# The Spectral Analysis of Time Series

Academic Press, May 18, 1995 - Mathematics - 366 pages
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

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### Contents

 Chapter 1 Preliminaries 1 Chapter 2 Models for Spectral AnalysisThe Univariate Case 29 Chapter 3 Sampling Aliasing and DiscreteTime Models 66 Chapter 4 Linear FiltersGeneral Properties with Applications to ContinuousTime Processes 79 Chapter 5 Multivariate Spectral Models and Their Applications 119 Chapter 6 Digital Filters 165 Chapter 7 Finite Parameter Models Linear Prediction and RealTime Filtering 210
 Chapter 8 The Distribution Theory of Spectral Estimates with Applications to Statistical Inference 257 Chapter 9 Sampling Properties of Spectral Estimates Experimental Design and Spectral Computations 294 References 354 Index 359 Probability and Mathematical Statistics 367 Copyright