Relationships between digital signal processing and control and estimation theory

The purpose of this paper is to explore several current research directions in the fields of digital signal processing and modern control and estimation theory. We examine topics such as stability theory, linear prediction, and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing, in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines.

[1]  S. Parker,et al.  Limit-cycle oscillations in digital filters , 1971 .

[2]  J. B. Knowles,et al.  Effect of a finite-word-length computer in a sampled-data feedback system , 1965 .

[3]  Roger W. Brockett,et al.  Frequency-domain instability criteria for time-varying and nonlinear systems , 1967 .

[4]  E. Noldus.  On the instability of nonlinear systems , 1973 .

[5]  Β. L. HO,et al.  Editorial: Effective construction of linear state-variable models from input/output functions , 1966 .

[6]  L. Ljung,et al.  Scattering theory and linear least squares estimation , 1976 .

[7]  Karl Johan Åström,et al.  BOOK REVIEW SYSTEM IDENTIFICATION , 1994, Econometric Theory.

[8]  Peter Pistor,et al.  Stability Criterion for Recursive Filters , 1974, IBM J. Res. Dev..

[9]  W. Wolovich.  State-space and multivariable theory , 1972 .

[10]  G. P. Szegö,et al.  ON THE ABSOLUTE STABILITY OF SAMPLED-DATA CONTROL SYSTEMS. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[11]  J. Willems,et al.  Some new rearrangement inequalities having application in stability analysis , 1968 .

[12]  L. Ljung,et al.  Scattering theory and linear least squares estimation: Part II: Discrete-time problems , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[13]  Nils Sandell.  Information Flow in Decentralized Systems , 1976 .

[14]  A. S. Morse,et al.  Introduction to linear system theory , 1972 .

[15]  W. Mecklenbrauker,et al.  Frequency domain criteria for the absence of zero-input limit cycles in nonlinear discrete-time systems, with applications to digital filters , 1975 .

[16]  L. Silverman,et al.  Modelling of two-dimensional covariance functions with application to image restoration , 1972, CDC 1972.

[17]  R. Kálmán.  LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[18]  S. Mitter,et al.  Controllability, observability, pole allocation, and state reconstruction , 1971 .

[19]  S. Attasi.  Modelling and Recursive Estimation for Double Indexed Sequences , 1976 .

[20]  S. Yakowitz,et al.  A general method for calculating quantization error bounds due to roundoff in multivariable digital filters , 1975, IEEE Transactions on Circuits and Systems.

[21]  P K Houpt,et al.  On decentralized estimation and control with application to freeway ramp metering , 1978 .

[22]  Pitu Mirchandani,et al.  State Estimation with Coarsely Quantized, High-Data-Rate Measurements , 1975, IEEE Transactions on Aerospace and Electronic Systems.

[23]  JOHN w. WOODS,et al.  Kalman filtering in two dimensions , 1977, IEEE Trans. Inf. Theory.

[24]  R. Parthasarathy,et al.  On suboptimal linear system reduction , 1975, Proceedings of the IEEE.

[25]  A. Willson.  Some effects of quantization and adder overflow on the forced response of digital filters , 1972 .

[26]  J. Markel,et al.  Application of a digital inverse filter for automatic formant and F o analysis , 1973 .

[27]  S. Hwang.  Roundoff noise in state-space digital filtering: A general analysis , 1976 .

[28]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[29]  D. Kleinman.  On the stability of linear stochastic systems , 1969 .

[30]  R. Kálmán.  Mathematical description of linear dynamical systems , 1963 .

[31]  N. Nahi,et al.  Estimation of object boundaries in noisy images , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[32]  Alan S. Willsky,et al.  A survey of design methods for failure detection in dynamic systems , 1976, Autom..

[33]  G. K. Roberts,et al.  Consideration of computer limitations in implementing on-line controls. M.S. Thesis , 1976 .

[34]  F. Schoute,et al.  Hierarchic recursive image enhancement , 1977 .

[35]  Vasile Mihai Popov,et al.  Hyperstability of Control Systems , 1973 .

[36]  M. Ekstrom,et al.  Two-dimensional spectral factorization with applications in recursive digital filtering , 1976 .

[37]  N. Nahi.  Role of recursive estimation in statistical image enhancement , 1972 .

[38]  Jan C. Willems,et al.  The Analysis of Feedback Systems , 1971 .

[39]  A. Sripad,et al.  A necessary and sufficient condition for quantization errors to be uniform and white , 1977 .

[40]  D.E. Dudgeon,et al.  Two-dimensional digital filtering , 1975, Proceedings of the IEEE.

[41]  J. Rissanen.  A fast algorithm for optimum linear predictors , 1973 .

[42]  L. Silverman,et al.  Image model representation and line-by-line recursive restoration , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[43]  A. Lindquist.  A New Algorithm for Optimal Filtering of Discrete-Time Stationary Processes , 1974 .

[44]  Alfred Fettweis,et al.  Suppression of parasitic oscillations in wave digital filters , 1975 .

[45]  R. Yarlagadda.  Network synthesis--A state-space approach , 1972 .

[46]  A. Venetsanopoulos,et al.  Design of circularly symmetric two-dimensional recursive filters , 1974 .

[47]  R. Rink,et al.  Performance of state regulator systems with floating-point computation , 1979 .

[48]  J. Rissanen.  Recursive identification of linear systems , 1971 .

[49]  Y. Tsypkin,et al.  Fundamentals of the theory of non-linear pluse control systems , 1963 .

[50]  B. Dickinson,et al.  Efficient solution of covariance equations for linear prediction , 1977 .

[51]  W. Wolovich.  Linear multivariable systems , 1974 .

[52]  E Tse,et al.  Optimal linear filtering theory and radiative transfer: Comparisons and interconnections , 1972 .

[53]  P. Dorato,et al.  Optimal linear regulators: The discrete-time case , 1971 .

[54]  S. Treitel,et al.  Stability and synthesis of two-dimensional recursive filters , 1972 .

[55]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[56]  L. Silverman,et al.  Modeling of two-dimensional covariance functions with application to image restoration , 1974 .

[57]  Jan C. Willems.  Mechanisms for the stability and instability in feedback systems , 1976 .

[58]  Moshe Zakai,et al.  Martingales and stochastic integrals for processes with a multi-dimensional parameter , 1974 .

[59]  A. Fettweis.  Pseudo-passivity, sensitivity, and stability of wave digital filters , 1972 .

[60]  W. Huggins,et al.  Best least-squares representation of signals by exponentials , 1968 .

[61]  Jr. A. Willson.  Limit cycles due to adder overflow in digital filters , 1972 .

[62]  C. Desoer,et al.  On the relation between pseudo-passivity and hyperstability , 1975 .

[63]  L. Silverman,et al.  Digital restoration of images degraded by general motion blurs , 1977 .

[64]  Roger W. Brockett,et al.  The status of stability theory for deterministic systems , 1966 .

[65]  N.K. Bose,et al.  Problems and progress in multidimensional systems theory , 1977, Proceedings of the IEEE.

[66]  A. Lindquist.  On Fredholm integral equations, Toeplitz equations and Kalman-Bucy filtering , 1975 .

[67]  Alfred Fettweis,et al.  On parasitic oscillations in digital filters under looped conditions , 1977 .

[68]  S. Melzer,et al.  Optimal regulation of systems described by a countably infinite number of objects , 1971 .

[69]  J. Willems.  Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[70]  John W. Woods,et al.  Two-dimensional discrete Markovian fields , 1972, IEEE Trans. Inf. Theory.

[71]  Y. Ho,et al.  Team decision theory and information structures in optimal control problems--Part II , 1972 .

[72]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[73]  M. R. Schroeder,et al.  Adaptive predictive coding of speech signals , 1970, Bell Syst. Tech. J..

[74]  W. Wegener,et al.  A new second-order digital filter without parasitic oscillations , 1975 .

[75]  Jr. Thomas G. Stockham,et al.  Image processing in the context of a visual model , 1972 .

[76]  T.H. Crystal,et al.  Linear prediction of speech , 1977, Proceedings of the IEEE.

[77]  R. L. SENGBUSH,et al.  Design and Application of Optimal Velocity Filters in Seismic Exploration , 1972, IEEE Transactions on Computers.

[78]  F. Itakura,et al.  A statistical method for estimation of speech spectral density and formant frequencies , 1970 .

[79]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[80]  J. Willems,et al.  Stability theory of dynamical systems , 1970 .

[81]  Thomas L. Marzetta.  A linear prediction approach to two-dimensional spectral factorization and spectral estimation , 1978 .

[82]  Ronald E Crochiere.  Digital network theory and its application to the analysis and design of digital filters. , 1974 .

[83]  M. Fahmy,et al.  Limit cycle oscillations in a cascade of two-dimensional digital filters , 1975 .

[84]  B. Atal,et al.  Speech analysis and synthesis by linear prediction of the speech wave. , 1971, The Journal of the Acoustical Society of America.

[85]  S. Parker,et al.  Correlated noise due to roundoff in fixed point digital filters , 1976 .

[86]  De Jong.  Numerical aspects of realization algorithms in linear systems theory , 1975 .

[87]  T. Kailath,et al.  An innovations approach to least-squares estimation--Part VI: Discrete-time innovations representations and recursive estimation , 1973 .

[88]  I. Sandberg,et al.  A bound on limit cycles in fixed-point implementations of digital filters , 1972 .

[89]  Ruzena Bajcsy,et al.  Computer Recognition of Roads from Satellite Pictures , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[90]  L. Silverman.  Realization of linear dynamical systems , 1971 .

[91]  Y. Genin,et al.  Two-dimensional stability and orthogonal polynomials on the hypercircle , 1977, Proceedings of the IEEE.

[92]  J. Justice,et al.  A Levinson-type algorithm for two-dimensional Wiener filtering using bivariate Szegö polynomials , 1977, Proceedings of the IEEE.

[93]  A.V. Oppenheim,et al.  Analysis of linear digital networks , 1975, Proceedings of the IEEE.

[94]  Sun-Yuan Kung,et al.  New results in 2-D systems theory, part I: 2-D polynomial matrices, factorization, and coprimeness , 1977, Proceedings of the IEEE.

[95]  A. Morse,et al.  Status of noninteracting control , 1971 .

[96]  W. Wonham,et al.  Topics in mathematical system theory , 1972, IEEE Transactions on Automatic Control.

[97]  吉澤 太郎.  An Invariance Principle in the Theory of Stability (常微分方程式及び函数微分方程式研究会報告集) , 1968 .

[98]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[99]  H. Witsenhausen.  Some Remarks on the Concept of State , 1976 .

[100]  James M. Davis.  Velocity Analysis: An Application of Deterministic Estimation to Reflection Seismology , 1972, IEEE Transactions on Computers.

[101]  K. Chu.  Optimal dencentralized regulation for a string of coupled systems , 1974 .

[102]  B. Anderson,et al.  Linear passive networks: Functional theory , 1976, Proceedings of the IEEE.

[103]  G. Johnson.  Upper bound on dynamic quantization error in digital control systems via the direct method of Liapunov , 1965 .

[104]  Thomas Kailath,et al.  Some new algorithms for recursive estimation in constant linear systems , 1973, IEEE Trans. Inf. Theory.

[105]  Jose B. Cruz,et al.  Feedback systems , 1971 .

[106]  C. Burrus,et al.  Time domain design of recursive digital filters , 1970 .

[107]  J. Slaughter.  Quantization errors in digital control systems , 1964 .

[108]  Jerry D. Gibson,et al.  Digital speech analysis using sequential estimation techniques , 1975 .

[109]  Michael Athans,et al.  Survey of decentralized control methods for large scale systems , 1978 .

[110]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.

[111]  L. Silverman,et al.  Restoration of motion degraded images , 1975 .

[112]  D. Siljak.  Stability criteria for two-variable polynomials , 1975 .

[113]  L. Ljung,et al.  Scattering theory and linear least squares estimation: Part I: Continuous-time problems , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[114]  J. Mendel,et al.  SPECIAL ISSUE ON LINEAR-QUADRATIC-GAUSSJAN PROBLEM , 1971 .

[115]  Ya. Z. Tsypkin,et al.  A Criterion for Absolute Stability of Automatic Pulse Systems with Monotonic Characteristics of the Nonlinear Element , 1964 .

[116]  M. M. Sondhi,et al.  Image restoration: The removal of spatially invariant degradations , 1972 .

[117]  J. Rissanen,et al.  1972 IFAC congress paper: Partial realization of random systems , 1972 .

[118]  C. K. Yuen,et al.  Theory and Application of Digital Signal Processing , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[119]  R. E. Rink.  Optimal utilization of fixed-capacity channels in feedback control , 1973 .

[120]  I. Rhodes.  A tutorial introduction to estimation and filtering , 1971 .

[121]  B. Dickinson,et al.  Canonical matrix fraction and state-space descriptions for deterministic and stochastic linear systems , 1974 .

[122]  T. Claasen,et al.  Effects of quantization and overflow in recursive digital filters , 1976 .

[123]  Lennart Ljung,et al.  A Comparative Study of Recursive Identification Methods , 1974 .

[124]  E. Robinson,et al.  Recursive solution to the multichannel filtering problem , 1965 .

[125]  Anil K. Jain,et al.  Image Restoration, Modelling, and Reduction of Dimensionality , 1974, IEEE Transactions on Computers.

[126]  B. Dickinson,et al.  A minimal realization algorithm for matrix sequences , 1973, CDC 1973.

[127]  B.D.O. Anderson,et al.  Stabilization of certain two-dimensional recursive digital filters , 1977, Proceedings of the IEEE.

[128]  A. Habibi.  Two-dimensional Bayesian estimate of images , 1972 .

[129]  G. Johnson.  Comments on "Upper bound on dynamic quantization error in digital control systems via the direct method of Liapunov" , 1966 .

[130]  L. C. Wood,et al.  Seismic signal processing , 1975, Proceedings of the IEEE.

[131]  James Durbin,et al.  The fitting of time series models , 1960 .

[132]  Alan S. Willsky,et al.  Digital Signal Processing and Control and Estimation Theory: Points of Tangency, Areas of Intersection, and Parallel Directions , 1979 .

[133]  L. Ljung,et al.  Scattering theory and linear least squares estimation—Part I: Continuous-time problems , 1976, Proceedings of the IEEE.

[134]  M. Morf,et al.  Fast algorithms for recursive identification , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[135]  N. Nahi,et al.  Decision-directed recursive image enhancement , 1975 .

[136]  J. Makhoul,et al.  Linear prediction: A tutorial review , 1975, Proceedings of the IEEE.

[137]  C. K. Yuen,et al.  Digital Filters , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[138]  Guner S. Robinson,et al.  A survey ol digital picture coding , 1974, Computer.

[139]  Thomas Kailath,et al.  Partial Realization of Random Systems , 1972 .

[140]  J. Aggarwal,et al.  Picture processing using one-dimensional implementations of discrete planar filters , 1974 .

[141]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .