Fourier analysis of time series : an introduction / Peter Bloomfield.

By: Bloomfield, Peter, 1946-.

Material type: materialTypeLabel

BookSeries: Wiley series in probability and statistics.Publisher: New York ; Chichester : Wiley, c2000Edition: 2nd ed.Description: xiv, 261 p. : ill. ; 25 cm. + hbk.ISBN: 0471889482.Subject(s): Time-series analysis

| Fourier analysis

DDC classification: 519.55

Contents:

Introduction -- Fitting sinusoids -- The search for periodicity -- Harmonic analysis -- The fast Fourier transform -- Examples of harmonic analysis -- Complex demodulation -- The spectrum -- Some stationary time series theory -- Analysis of multiple series -- Further topics.

Holdings
Item type	Current library	Call number	Copy number	Status	Date due	Barcode	Item holds
General Lending	MTU Bishopstown Library Lending	519.55 (Browse shelf(Opens below))	1	Available		00075271

Total holds: 0

Enhanced descriptions from Syndetics:

A new, revised edition of a yet unrivaled work on frequency domain analysis

Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample exercises acquaint readers with Fourier analysis and its applications. The Second Edition:
* Devotes an entire chapter to complex demodulation
* Treats harmonic regression in two separate chapters
* Features a more succinct discussion of the fast Fourier transform
* Uses S-PLUS commands (replacing FORTRAN) to accommodate programming needs and graphic flexibility
* Includes Web addresses for all time series data used in the examples

An invaluable reference for statisticians seeking to expand their understanding of frequency domain methods, Fourier Analysis of Time Series, Second Edition also provides easy access to sophisticated statistical tools for scientists and professionals in such areas as atmospheric science, oceanography, climatology, and biology.

"A Wiley-Interscience publication.".

Includes bibliographical references (pages 247-254) and indexes.

Table of contents provided by Syndetics

1 Introduction (p. 1)
1.1 Fourier Analysis (p. 2)
1.2 Historical Development of Fourier Methods (p. 5)
1.3 Why Use Trigonometric Functions? (p. 7)
2 Fitting Sinusoids (p. 9)
2.1 Curve-Fitting Approach (p. 9)
2.2 Least Squares Fitting of Sinusoids (p. 11)
2.3 Multiple Periodicities (p. 17)
2.4 Orthogonality of Sinusoids (p. 19)
2.5 Effect of Discrete Time: Aliasing (p. 21)
2.6 Some Statistical Results (p. 23)
Appendix (p. 24)
3 The Search for Periodicity (p. 25)
3.1 Fitting the Frequency (p. 25)
3.2 Fitting Multiple Frequencies (p. 28)
3.3 Some More Statistical Results (p. 30)
Appendix (p. 34)
4 Harmonic Analysis (p. 37)
4.1 Fourier Frequencies (p. 37)
4.2 Discrete Fourier Transform (p. 40)
4.3 Decomposing the Sum of Squares (p. 44)
4.4 Special Functions (p. 45)
4.5 Smooth Functions (p. 53)
5 The Fast Fourier Transform (p. 57)
5.1 Computational Cost of Fourier Transforms (p. 57)
5.2 Two-Factor Case (p. 58)
5.3 Application to Harmonic Analysis of Data (p. 61)
6 Examples of Harmonic Analysis (p. 63)
6.1 Variable Star Data (p. 63)
6.2 Leakage Reduction by Data Windows (p. 66)
6.3 Tapering the Variable Star Data (p. 72)
6.4 Wolf's Sunspot Numbers (p. 76)
6.5 Nonsinusoidal Oscillations (p. 78)
6.6 Amplitude and Phase Fluctuations (p. 81)
6.7 Transformations (p. 83)
6.8 Periodogram of a Noise Series (p. 87)
6.9 Fisher's Test for Periodicity (p. 91)
Appendix (p. 95)
7 Complex Demodulation (p. 97)
7.1 Introduction (p. 97)
7.2 Smoothing: Linear Filtering (p. 100)
7.3 Designing a Filter (p. 105)
7.4 Least Squares Filter Design (p. 110)
7.5 Demodulating the Sunspot Series (p. 118)
7.6 Complex Time Series (p. 124)
7.7 Sunspots: The Complex Series (p. 126)
Appendix (p. 130)
8 The Spectrum (p. 133)
8.1 Periodogram Analysis of Wheat Prices (p. 133)
8.2 Analysis of Segments of a Series (p. 140)
8.3 Smoothing the Periodogram (p. 142)
8.4 Autocovariances and Spectrum Estimates (p. 147)
8.5 Alternative Representations (p. 149)
8.6 Choice of a Spectral Window (p. 155)
8.7 Examples of Smoothing the Periodogram (p. 157)
8.8 Reroughing the Spectrum (p. 160)
Appendix (p. 164)
9 Some Stationary Time Series Theory (p. 167)
9.1 Stationary Time Series (p. 167)
9.2 Continuous Spectra (p. 173)
9.3 Time Averaging and Ensemble Averaging (p. 175)
9.4 Periodogram and Continuous Spectra (p. 176)
9.5 Approximate Mean and Variance (p. 177)
9.6 Properties of Spectral Windows (p. 190)
9.7 Aliasing and the Spectrum (p. 195)
10 Analysis of Multiple Series (p. 201)
10.1 Cross Periodogram (p. 202)
10.2 Estimating the Cross Spectrum (p. 204)
10.3 Theoretical Cross Spectrum (p. 211)
10.4 Distribution of the Cross Periodogram (p. 214)
10.5 Distribution of Estimated Cross Spectra (p. 218)
10.6 Alignment (p. 226)
Appendix (p. 230)
11 Further Topics (p. 233)
11.1 Time Domain Analysis (p. 233)
11.2 Spatial Series (p. 234)
11.3 Multiple Series (p. 236)
11.4 Higher Order Spectra (p. 238)
11.5 Nonquadratic Spectrum Estimates (p. 239)
11.6 Incomplete and Irregular Data (p. 242)
References (p. 247)
Author Index (p. 255)
Subject Index (p. 257)

Author notes provided by Syndetics

PETER BLOOMFIELD, PhD, is a professor in the Department of Statistics at North Carolina State University, Raleigh.