LEADER 05043nam 2200661Ia 450 001 9910143508503321 005 20170815110110.0 010 $a1-280-54195-4 010 $a9786610541959 010 $a0-471-65399-3 010 $a0-471-72223-5 035 $a(CKB)111087027145344 035 $a(EBL)469233 035 $a(OCoLC)53371691 035 $a(SSID)ssj0000157675 035 $a(PQKBManifestationID)11148855 035 $a(PQKBTitleCode)TC0000157675 035 $a(PQKBWorkID)10139895 035 $a(PQKB)10270467 035 $a(MiAaPQ)EBC469233 035 $a(PPN)198592760 035 $a(EXLCZ)99111087027145344 100 $a19991104d2000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFourier analysis of time series$b[electronic resource] $ean introduction /$fPeter Bloomfield 205 $a2nd ed. 210 $aNew York $cWiley$dc2000 215 $a1 online resource (285 p.) 225 1 $aWiley series in probability and statistics. Applied probability and statistics section 300 $a"A Wiley-Interscience publication." 311 $a0-471-88948-2 320 $aIncludes bibliographical references (p. 247-254) and indexes. 327 $aContents; 1 Introduction; 1.1 Fourier Analysis; 1.2 Historical Development of Fourier Methods; 1.3 Why Use Trigonometric Functions?; 2 Fitting Sinusoids; 2.1 Curve-Fitting Approach; 2.2 Least Squares Fitting of Sinusoids; 2.3 Multiple Periodicities; 2.4 Orthogonality of Sinusoids; 2.5 Effect of Discrete Time: Aliasing; 2.6 Some Statistical Results; Appendix; 3 The Search for Periodicity; 3.1 Fitting the Frequency; 3.2 Fitting Multiple Frequencies; 3.3 Some More Statistical Results; Appendix; 4 Harmonic Analysis; 4.1 Fourier Frequencies; 4.2 Discrete Fourier Transform 327 $a4.3 Decomposing the Sum of Squares4.4 Special Functions; 4.5 Smooth Functions; 5 The Fast Fourier Transform; 5.1 Computational Cost of Fourier Transforms; 5.2 Two-Factor Case; 5.3 Application to Harmonic Analysis of Data; 6 Examples of Harmonic Analysis; 6.1 Variable Star Data; 6.2 Leakage Reduction by Data Windows; 6.3 Tapering the Variable Star Data; 6.4 Wolf's Sunspot Numbers; 6.5 Nonsinusoidal Oscillations; 6.6 Amplitude and Phase Fluctuations; 6.7 Transformations; 6.8 Periodogram of a Noise Series; 6.9 Fisher's Test for Periodicity; Appendix; 7 Complex Demodulation; 7.1 Introduction 327 $a7.2 Smoothing: Linear Filtering7.3 Designing a Filter; 7.4 Least Squares Filter Design; 7.5 Demodulating the Sunspot Series; 7.6 Complex Time Series; 7.7 Sunspots: The Complex Series; Appendix; 8 The Spectrum; 8.1 Periodogram Analysis of Wheat Prices; 8.2 Analysis of Segments of a Series; 8.3 Smoothing the Periodogram; 8.4 Autocovariances and Spectrum Estimates; 8.5 Alternative Representations; 8.6 Choice of a Spectral Window; 8.7 Examples of Smoothing the Periodogram; 8.8 Reroughing the Spectrum; Appendix; 9 Some Stationary Time Series Theory; 9.1 Stationary Time Series 327 $a9.2 Continuous Spectra9.3 Time Averaging and Ensemble Averaging; 9.4 Periodogram and Continuous Spectra; 9.5 Approximate Mean and Variance; 9.6 Properties of Spectral Windows; 9.7 Aliasing and the Spectrum; 10 Analysis of Multiple Series; 10.1 Cross Periodogram; 10.2 Estimating the Cross Spectrum; 10.3 Theoretical Cross Spectrum; 10.4 Distribution of the Cross Periodogram; 10.5 Distribution of Estimated Cross Spectra; 10.6 Alignment; Appendix; 11 Further Topics; 11.1 Time Domain Analysis; 11.2 Spatial Series; 11.3 Multiple Series; 11.4 Higher Order Spectra 327 $a11.5 Nonquadratic Spectrum Estimates11.6 Incomplete and Irregular Data; References; Author Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Subject Index; A; B; C; D; E; F; G; H; I; J; L; M; N; O; P; Q; R; S; T; V; W 330 $aA new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ampl 410 0$aWiley series in probability and statistics.$pApplied probability and statistics. 606 $aTime-series analysis 606 $aFourier analysis 615 0$aTime-series analysis. 615 0$aFourier analysis. 676 $a515.2433 676 $a519.5/5 676 $a519.55 700 $aBloomfield$b Peter$f1946-$0254675 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143508503321 996 $aFourier analysis of time series$968132 997 $aUNINA