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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 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.
This text employs basic techniques of univariate and multivariate statistics for the analysis of time series and signals.
A comprehensive guide to the conceptual, mathematical, and implementational aspects of analyzing electrical brain signals, including data from MEG, EEG, and LFP recordings. This book offers a comprehensive guide to the theory and practice of analyzing electrical brain signals. It explains the conceptual, mathematical, and implementational (via Matlab programming) aspects of time-, time-frequency- and synchronization-based analyses of magnetoencephalography (MEG), electroencephalography (EEG), and local field potential (LFP) recordings from humans and nonhuman animals. It is the only book on the topic that covers both the theoretical background and the implementation in language that can be understood by readers without extensive formal training in mathematics, including cognitive scientists, neuroscientists, and psychologists. Readers who go through the book chapter by chapter and implement the examples in Matlab will develop an understanding of why and how analyses are performed, how to interpret results, what the methodological issues are, and how to perform single-subject-level and group-level analyses. Researchers who are familiar with using automated programs to perform advanced analyses will learn what happens when they click the “analyze now” button. The book provides sample data and downloadable Matlab code. Each of the 38 chapters covers one analysis topic, and these topics progress from simple to advanced. Most chapters conclude with exercises that further develop the material covered in the chapter. Many of the methods presented (including convolution, the Fourier transform, and Euler's formula) are fundamental and form the groundwork for other advanced data analysis methods. Readers who master the methods in the book will be well prepared to learn other approaches.
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). Each chapter has an exercise section, which makes Fourier Analysis and Stochastic Processes suitable for a graduate course in applied mathematics, as well as for self-study.
Preliminary concepts -- Preprocessing of data -- Recursive digital filtering -- Fourier series and Fourier transform computations -- General considerations in computing power spectral density -- Correlation function and Blackman-Tukey spectrum computations -- Power and cross spectra from fast Fourier transforms -- Filter methods for the power spectral density -- Transfer function and coherence function computations -- Probability density function computations -- Miscellaneous techniques -- Test case and examples.
The Spectral Analysis of Time Series ...
The subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, and the Kalman filter. Major topics include: * Moving average and autoregressive processes * Introduction to Fourier analysis * Spectral theory and filtering * Large sample theory * Estimation of the mean and autocorrelations * Estimation of the spectrum * Parameter estimation * Regression, trend, and seasonality * Unit root and explosive time series To accommodate a wide variety of readers, review material,especially on elementary results in Fourier analysis, large samplestatistics, and difference equations, has been included.
This open access book comprehensively covers the fundamentals of clinical data science, focusing on data collection, modelling and clinical applications. Topics covered in the first section on data collection include: data sources, data at scale (big data), data stewardship (FAIR data) and related privacy concerns. Aspects of predictive modelling using techniques such as classification, regression or clustering, and prediction model validation will be covered in the second section. The third section covers aspects of (mobile) clinical decision support systems, operational excellence and value-based healthcare. Fundamentals of Clinical Data Science is an essential resource for healthcare professionals and IT consultants intending to develop and refine their skills in personalized medicine, using solutions based on large datasets from electronic health records or telemonitoring programmes. The book’s promise is “no math, no code”and will explain the topics in a style that is optimized for a healthcare audience.
Hardbound. This volume of the Handbook is concerned particularly with the frequency side, or spectrum, approach to time series analysis. This approach involves essential use of sinusoids and bands of (angular) frequency, with Fourier transforms playing an important role. A principal activity is thinking of systems, their inputs, outputs, and behavior in sinusoidal terms. In many cases, the frequency side approach turns out to be simpler with respect to computational, mathematical, and statistical aspects. In the frequency approach, an assumption of stationarity is commonly made. However, the essential roles played by the techniques of complex demodulation and seasonal adjustment show that stationarity is far from being a necessary condition. Assumptions of Gaussianity and linearity are also commonly made and yet, as a variety of the papers illustrate, these assumptions are not necessary. This volume complements Handbook of Statistics 5: Time Series in the