Analog and Digital Signal Analysis: From Basics to Applications

Description

This 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 Front Matter....Pages i-xxiii Notions on Systems....Pages 1-10 First and Second Order Systems....Pages 11-34 Fourier Series....Pages 35-57 Fourier Transform....Pages 59-75 Fourier Transform and LTI Filter Systems....Pages 77-92 Fourier Transforms and Convolution Calculations....Pages 93-110 Impulse Response of LTI Systems....Pages 111-136 Laplace Transform....Pages 137-148 Analog Filters....Pages 149-158 Causal Signals—Analytic Signals....Pages 159-175 Time–Frequency Analysis....Pages 177-205 Notions on Digital Signals....Pages 207-226 Discrete Systems—Moving Average Systems....Pages 227-234 Z-Transform....Pages 235-251 Fourier Transform of Digital Signals....Pages 253-262 Autoregressive Systems (AR)—ARMA Systems....Pages 263-289 Minimum-Phase Systems—Deconvolution....Pages 291-320 Wavelets; Multiresolution Analysis....Pages 321-335 Parametric Estimate—Modeling of Deterministic Signals—Linear Prediction....Pages 337-373 Random Signals: Statistics Basis....Pages 375-405 Multiple Random Variables—Linear Regression Maximum Likelihood Estimation....Pages 407-444 Correlation and Covariance Matrices of a Complex Random Vector....Pages 445-465 Correlation Functions, Spectral Power Densities of Random Signals....Pages 467-481 Ergodicity; Temporal and Spectral Estimations....Pages 483-510 Parametric Modeling of Random Signals....Pages 511-528 Optimal Filtering: Wiener and Kalman Filters....Pages 529-542 Back Matter....Pages 543-562 ....Pages 563-608