Cohen Tenoudji F. Analog and Digital Signal Analysis: From Basics to Applications

Springer International Publishing, Switzerland, 2016. — 618 p. — ISBN: 9783319423807This book provides comprehensive, graduate-level treatment of analog and digital signal analysis suitable for course use and self-guided learning. This expert text guides the reader from the basics of signal theory through a range of application tools for use in acoustic analysis, geophysics, and data compression. Each concept is introduced and explained step by step, and the necessary mathematical formulae are integrated in an accessible and intuitive way. The first part of the book explores how analog systems and signals form the basics of signal analysis. This section covers Fourier series and integral transforms of analog signals, Laplace and Hilbert transforms, the main analog filter classes, and signal modulations. Part II covers digital signals, demonstrating their key advantages. It presents z and Fourier transforms, digital filtering, inverse filters, deconvolution, and parametric modeling for deterministic signals. Wavelet decomposition and reconstruction of non-stationary signals are also discussed. The third part of the book is devoted to random signals, including spectral estimation, parametric modeling, and Tikhonov regularization. It covers statistics of one and two random variables and the principles and methods of spectral analysis. Estimation of signal properties is discussed in the context of ergodicity conditions and parameter estimations, including the use of Wiener and Kalman filters. Two appendices cover the basics of integration in the complex plane and linear algebra. A third appendix presents a basic MatLAB toolkit for computer signal analysis. This expert text provides both a solid theoretical understanding and tools for real-world applications.Notions on Systems
First and Second Order Systems
Fourier Series
The Dirac Distribution
Fourier Transform
Fourier Transform and LTI Filter Systems
Fourier Transforms and Convolution Calculations
Impulse Response of LTI Systems
Laplace Transform
Analog Filters
Causal Signals—Analytic Signals
Time–Frequency Analysis
Notions on Digital Signals
Discrete Systems—Moving Average Systems
Z-Transform
Fourier Transform of Digital Signals
Autoregressive Systems (AR)—ARMA Systems
Minimum-Phase Systems—Deconvolution
Wavelets; Multiresolution Analysis
Parametric Estimate—Modeling of Deterministic Signals—Linear Prediction
Random Signals: Statistics Basis
Multiple Random Variables—Linear Regression Maximum Likelihood Estimation
Correlation and Covariance Matrices of a Complex Random Vector
Correlation Functions, Spectral Power Densities of Random Signals
Ergodicity; Temporal and Spectral Estimations
Parametric Modeling of Random Signals
Optimal Filtering; Wiener and Kalman Filters
Appendixes
Functions of a Complex Variable
Linear Algebra
Computer Calculations