Download or read book Fourier Analysis A Signal Processing Approach written by D. Sundararajan and published by Springer. This book was released on 2018-07-25 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sheds new light on Transform methods, which dominate the study of linear time-invariant systems in all areas of science and engineering, such as circuit theory, signal/image processing, communications, controls, vibration analysis, remote sensing, biomedical systems, optics and acoustics. It presents Fourier analysis primarily using physical explanations with waveforms and/or examples, only using mathematical formulations to the extent necessary for its practical use. Intended as a textbook for senior undergraduates and graduate level Fourier analysis courses in engineering and science departments, and as a supplementary textbook for a variety of application courses in science and engineering, the book is also a valuable reference for anyone – student or professional – specializing in practical applications of Fourier analysis. The prerequisite for reading this book is a sound understanding of calculus, linear algebra, signals and systems, and programming at the undergraduate level.

Download or read book Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design written by Radomir S. Stankovic and published by John Wiley & Sons. This book was released on 2005-08-08 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.

Download or read book Mathematical Principles of Signal Processing written by Pierre Bremaud and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "[...] the interested reader will find in Bremaud’s book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." Mathematical Reviews

Download or read book Discrete Fourier Analysis and Wavelets written by S. Allen Broughton and published by John Wiley & Sons. This book was released on 2018-04-03 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delivers an appropriate mix of theory and applications to help readers understand the process and problems of image and signal analysis Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing. Topical coverage includes: vector spaces, signals, and images; the discrete Fourier transform; the discrete cosine transform; convolution and filtering; windowing and localization; spectrograms; frames; filter banks; lifting schemes; and wavelets. Discrete Fourier Analysis and Wavelets introduces a new chapter on frames—a new technology in which signals, images, and other data are redundantly measured. This redundancy allows for more sophisticated signal analysis. The new coverage also expands upon the discussion on spectrograms using a frames approach. In addition, the book includes a new chapter on lifting schemes for wavelets and provides a variation on the original low-pass/high-pass filter bank approach to the design and implementation of wavelets. These new chapters also include appropriate exercises and MATLAB® projects for further experimentation and practice. Features updated and revised content throughout, continues to emphasize discrete and digital methods, and utilizes MATLAB® to illustrate these concepts Contains two new chapters on frames and lifting schemes, which take into account crucial new advances in the field of signal and image processing Expands the discussion on spectrograms using a frames approach, which is an ideal method for reconstructing signals after information has been lost or corrupted (packet erasure) Maintains a comprehensive treatment of linear signal processing for audio and image signals with a well-balanced and accessible selection of topics that appeal to a diverse audience within mathematics and engineering Focuses on the underlying mathematics, especially the concepts of finite-dimensional vector spaces and matrix methods, and provides a rigorous model for signals and images based on vector spaces and linear algebra methods Supplemented with a companion website containing solution sets and software exploration support for MATLAB and SciPy (Scientific Python) Thoroughly class-tested over the past fifteen years, Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing is an appropriately self-contained book ideal for a one-semester course on the subject.

Download or read book Discrete Wavelet Transform written by D. Sundararajan and published by John Wiley & Sons. This book was released on 2016-03-07 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides easy learning and understanding of DWT from a signal processing point of view Presents DWT from a digital signal processing point of view, in contrast to the usual mathematical approach, making it highly accessible Offers a comprehensive coverage of related topics, including convolution and correlation, Fourier transform, FIR filter, orthogonal and biorthogonal filters Organized systematically, starting from the fundamentals of signal processing to the more advanced topics of DWT and Discrete Wavelet Packet Transform. Written in a clear and concise manner with abundant examples, figures and detailed explanations Features a companion website that has several MATLAB programs for the implementation of the DWT with commonly used filters “This well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing.” -- Prof. Dr. Manfred Tasche - Institut für Mathematik, Uni Rostock Full review at https://zbmath.org/?q=an:06492561

Download or read book The Mathematics of Signal Processing written by Steven B. Damelin and published by Cambridge University Press. This book was released on 2012 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops mathematical and probabilistic tools needed to give rigorous derivations and applications of fundamental results in signal processing theory.

Download or read book Fourier Transforms in Radar and Signal Processing Second Edition written by David Brandwood and published by Artech House. This book was released on 2012 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a critical new chapter on periodic waveforms a topic not covered in any other book and detailed coverage of asymmetric triangular pulse. By building upon Woodward's well known "Rules and Pairs" method and related concepts and procedures, this book establishes a unified system that makes implicit the integration required for performing Fourier transforms on a wide variety of functions. It details how complex functions can be broken down to their constituent parts for analysis. You can now concentrate on functional relationships instead of getting bogged down in the details of integration. This approach to implementing Fourier transforms is illustrated with many specific examples from digital signal processing as well as radar and antenna operation. DVD-ROM Included! Contains MATLAB programs that implement many of the results presented in the book.

Download or read book Signal Processing for Neuroscientists written by Wim van Drongelen and published by Elsevier. This book was released on 2006-12-18 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Linear Algebra Signal Processing and Wavelets A Unified Approach written by Øyvind Ryan and published by Springer. This book was released on 2019-03-05 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended. The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the MATLAB code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.

Download or read book The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing written by Sonali Bagchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growth in the field of digital signal processing began with the simulation of continuous-time systems in the 1950s, even though the origin of the field can be traced back to 400 years when methods were developed to solve numerically problems such as interpolation and integration. During the last 40 years, there have been phenomenal advances in the theory and application of digital signal processing. In many applications, the representation of a discrete-time signal or a sys tem in the frequency domain is of interest. To this end, the discrete-time Fourier transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the discrete Fourier transform (DFT) which results in a finite length sequence in the frequency domain. The DFT is simply composed of the samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, the samples of its z-transform at equally spaced points on the unit circle. The DFT provides information about the spectral contents of the signal at equally spaced discrete frequency points, and thus, can be used for spectral analysis of signals. Various techniques, commonly known as the fast Fourier transform (FFT) algorithms, have been advanced for the efficient com putation of the DFT. An important tool in digital signal processing is the linear convolution of two finite-length signals, which often can be implemented very efficiently using the DFT.

Download or read book Foundations of Signal Processing written by Martin Vetterli and published by Cambridge University Press. This book was released on 2014-09-04 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Think DSP written by Allen B. Downey and published by "O'Reilly Media, Inc.". This book was released on 2016-07-12 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you understand basic mathematics and know how to program with Python, you’re ready to dive into signal processing. While most resources start with theory to teach this complex subject, this practical book introduces techniques by showing you how they’re applied in the real world. In the first chapter alone, you’ll be able to decompose a sound into its harmonics, modify the harmonics, and generate new sounds. Author Allen Downey explains techniques such as spectral decomposition, filtering, convolution, and the Fast Fourier Transform. This book also provides exercises and code examples to help you understand the material. You’ll explore: Periodic signals and their spectrums Harmonic structure of simple waveforms Chirps and other sounds whose spectrum changes over time Noise signals and natural sources of noise The autocorrelation function for estimating pitch The discrete cosine transform (DCT) for compression The Fast Fourier Transform for spectral analysis Relating operations in time to filters in the frequency domain Linear time-invariant (LTI) system theory Amplitude modulation (AM) used in radio Other books in this series include Think Stats and Think Bayes, also by Allen Downey.

Download or read book Fourier Theory in Optics and Optical Information Processing written by Toyohiko Yatagai and published by CRC Press. This book was released on 2022-05-26 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier analysis is one of the most important concepts when you apply physical ideas to engineering issues. This book provides a comprehensive understanding of Fourier transform and spectral analysis in optics, image processing, and signal processing. Written by a world renowned author, this book looks to unify the readers understanding of principles of optics, information processing and measurement. This book describes optical imaging systems through a linear system theory. The book also provides an easy understanding of Fourier transform and system theory in optics. It also provides background of optical measurement and signal processing. Finally, the author also provides a systematic approach to learning many signal processing techniques in optics. The book is intended for researchers, industry professionals, and graduate level students in optics and information processing.

Download or read book Fourier Methods in Imaging written by Roger L. Easton Jr. and published by John Wiley & Sons. This book was released on 2010-11-18 with total page 1005 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging “tasks” (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines "special" functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear "filters", including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography. Provides a unified mathematical description of imaging systems. Develops a consistent mathematical formalism for characterizing imaging systems. Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions. Offers parallel descriptions of continuous and discrete cases. Includes many graphical and pictorial examples to illustrate the concepts. This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists

Download or read book Digital Signal Processing written by Shlomo Engelberg and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous but accessible treatment of digital signal processing that intertwines basic theoretical techniques with hands-on laboratory instruction is provided by this book. The book covers various aspects of the digital signal processing (DSP) "problem". It begins with the analysis of discrete-time signals and explains sampling and the use of the discrete and fast Fourier transforms. The second part of the book — covering digital to analog and analog to digital conversion — provides a practical interlude in the mathematical content before Part III lays out a careful development of the Z-transform and the design and analysis of digital filters.

Download or read book Applied Fourier Analysis written by Tim Olson and published by Birkhäuser. This book was released on 2017-11-20 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medi cal imaging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects. Illuminating videos are available on Springer.com and Link.Springer.com that present animated visualizations of several concepts. The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.

Download or read book A First Course in Fourier Analysis written by David W. Kammler and published by Cambridge University Press. This book was released on 2008-01-17 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.