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Fourier analysis of time series [[electronic resource] ] : an introduction / / Peter Bloomfield
| Fourier analysis of time series [[electronic resource] ] : an introduction / / Peter Bloomfield |
| Autore | Bloomfield Peter <1946-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York, : Wiley, c2000 |
| Descrizione fisica | 1 online resource (285 p.) |
| Disciplina |
515.2433
519.5/5 519.55 |
| Collana | Wiley series in probability and statistics. Applied probability and statistics section |
| Soggetto topico |
Time-series analysis
Fourier analysis |
| ISBN |
1-280-54195-4
9786610541959 0-471-65399-3 0-471-72223-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 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
4.3 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 7.2 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 9.2 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 11.5 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 |
| Record Nr. | UNINA-9910143508503321 |
Bloomfield Peter <1946->
|
||
| New York, : Wiley, c2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis of time series [[electronic resource] ] : an introduction / / Peter Bloomfield
| Fourier analysis of time series [[electronic resource] ] : an introduction / / Peter Bloomfield |
| Autore | Bloomfield Peter <1946-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York, : Wiley, c2000 |
| Descrizione fisica | 1 online resource (285 p.) |
| Disciplina |
515.2433
519.5/5 519.55 |
| Collana | Wiley series in probability and statistics. Applied probability and statistics section |
| Soggetto topico |
Time-series analysis
Fourier analysis |
| ISBN |
1-280-54195-4
9786610541959 0-471-65399-3 0-471-72223-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 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
4.3 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 7.2 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 9.2 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 11.5 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 |
| Record Nr. | UNINA-9910830458003321 |
|
Bloomfield Peter <1946->
|
||
| New York, : Wiley, c2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis of time series [[electronic resource] ] : an introduction / / Peter Bloomfield
| Fourier analysis of time series [[electronic resource] ] : an introduction / / Peter Bloomfield |
| Autore | Bloomfield Peter <1946-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York, : Wiley, c2000 |
| Descrizione fisica | 1 online resource (285 p.) |
| Disciplina |
515.2433
519.5/5 519.55 |
| Collana | Wiley series in probability and statistics. Applied probability and statistics section |
| Soggetto topico |
Time-series analysis
Fourier analysis |
| ISBN |
1-280-54195-4
9786610541959 0-471-65399-3 0-471-72223-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 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
4.3 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 7.2 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 9.2 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 11.5 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 |
| Record Nr. | UNINA-9910877046303321 |
|
Bloomfield Peter <1946->
|
||
| New York, : Wiley, c2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||