Download or read book Computation of Two Dimensional Fourier Transforms for Noisy Band Limited Signals written by Weidong Chen and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The computation of the two-dimensional Fourier transform by the sampling points creates an ill-posed problem. In this chapter, we will cover this problem for the band-limited signals in the noisy case. We will present a regularized algorithm based on the two-dimensional Shannon Sampling Theorem, the two-dimensional Fourier series, and the regularization method. First, we prove the convergence property of the regularized solution according to the maximum norm. Then an error estimation is given according to the L2-norm. The convergence property of the regularized Fourier series is given in theory, and some examples are given to compare the numerical results of the regularized Fourier series with the numerical results of the Fourier series.
Download or read book Recent Advances in Integral Equations written by Francisco Bulnes and published by BoD – Books on Demand. This book was released on 2019-07-24 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral equations are functional equations in which an unknown function appears under an integral sign. This can involve aspects of function theory and their integral transforms when the unknown function appears with a functional non-degenerated kernel under the integral sign. The close relation between differential and integral equations does that in some functional analysis, and function theory problems may be formulated either way. This book establishes the fundamentals of integral equations and considers some deep research aspects on integral equations of first and second kind, operator theory applied to integral equations, methods to solve some nonlinear integral equations, and singular integral equations, among other things. This is the first volume on this theme, hoping that other volumes of this important functional analysis theme and operator theory to formal functional equations will be realized in the future.
Download or read book Mastering the Discrete Fourier Transform in One Two or Several Dimensions written by Isaac Amidror and published by Springer Science & Business Media. This book was released on 2013-07-19 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for ‘naive’ users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.
Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by McGraw-Hill Companies. This book was released on 1986 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groundwork. Convolution. Notation for some useful functions. The impulse symbol. The basic theorems. Doing transforms. The two domains. Electrical waveforms, spectra, and filters. Sampling and series. The laplace transform. Relatives of the fourier transform. Antennas. Television image formation. Convolution in statistics. Noise waveforms. Heat conduction and diffusion. The discrete fourier transform. The discrete hartley transform. The fast hartley transform. Pictorial dictionary of fourier transforms. Supplementary problems. Tables.
Download or read book Signal Analysis and Estimation written by Ronald Louis Fante and published by Wiley-Interscience. This book was released on 1988-01-18 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work introduces the analysis (using Fourier techniques) of continuous and discrete deterministic signals along with both estimation and spectral analysis of random signals. It is divided into two sections. Chapters 1-5 are devoted to the analysis of continuous and discrete deterministic signals, while Chapters 6-9 cover the properties, spectral analysis, and estimation of random signals. In addition, in order to assist readers, examples are liberally included throughout every chapter.
Download or read book Computational Imaging written by Ayush Bhandari and published by MIT Press. This book was released on 2022-10-25 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and up-to-date textbook and reference for computational imaging, which combines vision, graphics, signal processing, and optics. Computational imaging involves the joint design of imaging hardware and computer algorithms to create novel imaging systems with unprecedented capabilities. In recent years such capabilities include cameras that operate at a trillion frames per second, microscopes that can see small viruses long thought to be optically irresolvable, and telescopes that capture images of black holes. This text offers a comprehensive and up-to-date introduction to this rapidly growing field, a convergence of vision, graphics, signal processing, and optics. It can be used as an instructional resource for computer imaging courses and as a reference for professionals. It covers the fundamentals of the field, current research and applications, and light transport techniques. The text first presents an imaging toolkit, including optics, image sensors, and illumination, and a computational toolkit, introducing modeling, mathematical tools, model-based inversion, data-driven inversion techniques, and hybrid inversion techniques. It then examines different modalities of light, focusing on the plenoptic function, which describes degrees of freedom of a light ray. Finally, the text outlines light transport techniques, describing imaging systems that obtain micron-scale 3D shape or optimize for noise-free imaging, optical computing, and non-line-of-sight imaging. Throughout, it discusses the use of computational imaging methods in a range of application areas, including smart phone photography, autonomous driving, and medical imaging. End-of-chapter exercises help put the material in context.
Download or read book The Discrete Fourier Transform written by D. Sundararajan and published by World Scientific. This book was released on 2001 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and WalshOCoHadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book will be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. Errata(s). Preface, Page viii. OC www.wspc.com/others/software/4610/OCO. The above links should be replaced with. OC www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zipOCO. Contents: The Discrete Sinusoid; The Discrete Fourier Transform; Properties of the DFT; Fundamentals of the PM DFT Algorithms; The u X 1 PM DFT Algorithms; The 2 X 2 PM DFT Algorithms; DFT Algorithms for Real Data OCo I; DFT Algorithms for Real Data OCo II; Two-Dimensional Discrete Fourier Transform; Aliasing and Other Effects; The Continuous-Time Fourier Series; The Continuous-Time Fourier Transform; Convolution and Correlation; Discrete Cosine Transform; Discrete WalshOCoHadamard Transform. Readership: Upper level undergraduate students, graduates, researchers and lecturers in engineering and applied mathematics."
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Proceedings of the Symposium on New Directions in Electroanalytical Chemistry II written by Johna Leddy and published by The Electrochemical Society. This book was released on 1999 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Speech Processing written by Nilanjan Dey and published by Academic Press. This book was released on 2021-01-19 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Speech Processing: Algorithms and Case Studies is concerned with supporting and enhancing the utilization of speech analytics in several systems and real-world activities, including sharing data analytics related information, creating collaboration networks between several participants, and the use of video-conferencing in different application areas. The book provides a well-standing forum to discuss the characteristics of the intelligent speech signal processing systems in different domains. The book is proposed for professionals, scientists, and engineers who are involved in new techniques of intelligent speech signal processing methods and systems. It provides an outstanding foundation for undergraduate and post-graduate students as well. Includes basics of speech data analysis and management tools with several applications, highlighting recording systems Covers different techniques of big data and Internet-of-Things in speech signal processing, including machine learning and data mining Offers a multidisciplinary view of current and future challenges in this field, with extensive case studies on the design, implementation, development and management of intelligent systems, neural networks, and related machine learning techniques for speech signal processing
Download or read book Evaluation of the Two Dimensional Fourier Transform Applied to Acoustic Image Pattern Measurements written by Robert S. French and published by . This book was released on 1978 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this experimental study was to evaluate the use of the two-dimensional Fourier transform as an aid in extracting spatial frequency components in acoustic data images by means of direct operator observation. More specifically, the study addressed the question of the relative gain in precision of measurement which might be realized using the two-dimensional transform as compared to making these measurements directly from the original image. Of particular interest was the amount of gain at the weaker signal strengths typical of the class of processed acoustic data under investigation. As the signal power in the image decreases relative to the noise power, the probability increases that energy concentrations resulting from random noise patterning will appear in the transformed image. It is possible, therefore, that the human operator working with the original image alone may be able to separate signal related patterning from spurious noise patterning as well as can be achieved by using the transform. The experiment reported herein was designed to provide a definitive test of this hypothesis. Results showed that at high SNR levels the transform domain image representation was clearly superior to the original image as a mode for systematic measurement and ranking of periodic spatial features in the image. As the SNR level was reduced the accuracy of measurement in the transform domain fell off more rapidly than the original image domain, resulting in a convergence of the performance curves under the two modes. With the SNR level reduced so that the signal-related patterning was barely perceptible, measurement of periodic spatial features in the transform domain was no better than in the original image domain. (Author).
Download or read book Fourier Optics and Computational Imaging written by Kedar Khare and published by Springer Nature. This book was released on 2023-01-02 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is designed to serve as a textbook for advanced undergraduate and graduate students enrolled in physics and electronics and communication engineering and mathematics. The book provides an introduction to Fourier optics in light of new developments in the area of computational imaging over the last couple of decades. There is an in-depth discussion of mathematical methods such as Fourier analysis, linear systems theory, random processes, and optimization-based image reconstruction techniques. These techniques are very much essential for a better understanding of the working of computational imaging systems. It discusses topics in Fourier optics, e.g., diffraction phenomena, coherent and incoherent imaging systems, and some aspects of coherence theory. These concepts are then used to describe several system ideas that combine optical hardware design and image reconstruction algorithms, such as digital holography, iterative phase retrieval, super-resolution imaging, point spread function engineering for enhanced depth-of-focus, projection-based imaging, single-pixel or ghost imaging, etc. The topics covered in this book can provide an elementary introduction to the exciting area of computational imaging for students who may wish to work with imaging systems in their future careers.
Download or read book Inversion Based Fourier Transform as a New Tool for Noise Rejection written by Mihály Dobróka and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, a new inversion method is presented for performing two-dimensional (2D) Fourier transform. The discretization of the continuous Fourier spectra is given by a series expansion with the scaled Hermite functions as square-integrable set of basis functions. The expansion coefficients are determined by solving an overdetermined inverse problem. In order to define a quick algorithm in calculating the Jacobian matrix of the problem, the special feature that the Hermite functions are eigenfunctions of the Fourier transformation is used. In the field of inverse problem theory, there are numerous procedures for noise rejection, so if the Fourier transformation is formulated as an inverse problem, these tools can be used to reduce the noise sensitivity. It was demonstrated in many case studies that the use of Cauchy-Steiner weights could increase the noise rejection capability of geophysical inversion methods. Following this idea, the two-dimensional Fourier transform is formulated as an iteratively reweighted least squares (IRLS) problem using Cauchy-Steiner weights. The new procedure is numerically tested using synthetic data.
Download or read book Analytical and Experimental Modal Analysis written by Subodh V. Modak and published by CRC Press. This book was released on 2023-11-28 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the fundamentals and basic concepts of analytical and experimental approaches to modal analysis. In practice, the analytical approach based on lumped parameter and finite element models is widely used for modal analysis and simulation, and experimental modal analysis is widely used for modal identification and model validation. This book is inspired by this consideration and is written to give a complete picture of modal analysis. Features: Presents a systematic development of the relevant concepts and methods of the analytical and experimental modal analyses. Covers phase resonance testing and operational modal analysis. Provides the relevant signal processing concepts. Includes applications like model validation and updating, force identification and structural modification. Contains simulations, examples, and MATLAB® programs to enhance understanding. This book is aimed at senior undergraduates/graduates, researchers, and engineers from mechanical, aerospace, automotive, civil, and structural engineering disciplines.
Download or read book NASA Tech Briefs written by and published by . This book was released on 1992 with total page 1486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The DFT written by William L. Briggs and published by SIAM. This book was released on 1995-01-01 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.
Download or read book Journal of the Optical Society of America written by and published by . This book was released on 1990 with total page 838 pages. Available in PDF, EPUB and Kindle. Book excerpt:
