This book presents a first-ever detailed analysis of the complex notation of 2-D and 3-D signals and describes how you can apply it to image processing, modulation, and other fields. It helps you significantly reduce your literature research time, better enables you to simulate signals and communication systems, and helps you to design compatible single-sideband systems.

Hilbert Transform Applications in Mechanical Vibration addresses recent advances in theory and applications of the Hilbert transform to vibration engineering, enabling laboratory dynamic tests to be performed more rapidly and accurately. The author integrates important pioneering developments in signal processing and mathematical models with typical properties of mechanical dynamic constructions such as resonance, nonlinear stiffness and damping. A comprehensive account of the main applications is provided, covering dynamic testing and the extraction of the modal parameters of nonlinear vibration systems, including the initial elastic and damping force characteristics. This unique merger of technical properties and digital signal processing allows the instant solution of a variety of engineering problems and the in-depth exploration of the physics of vibration by analysis, identification and simulation. This book will appeal to both professionals and students working in mechanical, aerospace, and civil engineering, as well as naval architecture, biomechanics, robotics, and mechatronics. Hilbert Transform Applications in Mechanical Vibration employs modern applications of the Hilbert transform time domain methods including: The Hilbert Vibration Decomposition method for adaptive separation of a multi-component non-stationary vibration signal into simple quasi-harmonic components; this method is characterized by high frequency resolution, which provides a comprehensive account of the case of amplitude and frequency modulated vibration analysis. The FREEVIB and FORCEVIB main applications, covering dynamic testing and extraction of the modal parameters of nonlinear vibration systems including the initial elastic and damping force characteristics under free and forced vibration regimes. Identification methods contribute to efficient and accurate testing of vibration systems, avoiding effort-consuming measurement and analysis. Precise identification of nonlinear and asymmetric systems considering high frequency harmonics on the base of the congruent envelope and congruent frequency. Accompanied by a website at www.wiley.com/go/feldman, housing MATLAB®/ SIMULINK codes.

This book is written for scientists and engineers who use HHT (Hilbert-Huang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges.The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstanding mathematical research problems regarding HHT development are discussed in the first three chapters. The three new chapters of the second edition reflect the latest HHT development, including ensemble empirical mode decomposition (EEMD) and modified EMD.The book also provides a platform for researchers to develop the HHT method further and to identify more applications.

This book provides a modern and up-to-date treatment of the Hilberttransform of distributions and the space of periodic distributions.Taking a simple and effective approach to a complex subject, thisvolume is a first-rate textbook at the graduate level as well as anextremely useful reference for mathematicians, applied scientists,and engineers. The author, a leading authority in the field, shares with thereader many new results from his exhaustive research on the Hilberttransform of Schwartz distributions. He describes in detail how touse the Hilbert transform to solve theoretical and physicalproblems in a wide range of disciplines; these include aerofoilproblems, dispersion relations, high-energy physics, potentialtheory problems, and others. Innovative at every step, J. N. Pandey provides a new definitionfor the Hilbert transform of periodic functions, which isespecially useful for those working in the area of signalprocessing for computational purposes. This definition could alsoform the basis for a unified theory of the Hilbert transform ofperiodic, as well as nonperiodic, functions. The Hilbert transform and the approximate Hilbert transform ofperiodic functions are worked out in detail for the first time inbook form and can be used to solve Laplace's equation with periodicboundary conditions. Among the many theoretical results proved inthis book is a Paley-Wiener type theorem giving thecharacterization of functions and generalized functions whoseFourier transforms are supported in certain orthants of Rn. Placing a strong emphasis on easy application of theory andtechniques, the book generalizes the Hilbert problem in higherdimensions and solves it in function spaces as well as ingeneralized function spaces. It simplifies the one-dimensionaltransform of distributions; provides solutions to thedistributional Hilbert problems and singular integral equations;and covers the intrinsic definition of the testing function spacesand its topology. The book includes exercises and review material for all majortopics, and incorporates classical and distributional problems intothe main text. Thorough and accessible, it explores new ways to usethis important integral transform, and reinforces its value in bothmathematical research and applied science. The Hilbert transform made accessible with many new formulas anddefinitions Written by today's foremost expert on the Hilbert transform ofgeneralized functions, this combined text and reference covers theHilbert transform of distributions and the space of periodicdistributions. The author provides a consistently accessibletreatment of this advanced-level subject and teaches techniquesthat can be easily applied to theoretical and physical problemsencountered by mathematicians, applied scientists, and graduatestudents in mathematics and engineering. Introducing many new inversion formulas that have been developedand applied by the author and his research associates, the book: * Provides solutions to the distributional Hilbert problem andsingular integral equations * Focuses on the Hilbert transform of Schwartz distributions,giving intrinsic definitions of the space H(D) and its topology * Covers the Paley-Wiener theorem and provides many importanttheoretical results of importance to research mathematicians * Provides the characterization of functions and generalizedfunctions whose Fourier transforms are supported in certainorthants of Rn * Offers a new definition of the Hilbert transform of the periodicfunction that can be used for computational purposes in signalprocessing * Develops the theory of the Hilbert transform of periodicdistributions and the approximate Hilbert transform of periodicdistributions * Provides exercises at the end of each chapter--useful toprofessors in planning assignments, tests, and problems

The definitive reference on Hilbert transforms covering the mathematical techniques for evaluating them, and their application.

Signal Processing for Neuroscientists introduces analysis techniques primarily aimed at neuroscientists and biomedical engineering students with a reasonable but modest background in mathematics, physics, and computer programming. The focus of this text is on what can be considered the 'golden trio' in the signal processing field: averaging, Fourier analysis, and filtering. Techniques such as convolution, correlation, coherence, and wavelet analysis are considered in the context of time and frequency domain analysis. The whole spectrum of signal analysis is covered, ranging from data acquisition to data processing; and from the mathematical background of the analysis to the practical application of processing algorithms. Overall, the approach to the mathematics is informal with a focus on basic understanding of the methods and their interrelationships rather than detailed proofs or derivations. One of the principle goals is to provide the reader with the background required to understand the principles of commercially available analyses software, and to allow him/her to construct his/her own analysis tools in an environment such as MATLAB®. - Multiple color illustrations are integrated in the text - Includes an introduction to biomedical signals, noise characteristics, and recording techniques - Basics and background for more advanced topics can be found in extensive notes and appendices - A Companion Website hosts the MATLAB scripts and several data files: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123708670

This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

This book is tailored to fulfil the requirements in the area of the signal processing in communication systems. The book contains numerous examples, solved problems and exercises to explain the methodology of Fourier Series, Fourier Analysis, Fourier Transform and properties, Fast Fourier Transform FFT, Discrete Fourier Transform DFT and properties, Discrete Cosine Transform DCT, Discrete Wavelet Transform DWT and Contourlet Transform CT. The book is characterized by three directions, the communication theory and signal processing point of view, the mathematical point of view and utility computer programs. The contents of this book include chapters in communication system and signals, Fourier Series and Power Spectra, Fourier Transform and Energy Spectra, Fourier Transform and Power Spectra, Correlation Function and Spectral Density, Signal Transmission and Systems, Hilbert Transform, Narrow Band-Pass Signals and Systems and Numerical Computation of Transform Coding. This book is intended for undergraduate students in institutes, colleges, universities and academies who want to specialize in the field of communication systems and signal processing. The book will also be very useful to engineers of graduate and post graduate studies as well as researchers in research centers since it contains a great number of mathematical operations that are considered important in research results.

Amazon.com’s Top-Selling DSP Book for Seven Straight Years—Now Fully Updated! Understanding Digital Signal Processing, Third Edition, is quite simply the best resource for engineers and other technical professionals who want to master and apply today’s latest DSP techniques. Richard G. Lyons has updated and expanded his best-selling second edition to reflect the newest technologies, building on the exceptionally readable coverage that made it the favorite of DSP professionals worldwide. He has also added hands-on problems to every chapter, giving students even more of the practical experience they need to succeed. Comprehensive in scope and clear in approach, this book achieves the perfect balance between theory and practice, keeps math at a tolerable level, and makes DSP exceptionally accessible to beginners without ever oversimplifying it. Readers can thoroughly grasp the basics and quickly move on to more sophisticated techniques. This edition adds extensive new coverage of FIR and IIR filter analysis techniques, digital differentiators, integrators, and matched filters. Lyons has significantly updated and expanded his discussions of multirate processing techniques, which are crucial to modern wireless and satellite communications. He also presents nearly twice as many DSP Tricks as in the second edition—including techniques even seasoned DSP professionals may have overlooked. Coverage includes New homework problems that deepen your understanding and help you apply what you’ve learned Practical, day-to-day DSP implementations and problem-solving throughout Useful new guidance on generalized digital networks, including discrete differentiators, integrators, and matched filters Clear descriptions of statistical measures of signals, variance reduction by averaging, and real-world signal-to-noise ratio (SNR) computation A significantly expanded chapter on sample rate conversion (multirate systems) and associated filtering techniques New guidance on implementing fast convolution, IIR filter scaling, and more Enhanced coverage of analyzing digital filter behavior and performance for diverse communications and biomedical applications Discrete sequences/systems, periodic sampling, DFT, FFT, finite/infinite impulse response filters, quadrature (I/Q) processing, discrete Hilbert transforms, binary number formats, and much more

A digital filter can be pictured as a "black box" that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects. This book is a gentle introduction to digital filters, including mathematical theory, illustrative examples, some audio applications, and useful software starting points. The theory treatment begins at the high-school level, and covers fundamental concepts in linear systems theory and digital filter analysis. Various "small" digital filters are analyzed as examples, particularly those commonly used in audio applications. Matlab programming examples are emphasized for illustrating the use and development of digital filters in practice.