Spectral Analysis for Physical Applications
Multitaper and Conventional Univariate Techniques
By Donald B. Percival
By Andrew T. Walden
Publisher: Cambridge University Press
Print Publication Year: 1993
Online Publication Date:December 2009
Online ISBN:9780511622762
Hardback ISBN:9780521355322
Paperback ISBN:9780521435413
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511622762.004
Subjects: Mathematical Methods, Statistics for physical sciences and engineering
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Introduction
This chapter provides a quick introduction to the subject of spectral analysis. Except for some later references to the exercises of Section 1.6, this material is independent of the rest of the book and can be skipped without loss of continuity. Our intent is to use some simple examples to motivate the key ideas. Since our purpose is to view the forest before we get lost in the trees, the particular analysis techniques we use here have been chosen for their simplicity rather than their appropriateness.
Some Aspects of Time Series Analysis
Spectral analysis is part of time series analysis, so the natural place to start our discussion is with the notion of a time series. The quip (attributed to R. A. Fisher) that a time series is ‘one damned thing after another’ is not far from the truth: loosely speaking, a time series is a set of observations made sequentially in time. Examples abound in the real world, and Figures 2 and 3 show plots of small portions of four actual time series:
pp. i-viii
pp. ix-xiv
pp. xv-xviii
Conventions and Notation: Read PDF
pp. xix-xxvi
pp. xxvii-xxviii
1 - Introduction to Spectral Analysis: Read PDF
pp. 1-29
2 - Stationary Stochastic Processes: Read PDF
pp. 30-55
3 - Deterministic Spectral Analysis: Read PDF
pp. 56-125
4 - Foundations for Stochastic Spectral Analysis: Read PDF
pp. 126-152
5 - Linear Time-Invariant Filters: Read PDF
pp. 153-186
6 - Nonparametric Spectral Estimation: Read PDF
pp. 187-330
7 - Multitaper Spectral Estimation: Read PDF
pp. 331-377
8 - Calculation of Discrete Prolate Spheroidal Sequences: Read PDF
pp. 378-390
9 - Parametric Spectral Estimation: Read PDF
pp. 391-455
10 - Harmonic Analysis: Read PDF
pp. 456-545
pp. 546-561
pp. 562-565
pp. 566-583