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Approximation by structured lower rank matrices

Approximation by structured lower rank matrices

引用

SPIE Conference on advanced signal processing algorithms, architectures, and implementations VIII

作者： Chu, MT Funderlic, RE Plemmons, RJ N Carolina State Univ Dept Math Raleigh NC 27695 USA

ISBN: (纸本)0819429163

We consider two general procedures for constructing the nearest approximation of a given matrix by one with any lower rank and any linear structure. Nearness can be measured in any matrix norm. Structured low rank matrices arise in various applications, including image enhancement and model reduction. In practice, the empirical data collected in the matrix often either do not maintain the specified structure or do not induce the desirable rank. It is an important task to search for the nearest structured lower rank approximation of a given matrix. The techniques developed in this paper can easily be implemented for numerical computation. In particular, it is shown that the computations can be approached using efficient optimization packages. The special case of Toeplitz structure using the Frobenius matrix norm is discussed in detail to illustrate the ideas, and numerical tests are reported. The procedures developed herein can be generalized to consider a much broader range of approximation problems.

关键词： Matrices signal processing MATLAB Optimization (mathematics) Image enhancement Computer programming Computer science Fourier transforms Image processing Mathematics

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VHDL token-based performance modeling for 2D and 3D infrared search and track processing

VHDL token-based performance modeling for 2D and 3D infrared...

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SPIE Conference on advanced signal processing algorithms, architectures, and implementations VIII

作者： Pauer, EK Pettigrew, MN Myers, CS Madisetti, VK Signal Proc Ctr Nashua NH 03061 USA

ISBN: (纸本)0819429163

This study develops and evaluates a new VHDL-based performance modeling capability for multiprocessor systems.* The framework for this methodology involved modeling the following system aspects: processor characterization, task modeling, network characterization, and data set size. Initially, all aspects are specified at an abstract) level, and eventually become specified at a detailed level through the process of verification and refinement of design assumptions. Processor characterization involves modeling the processor's speed, instruction set, and memory hierarchy. Task modeling is concerned with the execution time and instruction mix of software tasks within the system. Network characterization models bus protocols, topology, and bandwidths. Data set size refers to how much data is represented by the tokens used in the models. In this study, we applied and evaluated this methodology using both two-dimensional (2D) and three-dimensional (3D) infrared search and track (IRST) algorithms. Two different candidate processors were investigated: IBM PowerPC 604 and Texas Instruments TMS320C80. For the 2D IRST algorithm, the abstract and detailed performance modeling results were obtained far both processors using partitioned data and pipelined algorithmic approaches. For the 3D IRST algorithm, abstract performance models for pipelined and parallelized implementations on the PowerPC were developed. These models examined the feasibility of the implementations, the potential risk areas, and laid the groundwork for detailed performance modeling.

关键词： performance modeling VHDL IRST architectures simulation

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How bad are symmetric Pick matrices

How bad are symmetric Pick matrices

引用

Conference on advanced signal processing algorithms, architectures, and implementations X

作者： Fasino, D Olshevsky, V Univ Udine Dipartimento Matemat & Informat I-33100 Udine Italy

ISBN: (纸本)0819437611

Let P be a symmetric positive definite Pick matrix of order n. The following facts will be proven here: 1. P is the Gram matrix of a set of rational functions, with respect to a inner product defined in terms of a "generating function" associated to P;2. Its condition number is lower-bounded by a function growing exponentially in n. 3. P can be effectively preconditioned by the Pick matrix generated by the same nodes and a constant function.

关键词： Matrices Condition numbers algorithms Computing systems Control systems Image information entropy Linear algebra Mathematics Platinum signal processing

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INSTANTANEOUS QUANTITIES AND UNCERTAINTY CONCEPTS FOR signal DEPENDENT TIME-FREQUENCY DISTRIBUTIONS

INSTANTANEOUS QUANTITIES AND UNCERTAINTY CONCEPTS FOR SIGNAL...

引用

CONF ON advanced signal processing algorithms, architectures, AND implementations 2

作者： JONES, G BOASHASH, B Queensland Univ. of Technology (Australia)

ISBN: (纸本)0819406945

This paper presents a review of some concepts associated with time-frequency distributions-- the instantaneous frequency, group delay, instantaneous bandwidth, and marginal properties-- and generalizes them in time-frequency via rotation of coordinates. This work emphasizes the need to examine time-frequency distributions in the general time-frequency plane, rather than restricting oneself to a time and/or frequency framework. This analysis leads to a generalized uncertainty principle, which has previously been introduced in radar theory. This uncertainty principle is invariant under rotation in the time-frequency plane, and should be used instead of the traditional definition of Gabor. It is desired to smooth a time-frequency distribution that is an energy density function into one that is an energy function. Most distributions are combinations of density and energy functions but the Wigner-Ville distribution is purely a density function. By using a local version of the generalized uncertainty principle, the Wigner- Ville distribution is smoothed into a signal dependent spectrogram using an iterative algorithm. It is believed that this procedure may represent, in some way an optimum removal of signal uncertainty in the time-frequency plane.

关键词： Time-frequency analysis Smoothing signal processing Radar signal processing signal analyzers Fermium Frequency modulation Algorithm development Radar Detection theory

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Time-varying frequencies of a signal

Time-varying frequencies of a signal

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Conference on advanced signal processing - algorithms, architectures, and implementations VII

作者： Loughlin, PJ Univ. of Pittsburgh (United States)

ISBN: (纸本)0819425842

We consider the definition and interpretation of instantaneous frequency and other time-varying frequencies of a signal, and related concepts of instantaneous amplitude, instantaneous bandwidth and the time-varying spectrum of a signal. A definition for the average frequency at each time is given, and we show that spectrograms and Cohen-Posch time-frequency distributions can yield this result for the first conditional moment in frequency. For some signals this result equals the instantaneous frequency, but generally instantaneous frequency is not the average frequency at each time in the signal. We discuss monocomponent versus multicomponent signals, and give an estimate of the time-varying spectrum given the instantaneous frequencies and bandwidths of the components. We also consider the role of the complex signal in defining instantaneous amplitude, frequency and bandwidth, and ways to obtain a complex signal satisfying certain physical properties, given a real signal (or its time-varying spectrum). Depending upon the physical properties desired (e.g., the instantaneous amplitude of a magnitude-bounded signal should itself be bounded), one obtains different complex representations - and hence different instantaneous amplitudes, frequencies and bandwidths - of the given signal.

关键词： instantaneous frequency, bandwidth Hilbert transform analytic signal time-frequency conditional moments maximum entropy density

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A spectral phase algorithm for detecting and estimating pitch

A spectral phase algorithm for detecting and estimating pitc...

引用

Conference on advanced signal processing algorithms, architectures, and implementations XI

作者： Tempkin, JA Nelson, DJ USA Dept Def Ft George G Meade MD 20755 USA

ISBN: (纸本)0819441880

We describe a fast and efficient algorithm for automatic detection and estimation of the fundamental frequency F0 of a harmonic time-domain signal. The method is based on differentiation of the short time Fourier transform (STFT) phase, which is implemented as a cross-spectral product. In estimating and isolating the fundamental frequency, several enhancement processes are developed and applied to the TF surface to improve the signal quality. We describe the algorithm in detail and demonstrate the processing gain achieved at each step. In addition, we apply the algorithm to human speech to recover the pitch fundamental F0 and report the evaluation of the algorithm's performance on the Western Michigan vowel corpus [3].

关键词： signal processing

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GPU implementations for Fast Factorizations of STAP Covariance Matrices

GPU Implementations for Fast Factorizations of STAP Covarian...

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Conference on advanced signal processing algorithms, architectures, and Implementantions xvIII

作者： Roeder, Michael Davis, Nolan Furtek, Jeremy Braunreiter, Dennis Healy, Dennis Sci Applicat Int Corp 10260 Campus Point Dr San Diego CA 92121 USA DARPA Microsyst Technol Off Arlington VA 22203 USA

ISBN: (纸本)9780819472946

One of the main goals of the STAP-BOY program has been the implementation of a, space-time adaptive processing (STAP) algorithm on graphics processing units (GPUs) with the goal of reducing the processing time. Within the context of GPU implementation, we have further developed algorithms that exploit data redundancy inherent in particular STAP applications. Integration of these algorithms with GPU architecture is of primary importance for fast algorithmic processing times. STAP algorithms involve solving a linear system in which the transformation matrix is a covariance matrix. A standard method involves estimating a covariance matrix from a data matrix, computing its Cholesky factors by one of several methods. and then solving the system by substitution. Some STAP applications have redundancy in successive data matrices from which the covariance matrices are formed. For STAP applications in which a data matrix is updated with the addition of a new data row at the bottom and the elimination of the oldest data in the top of the matrix, a sequence of data matrices have multiple rows in common. Two methods have been developed for exploiting this type of data redundancy when computing Cholesky factors. These two methods are referred to as 1) Fast QR factorizations of successive data matrices 2) Fast Cholesky factorizations of successive covariance matrices. We have developed GPU implementations of these two methods. We show that these two algorithms exhibit reduced computational complexity when compared to benchmark algorithms that do not exploit data, redundancy. More importantly, we show that when these algorithmic improvements are optimized for the GPU architecture, the processing times of a GPU implementation of these matrix factorization algorithms may be greatly improved.

关键词： Covariance cholesky QR factorization GPGPU Space Time Adaptive processing (STAP) block update CUDA thread parallelism block parallelism

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A near canonic double-based number system (DBNS) with applications in digital signal processing 6

A near canonic double-based number system (DBNS) with applic...

引用

Conference on advanced signal processing algorithms, architectures, and implementations VI

作者： Dimitrov, V SadeghiEmamchaie, S Jullien, GA Miller, WC UNIV WINDSOR VLSIRES GRPWINDSORON N9B 3P4CANADA

ISBN: (纸本)0819422347

In this paper we explore a new number system which uses a double base. The representation of the numbers has a very simple geometric interpretation, allowing potentially fast implementation of the basic arithmetic operations. The transformation of the integers into minimal form, however, leads to some problems associated with transcendental number theory, and we identify and open the discussion on these problems. An intriguing implementation vehicle, which has some of the properties associated with symbolic substitution in optical computing, is the use of Cellular Neural Networks (CNNs) to perform digit reduction. Brief details are presented on CNN implementation, and a system-level example is shown in order to justify the applicability of the proposed theory in digital signal processing. © 1996 SPIE. All rights reserved.

关键词： number systems computer arithmetic number theory diophantine equations symbolic substitution Cellular Neural Networks digital filtering

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RECENT ADVANCES IN NONSTATIONARY signal ANALYSIS - TIME-VARYING HIGHER-ORDER SPECTRA AND MULTILINEAR TIME-FREQUENCY signal ANALYSIS 4

RECENT ADVANCES IN NONSTATIONARY SIGNAL ANALYSIS - TIME-VARY...

引用

4TH CONF ON advanced signal processing algorithms, architectures, AND implementations

作者： BOASHASH, B Queensland Univ. of Technology (Australia)

ISBN: (纸本)0819412767

This paper is written to provide both a historical review of past work and an overview of recent advances in time-frequency signal analysis and time-varying higher-order spectra. The paper is organized as follows: Section 1 discusses the need for time-frequency signal analysis (TFSA), as opposed to either time or frequency analysis. Section 2 covers the many faceted developments which occurred in TFSA in the 1980s and early 1990s. It covers bilinear or energetic time-frequency distributions (TFDs). Section 3 deals with a generalization of bilinear TFDs to multilinear Polynomial TFDs and their relationship to time-varying higher order spectra (TVHOS). Section 4 provides a coverage of the Wigner-Ville trispectrum, which is a particular TVHOS, used for analyzing signals affected by Gaussian multiplicative noise. Section 5 is devoted to conclusions.

关键词： Frequency modulation Fermium Interference (communication) Fourier transforms signal to noise ratio Time-frequency analysis signal analysis signal processing signal analyzers Nonlinear optics

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signal processing algorithms by permutation test in radar application 6

Signal processing algorithms by permutation test in radar ap...

引用

Conference on advanced signal processing algorithms, architectures, and implementations VI

作者： AlvarezVaquero, F SanzGonzalez, JL UNIV POLITECN MADRID ETSI TELECOMUNDEPT SIGNAL SYST & RADIOCOMMUNE-28040 MADRIDSPAIN

ISBN: (纸本)0819422347

A hypothesis H is parametric if every distribution from the process defined by H belongs to a family of distributions characterized by a finite number of parameters; on the other hand, if the distribution can not be defined by a finite number of parameters, the hypothesis is nonparametric. In this paper, we analyze a detector based on the optimum permutation test, applied to nonparametric radar detection which provide good performances without a large computational work, and we compare it with the parametric test and rank test in the Neyman-Pearson sense. The computational complexity of the detector is high and its implementation in real time is difficult, due to the number of operations increase with the factorial of the number of samples. Also, we present an algorithm that reduces the computational work required. We also present the detectability characteristic of the optimum permutation test against rank test and parametric test under Gaussian noise environments and different types of target models (nonfluctuating, Swerling I and Swerling II). The detection probability versus signal-to-noise ratio is estimated by Monte-Carlo simulations for different parameter values (N pulse, M reference samples and false alarm probability P_fa).

关键词： nonparametric permutation test rank test radar detection detectability target models

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