Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Enhanced poisson sum representation for alpha-stable processes

In this paper we present Poisson sum series representations for α-stable (αS) random variables and a-stable processes, in particular concentrating on continuous-time autoregressive (CAR) models driven by α-stable Lévy processes. Our representations aim to provide a conditionally Gaussian framework, which will allow parameter estimation using Rao-Blackwellised versions of state of the art Bayesian computational methods such as particle filters and Markov chain Monte Carlo (MCMC). To overcome the issues due to truncation of the series, novel residual approximations are developed. Simulations demonstrate the potential of these Poisson sum representations for inference in otherwise intractable α-stable models. © 2011 IEEE.

Statistical signal extraction using stable processes

The standard models for statistical signal extraction assume that the signal and noise are generated by linear Gaussian processes. The optimum filter weights for those models are derived using the method of minimum mean square error. In the present work we study the properties of signal extraction models under the assumption that signal/noise are generated by symmetric stable processes. The optimum filter is obtained by the method of minimum dispersion. The performance of the new filter is compared with their Gaussian counterparts by simulation.

Modeling high-speed network traffic with truncated α-stable processes

It has been reported that high-speed communication network traffic exhibits both long-range dependence (LRD) and burstiness, which posed new challenges in network engineering. While many models have been studied in capturing the traffic LRD, they are not capable of capturing efficiently the traffic impulsiveness. It is desirable to develop a model that can capture both LRD and burstiness. In this letter, we propose a truncated a-stable LRD process model for this purpose, which can characterize both LRD and burstiness accurately. A procedure is developed further to estimate the model parameters from real traffic. Simulations demonstrate that our proposed model has a higher accuracy compared to existing models and is flexible in capturing the characteristics of high-speed network traffic. © 2012 Springer-Verlag GmbH.

(G, λ)-Extremal Processes and Their Relationship with Max-Stable Processes

2000 Mathematics Subject Classification: 60G70, 60G18.

A new approach to control of MIMO processes with static nonlinearities using an extended IMC framework

In this paper, a new control design method is proposed for stable processes which can be described using Hammerstein-Wiener models. The internal model control (IMC) framework is extended to accommodate multiple IMC controllers, one for each subsystem. The concept of passive systems is used to construct the IMC controllers which approximate the inverses of the subsystems to achieve dynamic control performance. The Passivity Theorem is used to ensure the closed-loop stability. (c) 2005 Elsevier Ltd. All rights reserved.

Risk Measures for Classical and Perturbed Risk Processes - a Survey

2000 Mathematics Subject Classification: 60B10, 60G17, 60G51, 62P05.

Estudo de uma metodologia para estabilização de processos

Para competir em nível internacional, as empresas brasileiras precisam atingir padrões de excelência em qualidade. Uma forma de atingir esses padrões é utilizando ferramentas de controle de qualidade que asseguremprocessos estáveis e capazes. A presente dissertação tem como objetivo principal o desenvolvimento de uma metodologia de estabilização de processos voltada às empresas de manufatura utilizando ferramentas de controle de qualidade. Sua importância está em apresentar uma metodologia que auxilie as empresas na obtenção de melhorias significativas em qualidade e produtividade. O método de trabalho utilizado envolveu as etapas de revisão da literatura, acompanhamento e análise da implantação de uma metodologia de estabilização de processos em uma empresa siderúrgica e, finalmente, proposta e discussão de uma nova metodologia de estabilização de processos.

Influência do tipo de chanfro, tecimento e sentido de laminação na distorção angular em soldagem GMAW-P robotizada de alumínio

The industry's interest in having a greater control of the deformations caused by welding is due to the geometric and dimensional tolerances been more and more precise in the project specifications, motivating the manufacturing engineering to develop stable processes and to ensure routine production. Aiming at it, the main goal of this present work is to analyze how much routine situations used in automatic aluminum welding can influence on the angular deformations of this material. Using the alloy AA 5052 H34, and the automatic welding in pulsed GMAW process, three types of weaving were applied throughout the length of the weld, in butt joints assembled without groove and with 60 degrees single-V-groove, arranged transversely as well as longitudinally to the rolling direction of the plate. The measurement of the deformations was made by a three-dimensional equipment, before and after the welding, in three distinct regions in the specimens. The profile of the weld bead was the main factor for the different types of deformations found, as revealed by macrographical analysis. The 60 degrees single-V-groove had higher amplitudes of deformations as the joint without groove. The torch oscillation wasn't a variable of statistically significant influence on this amplitudes.

Soldagem GMAW-P robotizada de alumínio: influência do tipo de chanfro, tecimento e sentido de laminação na distorção

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)