Thomas Kailath

Thomas Kailath
Stanford University | SU · Department of Electrical Engineering

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729
Publications
71,617
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52,522
Citations
Citations since 2016
0 Research Items
10468 Citations
201620172018201920202021202205001,0001,500
201620172018201920202021202205001,0001,500
201620172018201920202021202205001,0001,500
201620172018201920202021202205001,0001,500

Publications

Publications (729)
Article
Full-text available
In this paper, we present scalar implementations of multichannel fast Recursive Least-Squares algorithms in transversal filter form (so-called FTF algorithms). The point is that by processing the different channels sequentially, ie one at a time, the processing of any channel reduces to that of the single-channel algorithm. This sequential processi...
Article
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This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the...
Article
This paper reformulates the suboptimal (or level-gamma) H filtering problem into a Linear Matrix Inequality (LMI) problem by applying a bounded real lemma to the closed-loop transfer function. This formulation not only provides the condition of solvability but also constructs the suboptimal H filter. This formulation furthermore allows one to solve...
Article
In this paper, we identify a class of J-spectral factorization problems that can be cast in the form of ordinary spectral factorization problems. As a basic tool, we introduce the concept of Popov and dual Popov functions and study the relations between their J-spectral factorizations. Inertia relationships between the two Popov functions show that...
Article
Full-text available
We are deeply disturbed by the recent escalation of political assaults on scientists in general and on climate scientists in particular. All citizens should understand some basic scientific facts. There is always some uncertainty associated with scientific conclusions; science never absolutely proves anything. When someone says that society should...
Article
Full-text available
In this paper, we study the problem of linearly equalizing the multiple-input multiple-output (MIMO) communications channels from an H∞ point of view. H∞ estimation theory has been recently introduced as a method for designing filters that have acceptable performance in the face of model uncertainty and lack of statistical information on the exogen...
Chapter
In recent work, we have shown how least-squares estimation problems for arbitrary nonstationary processes can be speeded up by using the notion of an index of nonstationarity and a corresponding generalized Levinson algorithm. It was also shown that when the nonstationary processes have constant-parameter state-space models, the generalized Levinso...
Article
Full-text available
The optimal detection problem in multi-antenna wireless communication systems often reduces to the problem of finding the least-squares solution to a system of linear equations, where the unknown vector is comprised of integers, but the matrix coefficients and the given vector are real-valued. The problem is equivalent to finding the closest lattic...
Article
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1961. Vita. Includes bibliographical references (leaves 155-163). by Thomas Kailath. Sc.D.
Article
We show how to use the classical Schur algorithm to design multi-mirror optical interferometers (or filters). Our derivation is simple and straightforward, clearly revealing its connection to the previously known orthogonal digital filter structures. We also give a complete detailed description of an FFT-based algorithm for the reciprocal polynomia...
Article
A thermal system is developed to rapidly characterize the linewidth sensitivity of advanced resists to process temperature variations in the photolithographic manufacturing sequence. This thermal array consists of a 77 grid of individually programmable heating zones distributed within a thermal cycling apparatus. It is used to improve the quality a...
Article
We study the design of synthesis filters in noisy filter bank systems using an H∞ estimation point of view. The H∞ approach is most promising in situations where the statistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank is unknown, or is too difficult to model and analyze. For t...
Article
Full-text available
In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiantenna systems employing space-time codes, however, it is not clear what is the best way to obtain the soft information required of the iterative scheme with low complexity. In this paper,...
Article
Full-text available
Communication systems transmitting over frequency-selective channels generally employ an equalizer to recover the transmitted sequence corrupted by intersymbol interference (ISI). Most practical systems use a training sequence to learn the channel impulse response and thereby design the equalizer. An important issue is determining the optimal amoun...
Article
A design procedure for feedforward filters is proposed to improve the tracking performance of existing closed-loop systems. A parametric model is not required because it directly utilizes the frequency response of the closed-loop system, which can be measured accurately. This frequency-shaping approach enables the tradeoff between the quality of mo...
Article
This paper proposes the use of multivariable control methods to design a thermal platform for processing semiconductor substrates (semiconductor wafers and/or quartz reticles for photomasks) that far exceeds conventional methods in performance and flexibility. A thermal processing module for lithography applications is presented and demonstrated. T...
Article
Full-text available
As an alternative to existing techniques and algorithms, we investigate the merit of the H # approach to the linear equalization of communication channels. We first give the formulation of all causal H # equalizers using the results of [1] and then look at the finite delay case. We compare the risk sensitive, H # equalizer with the MMSE equalizer w...
Article
Full-text available
We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an H∞ estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H∞ optimal DFEs. In particular, we show that, under t...
Article
A thermal array, which consists of a dense distribution of multivariate controlled heat/chill elements, is developed to achieve temperature uniformity of a quartz photomask throughout the processing temperature cycle of ramp, hold and quench. The thermal array spatially tunes the uniformity in response to calibrated feedback provided by temperature...
Conference Paper
Summary form only given. A "sphere decoding" algorithm is suggested for finding the ML solution with a specified (high) probability; it is closely related to the Wozencraft sequential decoding algorithm. Closed-form expressions for the expected complexity are then found by using and extending some classical number-theoretic results and techniques....
Article
We approach "nite impulse response (FIR) equalization problem from an H# perspective. First, we formulate the calculation of the optimal H# performance for a given equalization setting as a semide"nite programming (SDP) problem. H# criterion provides a set of FIR equalizers with di!erent optimality properties. Among these, we formulate the calculat...
Article
We approach the Multiple Input Multiple Output (MIMO) decision feedback equalization problem in digital communications from an H # estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H # optimal decision feedback equalizers. In particular we...
Article
A temperature processing module and control system is presented for the thermal cycling of substrates such as semiconductor wafers and/or quartz photomasks. The module consists of a multizone etched foil heater adhered to the surface of a fluid heat exchanger. The heat exchanger is designed with aluminum foam that enables an angularly uniform tempe...
Article
The two-dimensional tracking problem in a clutter environment is solved in the discrete-time Bayes optimal (nonlinear, and non-Gaussian) estimation framework. The proposed method recursively finds the probability density functions of the target position and velocity. With our approach, the nonlinear estimation problem is converted into simpler line...
Article
Since Tong et al, (1991) demonstrated the feasibility of identifying possibly nonminimum phase channels using second-order statistics, considerable research activity, both in algorithm development and fundamental analysis, has been seen in the area of blind identification of multiple FIR channels. Many of the recently developed approaches invoke, e...
Article
Full-text available
Three fast O(n2) algorithms for solving Cauchy linear systems of equations are proposed. A rounding error analysis indicates that the backward stability of these new Cauchy solvers is similar to that of Gaussian elimination, thus suggesting to employ various pivoting techniques to achieve a favorable backward stability. It is shown that Cauchy stru...
Article
This paper deals with a general matrix extension problem with structural constraints and provides a recursive solution in terms of an inverse scattering experiment. Both the stationary and nonstationary cases are considered, in addition to connections to tensor algebra.
Article
J. P. Burg gave a now-famous solution of the problem of finding the maximum-entropy extension of a section {c o, c 1,…, c n } of a scalar (stationary) covariance sequence, with a nice interpretation in terms of the reflection coefficients of an associated discrete transmission line: namely, that the maximum-entropy extension is obtained by adding t...
Article
Spectral factorization is a crucial step in the solution of linear quadratic estimation and control problems. It is no wonder that a variety of methods has been developed over the years for the computation of canonical spectral factors. This paper provides a survey of several of these methods with special emphasis on clarifying the connections that...
Article
We approach finite impulse response (FIR) equalization problem from an H ∞ perspective. First, we formulate the calculation of the optimal H ∞ performance for a given equalization setting as a semidefinite programming (SDP) problem. H ∞ criterion provides a set of FIR equalizers with different optimality properties. Among these, we formulate the ca...
Article
Full-text available
We use a displacement structure approach to design a class of new preconditioners for the conjugate gradient method applied to the solution of large Toeplitz linear equations. Explicit formulas are suggested for the G.Strang-type and for the T.Chan-type preconditioners belonging to any of eight classes of matrices diagonalized by the corresponding...
Article
In an earlier paper we exploited the displacement structure of Cauchy-like matrices to derive for them a fast O(n2) implementation of Gaussian elimination with partial pivoting. One application is to the rapid and numerically accurate solution of linear systems with Toeplitz-like coefficient matrices, based on the fact that the latter can be transf...
Conference Paper
Full-text available
Many communications systems employ training, ie, the transmission of known signals, so that the channel parameters may be learned at the receiver. This has a dual effect: too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We use an information-theo...
Article
We consider the design of synthesis filters in noisy filter bank system, using an exponential-quadratic criterion. We assume that the analysis filters have been design to achieve good coding of the input signal. Then we design the synthesis filters to minimize reconstruction error according to the adopted criterion. When the synthesis filters are r...
Article
Full-text available
This report summarizes the results associated with instrumentation purchased under DURIP contract F49620-98-1-0263 in support of AFOSR/DARPA MURI Program on 'Multivariable Control, Simulation, Optimization, and Signal Processing for the Microlithographic Process'. This project is generally concerned with the application of systems techniques to the...
Article
We have built a spacecraft simulator which displays realistic graphics in real-time on an inexpensive personnel computer (PC). The dynamics of the spacecraft, the positions of the sun, the moon and the earth, and the direction of stars are calculated accurately. The primary use of the simulator would be in the education of statistical signal proces...
Article
This paper derives an expression for the optimal error nonlinearity in adaptive filter design. Using an energy conservation relation, and some typical assumptions, the choice of the error function is optimized by minimizing the mean-square deviation subject to a fixed rate of convergence. The resulting optimal choice is shown to subsume earlier res...
Article
Full-text available
Many problems in linear prediction, signal processing digital filtering and in several other areas can be formulated in terms of structured matrices and their inverses. Most of the algorithms which respect the structure in Matrices suffer from propagation of round-off errors. Hence all the prevalent mathematical software tools explore structure ign...
Article
: This paper formulates and solves a parameter estimation problem that shows how to combine, in a certain optimal and robust manner, measurements that arise from a finite collection of uncertain models. This scenario occurs, for example, in data fusion applications and in cases that involve systems that can operate under different failure condition...
Article
Full-text available
We describe a novel approach to analytic rational interpolation problems of the Hermite-Fejer type, ba,sed on the fast generalized Schur algorithm for the recursive triangular factorization of structured matrices. We use the interpolation data to construct a convenient so-called generator for the factorization algorithm. The recursive algorithm the...
Article
. In this survey paper, we describe how strands of work important in two different fields, matrix theory and complex function theory, have come together in some work on fast computational algorithms for matrices with what we have called displacement structure. In particular, a fast triangularization procedure can be developed for such matrices, gen...
Article
Introduction Wilhelm Cauer was a pioneer in the development of modern theories of network synthesis. After early contributions to the theory of synthesis of two-terminal networks [1], he made a visit to MIT (the Massachusetts Institute of Technology) where he inspired the famous thesis of O. Brune [2]. Here it was shown that impedance functions of...
Article
The literature contains several recent fast algorithms for the triangular factorization of strongly regular Toeplitz-plus-Hankel matrices. In this paper we study the rather more general sum of quasi-Toeplitz and quasi-Hankel matrices, both Hermitian and non-Hermitian. Quasi-Toeplitz and quasi-Hankel matrices are those that are congruent to Toeplitz...
Article
. We present a new approach to the discrete-time Chandrasekhar recursions and some generalizations thereof. We extend the recursions to a class of structured time-variant state-space models, and discuss connections with the (generalized) Schur algorithm. We also apply the extended recursions to the adaptive filtering problem and give a transparent...
Article
Full-text available
An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recursive procedure admits a physical interpretation in terms of discretized transmission lines. In...
Article
Full-text available
We study the relation between the solutions of two estimation problems with indefinite quadratic forms. We show that a complete link between both solutions can be established by invoking a fundamental set of inertia conditions. While these inertia conditions are automatically satisfied in a standard Hilbert space setting, they nevertheless turn out...
Article
We introduce a generalized displacement structure that includes a variety of previously studied cases, and leads to a unified approach to fast O(n 2 ) algorithms for the triangular factorization of structured matrices such as Toeplitz-like and Hankel-like structures. The algorithm is derived through a recursive state-space procedure and can be used...
Article
Full-text available
We develop array algorithms for H<sup>∞</sup> filtering. These algorithms can be regarded as the Krein space generalizations of H <sup>2</sup> array algorithms, which are currently the preferred method fur implementing H<sup>2</sup> filters. The array algorithms considered include two main families: square-root array algorithms, which are typically...
Article
In this paper we develop array algorithms for H-infinity filtering. These algorithms can be regarded as the Krein space generalizations of H-2 array algorithms, which are currently the preferred method for implementing H-2 biters, The array algorithms considered include typo main families: square-root array algorithms, which are typically numerical...
Conference Paper
We study the design of synthesis filters in noisy filter bank systems using an H^∞ estimation point of view. The H^∞ approach is most promising in situations where the statistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank are unknown, or are too difficult to model and analyze. F...
Conference Paper
Full-text available
This paper derives an expression for the optimal error nonlinearity in adaptive filter design. Using an energy conservation relation, and some typical assumptions, the choice of the error function is optimized by minimizing the mean-square deviation subject to a fixed rate of convergence. The resulting optimal choice is shown to subsume earlier res...
Conference Paper
We have built a spacecraft simulator which displays realistic graphics in real-time on inexpensive personal computers. The dynamics of the spacecraft, the positions of the Sun, the Moon and the Earth, and the direction of stars are calculated accurately. The primary use of the simulator would be in the education of statistical signal processing and...
Conference Paper
Full-text available
We study the design of multiuser detectors from an H/sup /spl infin// point of view. The H/sup /spl infin// approach is most appropriate in the situations where the statistical properties of the disturbances are not known or are too hard to model and analyze. The design of the H/sup /spl infin// optimal FIR multiuser detectors can be efficiently pe...
Conference Paper
Full-text available
We propose a new space-time multiuser receiver for CDMA wireless systems. The receiver is based on the fixed-lag smoothed estimator which occurs in the well-researched area of state-space estimation. The receiver can work with long codes as opposed to most other multiuser detectors that require cyclic spreading codes. It is also naturally suited fo...
Article
We study the design of synthesis filters in noisy filter bank systems using an H/sup /spl infin// estimation point of view. The H/sup /spl infin// approach is most promising in situations where the statistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank are unknown, or are too dif...
Article
Full-text available
This paper addresses the problem of blind channel equalization in the context of digital communications. Recent results have shown that certain operations applied to the source signal at the transmitter help in the blind identification and equalization of the channel at the receiver. For example, cyclostationarity is induced by multiplying the base...
Article
As an alternative to existing techniques and algorithms, we investigate the merit of the approach to the linear equalization of com- munication channels. We first give the formulation of all causal equal- izers using the results of and then look at the finite delay case. We compare the risk-sensitive equalizer with the MMSE equalizer with respect t...
Article
The solution of H ∞ problems requires the determination of contractive operators that map certain input signals to certain output signals. Such operators, and tests for their contractiveness, arise naturally in a scattering formulation of the generalized Schur algorithm, which is an efficient procedure for the triangular factorization of matrices w...
Conference Paper
We approach FIR equalization problem from an H∞ perspective. First, we formulate the calculation of the optimal H∞ performance for a given equalization setting as a semidefinite programming (SDP) problem. H∞ criterion provides a set of FIR equalizers with different optimality properties. Among these, we formulate the calculation of risk sensitive o...
Chapter
The sections in this article are
Article
We propose a new fast O(n2) parallel algorithm for solving Cauchy systems of linear equations. We perform an a priori rounding error analysis and obtain componentwise bounds for the forward, backward and residual errors. These bounds indicate that for the class of totally positive Cauchy matrices the new algorithm is forward and backward stable, pr...
Article
Spatial and transient control of temperature trajectories by a new thermal cycling module is presented, with a focus on photoresist processing applications for semiconductor wafers and quartz reticles. In the proposed unit, the bake and chill steps are conducted sequentially within the same module without any substrate movement. The unit includes t...
Article
Decentralized control is shown through analysis and experimentation to be an appropriate strategy for wafer temperature control in certain multizone rapid thermal processing (RTP) systems. An input-output controllability analysis is conducted to illustrate that the direction associated with the reference command (set-point) corresponding to a spati...
Article
A thermal cycling system for baking and chilling semiconductor wafers is presented for photoresist processing applications. The proposed unit differs from conventional systems as the bake and chill steps are conducted sequentially within the same module without substrate movement. The unit includes a circulating fluid that can be switched between h...
Conference Paper
We study the design of synthesis filters in noisy filter bank systems using an H<sup>∞</sup> point of view. For unitary analysis polyphase matrices we obtain an explicit expression for the minimum achievable disturbance attenuation. Numerical examples and comparisons with existing methods are also included
Conference Paper
The lithography process is the critical step in the fabrication of nanostructures for integrated circuit manufacturing. In this paper, a summary is presented of several projects applying control and signal processing techniques to lithography. We begin with a discussion of areas in the optical exposure process where systems techniques make a signif...
Conference Paper
A mixed H<sub>2</sub>/H<sub>∞</sub> controller minimizes the H<sub>2</sub> norm of a closed-loop map over all admissible controllers while satisfying an H<sub>∞</sub> constraint on another closed-loop map. In the paper we develop an efficient iterative algorithm for numerical computation of the fixed-order mixed controllers. In the proposed techniq...
Conference Paper
An overview is given describing applications of multivariable control, signal processing, optimization, modeling and computation to the lithography sequence. We discuss areas in the patterning process where mathematical methods can play a significant role including optical proximity correction, phase shifting mask design, alignment, and stage contr...
Conference Paper
An overview is given describing applications of multivariable control, signal processing, optimization, modeling and computation to the lithography sequence. We discuss areas in the patterning process where mathematical methods can play a significant role including optical proximity correction, phase shifting mask design, alignment, and stage contr...
Conference Paper
An efficient and numerically-stable implementation of a class of adaptive beamforming algorithms is presented. The method is based on a variant of the URV factorization, and is particularly useful when the effective rank of the data matrix is smaller than the number of antenna elements, which is usually the case when the number of signal sources is...
Conference Paper
We present a Schur type algorithm with O(n<sup>2</sup>) operations for the triangular factorization of n×n ill-conditioned Hankel matrices. The proposed algorithm gives the factorization result almost as good as that of the more expensive Gaussian elimination algorithm with the partial pivoting
Article
A technique is proposed for estimating the parameters of two-dimensional (2-D) uniform motion of multiple moving objects in a scene, based on long-sequence image processing and the application of a multiline fitting algorithm. Plots of the vertical and horizontal projections versus frame number give new images in which uniformly moving objects are...
Article
An abstract is not available.
Article
Currently, the preferred method for implementing H2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the c...
Article
This monograph presents a unified mathematical framework for a wide range of problems in estimation and control. The authors discuss the two most commonly used methodologies: the stochastic H^2 approach and the deterministic (worst-case) H∞ approach. Despite the fundamental differences in the philosophies of these two approaches, the authors have d...
Article
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Nombrado Doctor Honoris Causa en el acto del día de la Universidad del curso 98/99
Article
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This paper reviews two streams of development, from the 1940's to the present, in signal detection theory: the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance. This treatme...
Conference Paper
We study the problem of linear equalization from an H<sup>∞ </sup> point of view and parameterize, in closed form, all possible H <sup>∞</sup>-optimal equalizers. The results indicate an interesting dichotomy between minimum phase and non-minimum phase channels: for minimum phase channels the best causal equalizer performs as well as the best nonca...
Conference Paper
Full-text available
Summary form only given. The famous matched filter solution for maximizing the output SNR of a known signal in additive white noise was independently discovered by several investigators in the mid-forties. Since then it has appeared as a key component of optimal detectors in a variety of scenarios. Its first appearance was perhaps in D.O. North's 1...
Article
The authors present the analysis of the asymptotic stability of multiple slope-restricted nonlinear (Lur'e) systems. By providing a Lyapunov function, they obtain a matrix-language criterion in terms of algebraic Riccati equations and linear matrix inequalities, which are discussed at the point of computational issues. Additionally, they consider t...
Article
Full-text available
The signal-to-noise ratio (SNR) and signal bandwidth have been viewed as the dominant factors determining the channel capacity. In wireless communications, the channel capacity can be increased for a given SNR and a given spectral region, by exploiting the spatial diversity provided by the use of multiple antennas and transceivers at a base station...
Conference Paper
Despite advances in robust control theory, the robust performance problem formulated in the mixed H_2/H_∞ framework largely remains an open problem. In this approach, one seeks a controller that minimizes the H_2 norm of a closed-loop map over all admissible controllers while satisfying an H_∞ constraint on another closed-loop map. Unlike the optim...
Conference Paper
Full-text available