Spectral Analysis Methods For Noisy Sampled Data Systems

This dissertation covers both the theory and practice of estimating the spectrum of signals in noise using digital data. The theory of describing some of the signal processing concepts for digital data are given and various spectral estimation methods are given. The theory of MEM is described in detail using approaches from estimation theory, communication theory, and statistics. The work was intended to give researchers the theory and practice of practical means of spectral estimation using communications or scientific data. The Maximum Entropy Method by John Parker Burg is explained from what was known in 1974-75. KEY WORDS: Calculus-of-Variations, Data Systems, Noise , Spectrum Analysis, Time Series Analysis, Autocorrelation, Computer Programs, Data Windowing, Ergodic Process, Maximum Entropy Method (MEM, Fourier Transformation, Optimum Order of Estimation, Sampling, Spectral Resolution, Statistical Significance Test, Systems Analysis, Wiener-Khinchine Theorem. From The Smithsonian/NASA Astrophysics Data System -- The practical aspects of spectral analysis are contrasted with the mathematical theory. Treatment is limited to ergodic processes and emphasizes data window and noise effects. The Discrete Fourier Transform (DFT) and Maximum Entropy Method (MEM) are covered extensively both in theory and application with FORTRAN programs and many examples being provided. Several of the chapters are tutorial and discuss the important topics of sampling theory and system analysis. Topics on MEM include a complete calculus-of-variations solution, relationship between MEM and the Wiener-Khinchine relations, spectral resolution, and choosing the optimum order of the estimation. DFT leakage effects are modeled. A statistical significance test was developed to determine the realness of a spectral component. Keywords: Data Systems, Noise (Sound), Spectrum Analysis, Time Series Analysis, Autocorrelation, Computer Programs, Ergodic Process, Fourier Transformation, Sampling, Systems Analysis [less]

The International Conference on Noise in Physical Systems and 1/f Fluctuations brings together physicists and engineers interested in all aspects of noise and fluctuations in materials, devices, circuits, and physical and biological systems. The experimental research on novel devices and systems and the theoretical studies included in this volume provide the reader with a comprehensive, in-depth treatment of present noise research activities worldwide.

The International Conference on Noise in Physical Systems and 1/f Fluctuations brings together physicists and engineers interested in all aspects of noise and fluctuations in materials, devices, circuits, and physical and biological systems. The experimental research on novel devices and systems and the theoretical studies included in this volume provide the reader with a comprehensive, in-depth treatment of present noise research activities worldwide.

This book covers the basics of processing and spectral analysis of monovariate discrete-time signals. The approach is practical, the aim being to acquaint the reader with the indications for and drawbacks of the various methods and to highlight possible misuses. The book is rich in original ideas, visualized in new and illuminating ways, and is structured so that parts can be skipped without loss of continuity. Many examples are included, based on synthetic data and real measurements from the fields of physics, biology, medicine, macroeconomics etc., and a complete set of MATLAB exercises requiring no previous experience of programming is provided. Prior advanced mathematical skills are not needed in order to understand the contents: a good command of basic mathematical analysis is sufficient. Where more advanced mathematical tools are necessary, they are included in an Appendix and presented in an easy-to-follow way. With this book, digital signal processing leaves the domain of engineering to address the needs of scientists and scholars in traditionally less quantitative disciplines, now facing increasing amounts of data.

"Spectral Audio Signal Processing is the fourth book in the music signal processing series by Julius O. Smith. One can say that human hearing occurs in terms of spectral models. As a result, spectral models are especially useful in audio applications. For example, with the right spectral model, one can discard most of the information contained in a sound waveform without changing how it sounds. This is the basis of modern audio compression techniques."--Publisher's description.

Digital Spectral Analysis offers a broad perspective of spectral estimation techniques and their implementation. Coverage includes spectral estimation of discrete-time or discrete-space sequences derived by sampling continuous-time or continuous-space signals. The treatment emphasizes the behavior of each spectral estimator for short data records and provides over 40 techniques described and available as implemented MATLAB functions. In addition to summarizing classical spectral estimation, this text provides theoretical background and review material in linear systems, Fourier transforms, matrix algebra, random processes, and statistics. Topics include Prony's method, parametric methods, the minimum variance method, eigenanalysis-based estimators, multichannel methods, and two-dimensional methods. Suitable for advanced undergraduates and graduate students of electrical engineering — and for scientific use in the signal processing application community outside of universities — the treatment's prerequisites include some knowledge of discrete-time linear system and transform theory, introductory probability and statistics, and linear algebra. 1987 edition.