Synopses & Reviews
Signal processing—the concept of frequency often referred to as spectral concepts—is the focal point of this collection of essays. Discussing parametric methods, with specific focus on time-series models, Capon's method, and notions of sub-spaces, as well as the popular and traditional analog methods, this text also addresses the quests for better frequency resolution in spectral concepts with advancements in digital tools.
This book deals with these parametric methods, first discussing those based on time series models, Capon’s method and its variants, and then estimators based on the notions of sub-spaces. However, the book also deals with the traditional “analog” methods, now called non-parametric methods, which are still the most widely used in practical spectral analysis.
About the Author
Francis Castanié is the Director of the Research Laboratory Telecommunications for Space and Aeronautics (TeSA). He joined the CNRS Institut de Recherche en Informatique de Toulouse (IRIT) in 2002, where he heads the Signal and Communication Group.
Table of Contents
Part 1: Tools for spectral analysis.
Chapter 1. Fundamentals, Francis Castanié.
1.1 Classes of Signals.
1.2 Representations of Signals.
1.3 Spectral Analysis: Position of the Problem.
Chapter 2. Digital processing of signals, Eric Le Carpentier.
2.2 Transform Properties.
2.4 Examples of Application.
Chapter 3. Estimation in spectral analysis, Olivier Besson and André Ferrari.
3.1 Introduction to Estimation.
3.2 Estimation of 1st and 2nd Order Moments.
3.3 Periodogram Analysis.
3.4 Analysis of Estimators based on cxx (m).
Chapter 4. Time-series models, Francis Castanié.
4.2 Linear Models.
4.3 Exponential Models.
4.4 Non-linear Models.
Part 2: Non-parametric methods.
Chapter 5. Non-parametric methods, Eric Le Carpentier.
5.2 Estimation of the Power Spectral Density.
5.3 Generalization to Higher Order Spectra.
Part 3: Parametric methods.
Chapter 6. Modeling of stationary time series, Corinne Mailhes and Francis Castanié.
6.1 Parametric Models.
6.2 Estimation of Model Parameters.
6.3 Properties of Spectral Estimators Produced.
Chapter 7. Minimum variance, Nadine Martin.
7.1 Principle of the MV Method.
7.2 Properties of the MV Estimator.
7.3 Link with the Fourier estimators.
7.4 Link with a Maximum Likelihood Estimator.
7.5 Lagunas Methods: Normalized and Generalized MV.
7.6 The CAPNORM Estimotor.
Chapter 8. Sub-space based estimators, Sylvie Marcos.
8.1 Model, Concept of Subspace, Definition of High Resolution.
8.3 Determination Criteria of the Number of Complex Sine Waves.
8.4 The MinNorm Method.
8.5 "Linear" Subspace Methods.
8.6 The ESPRIT Method.
8.7 Illustration of Subspace-based Methods Performance.
8.8 Adaptive Research of Subspaces.
Chapter 9. Spectral analysis of random non-stationary signals, Corinne Mailhes and Francis Castanié.
9.1 Evolution Spectra.
9.2 Non-parametric Spectral Estimation.
9.3 Parametric Spectral Estimation.
List of Authors.