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Bibliography: l. 124-125

We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt breakdown of linear model selection, robust data fitting or compressed sensing reconstructions, when the complexity of the model or the number of outliers increases beyond a threshold. In combinatorial geometry these transitions appear as abrupt changes in the properties of face counts of convex polytopes when the dimensions are varied. The thresholds in these very different problems appear in the same critical locations after appropriate calibration of variables. These thresholds are important in each subject area: for linear modelling, they place hard limits on the degree to which the now-ubiquitous high-throughput data analysis can be successful; for robustness, they place hard limits on the degree to which standard robust fitting methods can tolerate outliers before breaking down; for compressed sensing, they define the sharp boundary of the undersampling/sparsity tradeoff in undersampling theorems. Existing derivations of phase transitions in combinatorial geometry assume the underlying matrices have independent and identically distributed (iid) Gaussian elements. In applications, however, it often seems that Gaussianity is not required. We conducted an extensive computational experiment and formal inferential analysis to test the hypothesis that these phase transitions are {\it universal} across a range of underlying matrix ensembles. The experimental results are consistent with an asymptotic large-$n$ universality across matrix ensembles; finite-sample universality can be rejected.

We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt breakdown of linear model selection, robust data fitting or compressed sensing reconstructions, when the complexity of the model or the number of outliers increases beyond a threshold. In combinatorial geometry these transitions appear as abrupt changes in the properties of face counts of convex polytopes when the dimensions are varied. The thresholds in these very different problems appear in the same critical locations after appropriate calibration of variables. These thresholds are important in each subject area: for linear modelling, they place hard limits on the degree to which the now-ubiquitous high-throughput data analysis can be successful; for robustness, they place hard limits on the degree to which standard robust fitting methods can tolerate outliers before breaking down; for compressed sensing, they define the sharp boundary of the undersampling/sparsity tradeoff in undersampling theorems. Existing derivations of phase transitions in combinatorial geometry assume the underlying matrices have independent and identically distributed (iid) Gaussian elements. In applications, however, it often seems that Gaussianity is not required. We conducted an extensive computational experiment and formal inferential analysis to test the hypothesis that these phase transitions are {\it universal} across a range of underlying matrix ensembles. The experimental results are consistent with an asymptotic large-$n$ universality across matrix ensembles; finite-sample universality can be rejected.

We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt breakdown of linear model selection, robust data fitting or compressed sensing reconstructions, when the complexity of the model or the number of outliers increases beyond a threshold. In combinatorial geometry these transitions appear as abrupt changes in the properties of face counts of convex polytopes when the dimensions are varied. The thresholds in these very different problems appear in the same critical locations after appropriate calibration of variables. These thresholds are important in each subject area: for linear modelling, they place hard limits on the degree to which the now-ubiquitous high-throughput data analysis can be successful; for robustness, they place hard limits on the degree to which standard robust fitting methods can tolerate outliers before breaking down; for compressed sensing, they define the sharp boundary of the undersampling/sparsity tradeoff in undersampling theorems. Existing derivations of phase transitions in combinatorial geometry assume the underlying matrices have independent and identically distributed (iid) Gaussian elements. In applications, however, it often seems that Gaussianity is not required. We conducted an extensive computational experiment and formal inferential analysis to test the hypothesis that these phase transitions are {\it universal} across a range of underlying matrix ensembles. The experimental results are consistent with an asymptotic large-$n$ universality across matrix ensembles; finite-sample universality can be rejected.

The purpose of this thesis is to investigate the state of the art of radar signal design as well as radar signal processors and determine the actual trends in modern radar design. The use of a digital general purpose radar signal processor is discussed. The concepts of ambiguity and auto-correlation function are investigated in regard to radar resolution capabilities. the concept and analytical development of the DFT/FFT are presented. Quantization noise in a digital MTI processor and its effects in the improvement factor are analyzed. Optimization techniques for the response curve of digital MTI processors using staggered PRF are investigated. The SAR concept and analysis as well as techniques to obtain low correlator rates in the SAR digital processors are presented.

This report describes our research activities under SRO project, performed by University of Southern California, Naval Ocean System Center, Hughes Research Laboratories, Univ. of Calif., San Diego, Standford University and Integrated Systems, Inc., for the period 1 March 1981 to 28 February 1982 with the Office of Naval Research. This research activities have focussed on the VLSI signal processing theory and algorithms and the development of parallel computing architectures. A solution in today's VLSI research challenge lies in a cross-disciplinary research encompassing the areas of mathematics, algorithms, computers and applications. To this end, this report summarizes two parallel major research tasks: (1) Signal processing algorithm and theory - emphasizing spectral analysis and its applications; and (2) parallel computing structures - utilizing VLSI potential for high-speed signal processing.

This report describes our research activities under SRO project, performed by University of Southern California, Naval Ocean System Center, Hughes Research Laboratories, Univ. of Calif., San Diego, Standford University and Integrated Systems, Inc., for the period 1 March 1981 to 28 February 1982 with the Office of Naval Research. This research activities have focussed on the VLSI signal processing theory and algorithms and the development of parallel computing architectures. A solution in today's VLSI research challenge lies in a cross-disciplinary research encompassing the areas of mathematics, algorithms, computers and applications. To this end, this report summarizes two parallel major research tasks: (1) Signal processing algorithm and theory - emphasizing spectral analysis and its applications; and (2) parallel computing structures - utilizing VLSI potential for high-speed signal processing.

This report describes our research activities under SRO project, performed by University of Southern California, Naval Ocean System Center, Hughes Research Laboratories, Univ. of Calif., San Diego, Standford University and Integrated Systems, Inc., for the period 1 March 1981 to 28 February 1982 with the Office of Naval Research. This research activities have focussed on the VLSI signal processing theory and algorithms and the development of parallel computing architectures. A solution in today's VLSI research challenge lies in a cross-disciplinary research encompassing the areas of mathematics, algorithms, computers and applications. To this end, this report summarizes two parallel major research tasks: (1) Signal processing algorithm and theory - emphasizing spectral analysis and its applications; and (2) parallel computing structures - utilizing VLSI potential for high-speed signal processing.

This report describes our research activities under SRO project, performed by University of Southern California, Naval Ocean System Center, Hughes Research Laboratories, Univ. of Calif., San Diego, Standford University and Integrated Systems, Inc., for the period 1 March 1981 to 28 February 1982 with the Office of Naval Research. This research activities have focussed on the VLSI signal processing theory and algorithms and the development of parallel computing architectures. A solution in today's VLSI research challenge lies in a cross-disciplinary research encompassing the areas of mathematics, algorithms, computers and applications. To this end, this report summarizes two parallel major research tasks: (1) Signal processing algorithm and theory - emphasizing spectral analysis and its applications; and (2) parallel computing structures - utilizing VLSI potential for high-speed signal processing.

This report describes our research activities under SRO project, performed by University of Southern California, Naval Ocean System Center, Hughes Research Laboratories, Univ. of Calif., San Diego, Standford University and Integrated Systems, Inc., for the period 1 March 1981 to 28 February 1982 with the Office of Naval Research. This research activities have focussed on the VLSI signal processing theory and algorithms and the development of parallel computing architectures. A solution in today's VLSI research challenge lies in a cross-disciplinary research encompassing the areas of mathematics, algorithms, computers and applications. To this end, this report summarizes two parallel major research tasks: (1) Signal processing algorithm and theory - emphasizing spectral analysis and its applications; and (2) parallel computing structures - utilizing VLSI potential for high-speed signal processing.

Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered.

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Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered.

Modern Signal Processing

Modern signal processing technique for optimal signal to noise ratios - Princeton Applied Research Corp. 1963

The broad range of the presentations in the workshop can roughly be divided into three main categories: (A) Signal processing methods and architectures: This category is subdivided into: (1) modern signal processing, (2) signal processing architectures and the speech processing architectures, (3) image processing, recognition and analysis, and (4) implementation of signal processors. (B) Parallel processors: algorithms, languages, and architectures: This category is subdivided into: (1) systolic processors, (2) Fault tolerant computing structures, (3) reconfiguration and partitioning (4) numerical algorithms and arithmetics and (5) language and formal descriptions, and (C) VLSI and Signal processing: As the central theme of the workshop, this issue has been, at least partially, addressed by all the papers. However, there are several of them more directly confronting the issue.

The semiconductor manufacturing industry faces the need for tighter control of thermal budget and process variations as circuit feature sizes decrease. Strategies to meet this need include supervisory control, run-to-run control, and real-time feedback control. Typically, the level of control chosen depends upon the actuation and sensing available. Rapid Thermal (RTP) is one step of the manufacturing cycle requiring precise temperature control and hence real-time feedback control. At the outset of this research, the primary ingredient lacking from in-situ RTP temperature control was suitable sensor. This research looks at an alternative to the traditional approach of pyrometry, which is limited by the unknown and possibly time-varying wafer emissivity. the technique is based upon the temperature dependence of the propagation time of an acoustic wave in the wafer. The aim of this thesis is to demonstrate that ultrasonic sensors are a viable sensor for control in RTP. To do this, an experimental implementation was developed at the Center for Integrated Systems. Because of the difficulty in applying a known temperature standard in an RTP environment, calibration to absolute temperature is nontrivial Given reference propagation delays, multivariable model-based feedback control is applied to the system. The modelling and implementation details are described. The control techniques have been applied to a number of research processes including rapid thermal annealing and rapid thermal crystallization of thin silicon films on quartz/glass substrates.

In this paper, two modern adaptive signal processing techniques, Empirical Intrinsic Geometry and Synchrosqueezing transform, are applied to quantify different dynamical features of the respiratory and electroencephalographic signals. We show that the proposed features are theoretically rigorously supported, as well as capture the sleep information hidden inside the signals. The features are used as input to multiclass support vector machines with the radial basis function to automatically classify sleep stages. The effectiveness of the classification based on the proposed features is shown to be comparable to human expert classification -- the proposed classification of awake, REM, N1, N2 and N3 sleeping stages based on the respiratory signal (resp. respiratory and EEG signals) has the overall accuracy $81.7\%$ (resp. $89.3\%$) in the relatively normal subject group. In addition, by examining the combination of the respiratory signal with the electroencephalographic signal, we conclude that the respiratory signal consists of ample sleep information, which supplements to the information stored in the electroencephalographic signal.