The Spectral Analysis of Time Series

Lambert H. Koopmans

• Éditeur: Academic Press
• Année: 1995
• ISBN:
  9780080541563
• Sujet: Mathematics
• Sous-sujet: Mathematical Analysis

To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results.The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications.Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction.

• Hilbert spaces
• univariate models for spectral analysis
• multivariate spectral models
• sampling, aliasing, and discrete-time models
• real-time filtering
• digital filters
• linear filters
• distribution theory
• sampling properties of spectral estimates
• linear prediction

Table des matières

• Cover image
• Title page
• Table of Contents
• Inside Front Cover
• Copyright
• Dedication
• Preface
• Acknowledgments
• Preface to the Second Edition
• Chapter 1: Preliminaries
• Chapter 2: Models for Spectral Analysis—The Univariate Case
• Chapter 3: Sampling, Aliasing, and Discrete-Time Models
• Chapter 4: Linear Filters—General Properties with Applications to Continuous-Time Processes
• Chapter 5: Multivariate Spectral Models and Their Applications
• Chapter 6: Digital Filters
• Chapter 7: Finite Parameter Models, Linear Prediction, and Real-Time Filtering
• Chapter 8: The Distribution Theory of Spectral Estimates with Applications to Statistical Inference
• Chapter 9: Sampling Properties of Spectral Estimates, Experimental Design, and Spectral Computations
• References
• Index
• Probability and Mathematical Statistics