particular emphasis on (a) the development of asymptotic methods and theories for nearly singular systems; (b) the investigation of theoretical questions related to singular systems; and (c) the analysis of complex systems subject to or characterized by sequences of discrete events. These three topics are described in the next three sections of this report. A full list of publications supported by Grant AFOSR880032 is also included. The principal investigator for this effort is Professor Alan S. Willsky, and Professor George C. Verghese is coprincipal investigator. Professors Willsky and Verghese were assisted by several graduate research assistants as well as additional thesis students not requiring stipend or tuition support from this grant
A realization theory for twopoint boundaryvalue descriptor systems = Une theorie de realisation deterministe pour les systemes implicites aux deux bouts
by
Ramine Nikoukhah(
Book
)
2 editions published in 1989 in English and held by 6 WorldCat member libraries worldwide
Using this new transform method, we are able to determine the dimension of minimal realizations and construct minimal realizations by performing, in general more than one, factorizations of rational matrices."
2 editions published in 1989 in English and held by 6 WorldCat member libraries worldwide
Using this new transform method, we are able to determine the dimension of minimal realizations and construct minimal realizations by performing, in general more than one, factorizations of rational matrices."
Stability, stochastic stationarity and generalized Lyapunov equations for twopoint boundaryvalue descriptor systems
by
Ramine Nikoukhah(
Book
)
5 editions published in 1988 in English and held by 6 WorldCat member libraries worldwide
This paper introduces the concept of internal stability for twopoint boundaryvalue descriptor systems (TPBVDSs). Since TPBVDSs are defined only over a finite interval, the concept of stability is not easy to formulate for these systems. The definition which is used here consists in requiring that as the length of the interval of definition increases, the effect of boundary conditions on states located close to the center of the interval should go to zero. Stochastic TPBVDSs are studied, and the property of stochastic stationarity is characterized in terms of a generalized Lyapunov equation satisfied by the variance of the boundary vector. A second generalized Lyapunov equation satisfied by state variance of a stochastically stationary TPBVDS is also introduced, and the existence and uniqueness of positive definite solutions to this equation is then used to characterize the property of internal stability. Keywords: Stability, Twopoint boundary value problems. (hde)
5 editions published in 1988 in English and held by 6 WorldCat member libraries worldwide
This paper introduces the concept of internal stability for twopoint boundaryvalue descriptor systems (TPBVDSs). Since TPBVDSs are defined only over a finite interval, the concept of stability is not easy to formulate for these systems. The definition which is used here consists in requiring that as the length of the interval of definition increases, the effect of boundary conditions on states located close to the center of the interval should go to zero. Stochastic TPBVDSs are studied, and the property of stochastic stationarity is characterized in terms of a generalized Lyapunov equation satisfied by the variance of the boundary vector. A second generalized Lyapunov equation satisfied by state variance of a stochastically stationary TPBVDS is also introduced, and the existence and uniqueness of positive definite solutions to this equation is then used to characterize the property of internal stability. Keywords: Stability, Twopoint boundary value problems. (hde)
Multiscale Riccati equations and a twosweep algorithm for the optimal fusion of multiresolution data
by Kenneth C Chou(
Book
)
4 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
In a previous paper [7] we introduced a class of multiscale dynamic models evolving on dyadic trees in which each level in the tree corresponds to the representation of a signal at a particular scale. One of the estimation algorithms suggested in [7] led to the introduction of a new class of Riccati equations describing the evolution of the estimation error covariance as multiresolution data is fused in a finetocoarse direction. This equation can be thought of as having 3 steps in its recursive description: a measurement update step, a finetocoarse prediction step, and a fusion step. In this paper we analyze this class of equations. In particular by introducing several rudimentary elements of a system theory for processes on trees we develop bounds on the error covariance and use these in analyzing stability and steadystate behavior of the fineto coarse filter and the Riccati equations. While this analysis is similar in spirit to that for standard Riccati equations and Kalman filters, there are substantial differences that arise in the multiscale context. For example, the asymmetry of the dyadic tree makes it necessary to define multiscale processes via a coarse tofine dynamic model and also to define the first step in a fusion processor in the opposite direction  i.e. finetocoarse. Also, the notions of stability, reachability, and observability are different. Most importantly for the analysis here, we will see that the fusion step in the finetocoarse filter and Riccati equation requires that we focus attention on the maximum likelihood estimator in order to develop a stability and steadystate theory
4 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
In a previous paper [7] we introduced a class of multiscale dynamic models evolving on dyadic trees in which each level in the tree corresponds to the representation of a signal at a particular scale. One of the estimation algorithms suggested in [7] led to the introduction of a new class of Riccati equations describing the evolution of the estimation error covariance as multiresolution data is fused in a finetocoarse direction. This equation can be thought of as having 3 steps in its recursive description: a measurement update step, a finetocoarse prediction step, and a fusion step. In this paper we analyze this class of equations. In particular by introducing several rudimentary elements of a system theory for processes on trees we develop bounds on the error covariance and use these in analyzing stability and steadystate behavior of the fineto coarse filter and the Riccati equations. While this analysis is similar in spirit to that for standard Riccati equations and Kalman filters, there are substantial differences that arise in the multiscale context. For example, the asymmetry of the dyadic tree makes it necessary to define multiscale processes via a coarse tofine dynamic model and also to define the first step in a fusion processor in the opposite direction  i.e. finetocoarse. Also, the notions of stability, reachability, and observability are different. Most importantly for the analysis here, we will see that the fusion step in the finetocoarse filter and Riccati equation requires that we focus attention on the maximum likelihood estimator in order to develop a stability and steadystate theory
A wavelet packet approach to transient signal classification
by Rachel E Learned(
Book
)
4 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Timefrequency transforms, including wavelet and wavelet packet transforms, are generally acknowledged to be useful for studying nonstationary phenomena and, in particular, have been shown or claimed to be of value in the detection and characterization of transient signals. In many applications timefrequency transforms are simply employed as a visual aid to be used for signal display. Although there have been several studies reported in the literature, there is still considerable work to be done investigating the utility of wavelet and wavelet packet timefrequency transforms for automatic transient signal classification. In this paper, we contribute to this ongoing investigation by exploring the feasibility of applying the wavelet packet transform to automatic detection and classification of a specific set of transient signals in background noise. In particular, a noncoherent waveletpacketbased algorithm specific to the detection and classification of underwater acoustic signals generated by snapping shrimp and sperm whale clicks is proposed. We develop a systematic feature extraction process which exploits signal class differences in the wavelet packet transform coefficients. The waveletpacketbased features obtained by our method for the biologically generated underwater acoustic signals yield excellent classification results when used as input for a neural network and a nearest neighbor rule
4 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Timefrequency transforms, including wavelet and wavelet packet transforms, are generally acknowledged to be useful for studying nonstationary phenomena and, in particular, have been shown or claimed to be of value in the detection and characterization of transient signals. In many applications timefrequency transforms are simply employed as a visual aid to be used for signal display. Although there have been several studies reported in the literature, there is still considerable work to be done investigating the utility of wavelet and wavelet packet timefrequency transforms for automatic transient signal classification. In this paper, we contribute to this ongoing investigation by exploring the feasibility of applying the wavelet packet transform to automatic detection and classification of a specific set of transient signals in background noise. In particular, a noncoherent waveletpacketbased algorithm specific to the detection and classification of underwater acoustic signals generated by snapping shrimp and sperm whale clicks is proposed. We develop a systematic feature extraction process which exploits signal class differences in the wavelet packet transform coefficients. The waveletpacketbased features obtained by our method for the biologically generated underwater acoustic signals yield excellent classification results when used as input for a neural network and a nearest neighbor rule
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Related Identities
 Oppenheim, Alan V. 1937 Author
 Young, Ian T.
 Nawab, Syed Hamid
 Massachusetts Institute of Technology Laboratory for Information and Decision Systems
 Center for Intelligent Control Systems (U.S.)
 MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
 Levy, Bernard C.
 Ames Research Center
 United States Office of Naval Research
 Langley Research Center
Associated Subjects
Boundary value problems Computer vision Control theory Differential equations Digital control systems Estimation theory Kalman filtering Linear programming Matrices Multigrid methods (Numerical analysis) Riccati equation Signal processing Signal processingDigital techniques Signal theory (Telecommunication) System analysis System theory