1 - Introduction to Spectral Analysis  pp. 1-29

Introduction to Spectral Analysis

By Donald B. Percival and Andrew T. Walden

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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:

  • the speed of the wind in a certain direction at a certain location, measured every 0.025 second;
  • the monthly average measurements related to the flow of water in the Willamette River at Salem, Oregon;
  • the daily record of a quantity (to be precise, the change in average daily frequency) that tells how well an atomic clock keeps time on a day to day basis (a constant value of 0 would indicate that the clock agreed perfectly with a time scale maintained by the U. S. Naval Observatory); and
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