Digital Fourier Analysis Advanced Techniques
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| Author | : Ken'iti Kido |
| Publisher | : Springer |
| Total Pages | : 185 |
| Release | : 2014-06-26 |
| Genre | : Science |
| ISBN | : 1493911279 |
This textbook is a thorough, accessible introduction to advanced digital Fourier analysis for advanced students. Assuming knowledge of the Fast Fourier Transform, this book covers advanced topics including the Hilbert transform, cepstrum analysis and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis: Volume 2" includes practice problems and thorough Appendices. As a central feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. The applet source code in Visual Basic is provided online, enabling advanced students to tweak and change the programs for more sophisticated results. A complete, intuitive guide, "Digital Fourier Analysis, Volume 2" is an essential reference for students in science and engineering.
| Author | : Ken'iti Kido |
| Publisher | : Springer |
| Total Pages | : 210 |
| Release | : 2014-06-26 |
| Genre | : Science |
| ISBN | : 1461492602 |
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader can test various cases and view the results until they fully understand the principle. Additionally, the applet source code in Visual Basic is provided online, allowing this book to be used for teaching simple programming techniques. A complete, intuitive guide to the basics, "Digital Fourier Analysis - Fundamentals" is an essential reference for undergraduate students in science and engineering.
| Author | : Ronald Newbold Bracewell |
| Publisher | : |
| Total Pages | : |
| Release | : 1978 |
| Genre | : Fourier transformations |
| ISBN | : |
| Author | : Roger L. Easton Jr. |
| Publisher | : John Wiley & Sons |
| Total Pages | : 1005 |
| Release | : 2010-11-18 |
| Genre | : Technology & Engineering |
| ISBN | : 1119991862 |
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
| Author | : Eleanor Chu |
| Publisher | : CRC Press |
| Total Pages | : 423 |
| Release | : 2008-03-19 |
| Genre | : Mathematics |
| ISBN | : 1420063642 |
Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform
| Author | : Wim van Drongelen |
| Publisher | : Elsevier |
| Total Pages | : 319 |
| Release | : 2006-12-18 |
| Genre | : Science |
| ISBN | : 008046775X |
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
| Author | : Jim Bernard Breckinridge |
| Publisher | : SPIE-International Society for Optical Engineering |
| Total Pages | : 232 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 9780819482044 |
Computational Fourier Optics is a text that shows the reader in a tutorial form how to implement Fourier optical theory and analytic methods on the computer. A primary objective is to give students of Fourier optics the capability of programming their own basic wave optic beam propagations and imaging simulations. The book will also be of interest to professional engineers and physicists learning Fourier optics simulation techniques-either as a self-study text or a text for a short course. For more advanced study, the latter chapters and appendices provide methods and examples for modeling beams and pupil functions with more complicated structure, aberrations, and partial coherence. For a student in a course on Fourier optics, this book is a concise, accessible, and practical companion to any of several excellent textbooks on Fourier optical theory.
| Author | : Sonali Bagchi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 216 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1461549256 |
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.
| Author | : K.R. Rao |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 437 |
| Release | : 2011-02-21 |
| Genre | : Mathematics |
| ISBN | : 1402066295 |
This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
| Author | : Sandeep Singh |
| Publisher | : CRC Press |
| Total Pages | : 189 |
| Release | : 2024-11-13 |
| Genre | : Technology & Engineering |
| ISBN | : 1040152228 |
Currently, the techniques of operation research are widely used in every aspect of day-to-day life. This book discusses a variety of problems that arise in various businesses and develops mathematical theories as well as technology answers to solve them from an industry perspective. Optimization Techniques and Associated Applications incorporates cutting-edge methods for locating early workable answers to an optimization challenge and acts as a road map for creating a catastrophe management paradigm that is sustainable. This book offers numerical methods for resolving mathematical issues that can be found in numerous sectors and includes specific case studies of actual industrial optimization applications. The uncertainty that arises in various businesses is explored and new and recently developed techniques are discussed. Because this book primarily focuses on operations research and solutions to the challenges across a variety of disciplines, the audience is expansive and can include professionals, students, and researchers from mathematics as well as engineers from industrial engineering, computer science, information technology, mechanical, civil, electrical, petroleum, chemical, aerospace, aviation, meteorology, disaster management, and other departments.
