Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

An Updated Vision of Discrete-Time Fractional Models

A few days before the end of the revision procedure, my friend J. Tenreiro Machado had a sudden cardio-respiratory arrest and died. Here I want to express my gratitude and tribute to a great man and scientist. He was a very friendly and helpful person, with an unusual work capacity that allowed him to publish interesting articles on a wide range of topics. Publisher Copyright: © 2001-2012 IEEE.Two different approaches for describing discrete-time fractional linear systems are presented. The first is based on the nabla and delta discrete-time derivatives. In this case, suitable exponentials are introduced and used to define discrete Laplace transforms. The second approach is based on the bilinear (Tustin) transformations. For both cases, appropriate algorithms for obtaining the impulse, step, and frequency responses are presented. The state-variable representation is also analysed.authorsversionpublishe

Algorithms in time series

The use of finitely parametrized linear models such as ARMA models in analysing time series data has been extensively studied and in recent years there has been an increasing emphasis on the development of fast regression—based algorithms for the problem of model identification. In this thesis we investigate the statistical properties of pseudo—linear regression algorithms in the context of off-line and online (real-time) identification. A review of these procedures is presented in Part I in relation to the problem of identifying an appropriate ARMA model from observed time series data. Thus, criteria introduced by Akaike and Rissanen are important here to ensure a model of sufficient complexity is selected, based on the data. In chapter 1 we survey published results pertaining to the statistical properties of identification procedures in the off-line context and show there are important differences as concerns the asymptotic performance of certain parameter estimation algorithms. However, to effect the identification process in real-time recursive estimation algorithms are required. Furthermore, these procedures need to be adaptive to be applicable in practice. This is discussed in chapter 2. Technical results and limit theorems required for the theoretical analysis conducted in Part II are collated in chapter 3. Chapters 4 and 5 of Part II are therefore devoted to the detailed investigation of particular algorithms discussed in Part I. Chapter 4 deals with off-line parameter estimation algorithms and in chapter 5, the important idea of a Description Length Principle introduced by Rissanen, is examined in the context of the recursive estimation of autoregressions. Empirical evidence from simulation experiments are also reported in each chapter and in chapter 5, aspects of speech analysis are incorporated in the simulation study. The simulation results bear out the theory and the proofs of asymptotic results are given at the end of the chapter

Some fast algorithms in signal and image processing.

Kwok-po Ng.Thesis (Ph.D.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 138-139).AbstractsSummaryIntroduction --- p.1Summary of the papers A-F --- p.2Paper A --- p.15Paper B --- p.36Paper C --- p.63Paper D --- p.87Paper E --- p.109Paper F --- p.12

Generalized linear-in-parameter models : theory and audio signal processing applications

This thesis presents a mathematically oriented perspective to some basic concepts of digital signal processing. A general framework for the development of alternative signal and system representations is attained by defining a generalized linear-in-parameter model (GLM) configuration. The GLM provides a direct view into the origins of many familiar methods in signal processing, implying a variety of generalizations, and it serves as a natural introduction to rational orthonormal model structures. In particular, the conventional division between finite impulse response (FIR) and infinite impulse response (IIR) filtering methods is reconsidered. The latter part of the thesis consists of audio oriented case studies, including loudspeaker equalization, musical instrument body modeling, and room response modeling. The proposed collection of IIR filter design techniques is submitted to challenging modeling tasks. The most important practical contribution of this thesis is the introduction of a procedure for the optimization of rational orthonormal filter structures, called the BU-method. More generally, the BU-method and its variants, including the (complex) warped extension, the (C)WBU-method, can be consider as entirely new IIR filter design strategies.reviewe

Processamento largamente linear aplicado ao problema de equalização de canal de comunicação digital

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica.Esta tese aborda o desenvolvimento e a implementação de técnicas de processamento largamente linear (LL) aplicadas aos problemas de equalização treinada e equalização cega do canal de comunicação. O processamento largamente linear vem se mostrando uma técnica de grande interesse de pesquisa, pois, sob algumas condições, leva a um desempenho muito superior às técnicas lineares convencionais de equalização, predição, formatação de feixe entre outras aplicações, com custo computacional reduzido. Inicialmente, este documento apresenta a fundamentação teórica do processamento largamente linear onde revisamos os conceitos de sinal impróprio, ruído duplamente branco, circularidade e outros. Em seguida, com base nestes conceitos, apresentamos exemplos de sinais reais e complexos que são não-circulares onde o processamento largamente linear pode, portanto, ser aplicado vantajosamente. Investigamos as propriedades dos equalizadores largamente lineares cujo desempenho é superior ao dos equalizadores lineares, tanto em relação à complexidade computacional quanto à compensação dos efeitos do canal. Nesse estudo, incluímos o cálculo do atraso ótimo de equalização e aliamos a técnica multi-split aos equalizadores largamente lineares com o objetivo de obter uma maior taxa de convergência e um menor erro de convergência sem elevar muito o custo computacional. Um dos principais resultados obtidos é o desenvolvimento de um novo equalizador cego baseado em um filtro de erro de predição largamente linear (FEPLL). Este novo equalizador, em contraste com a equalização usando um filtro de erro de predição linear (FEPL), é capaz de equalizar canais de fase não-mínima, inclusive aqueles com nulos espectrais. Adaptamos os algoritmos LMS (com passo fixo ou variável) e RLS para o uso com este equalizador LL. Usando um conjunto de FEPLL obtivemos uma solução de equalização cega mais robusta e de melhor desempenho que a conseguida por um único FEPLL. Parte do trabalho teórico desenvolvido (equalizador largamente linear e FEPLL de passo fixo) foi implementado em FPGA. Todas as propostas desta tese foram validadas por meio de simulações de Monte Carlo

Methodik zur Integration von Vorwissen in die Modellbildung

Das Buch zeigt, wie Vorwissen über Eigenschaften dynamischer Systeme und über Funktionen in die mathematische Modellbildung integriert werden kann. Hierzu wird im ersten Teil der Arbeit das verbale Vorwissen mathematisch formuliert. Der zweite Teil beschreibt vier Zugängen, um die entstehenden restringierten Probleme zu lösen. Zahlreiche Beispiele, Tabellen und Zusammenstellungen vervollständigen das Buch

Methodik zur Integration von Vorwissen in die Modellbildung

This book describes how prior knowledge about dynamical systems and functions can be integrated in mathematical modelling. The first part comprises the transformation of the known properties into a mathematical model and the second part explains four approaches for solving the resulting constrained optimization problems. Numerous examples, tables and compilations complete the book