Fast Algorithms For The Digital Computation Of Linear Canonical Transforms

Download Fast Algorithms For The Digital Computation Of Linear Canonical Transforms full books in PDF, epub, and Kindle. Read online Fast Algorithms For The Digital Computation Of Linear Canonical Transforms ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Fast Algorithms for the Digital Computation of Linear Canonical Transforms

Author : Aykut Koc
Publisher : Stanford University
ISBN 13 :
Total Pages : 173 pages
Book Rating : 4.F/5 ( download)

DOWNLOAD NOW!

Book Synopsis Fast Algorithms for the Digital Computation of Linear Canonical Transforms by : Aykut Koc

Download or read book Fast Algorithms for the Digital Computation of Linear Canonical Transforms written by Aykut Koc and published by Stanford University. This book was released on 2011 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although it is straightforward to determine the relationship between the in-focus image and the object of a simple optical system such as a lens, it is far more challenging to compute the input/output relationships of general first-order and astigmatic optical systems. Such optical systems are known as quadratic-phase systems (QPS) and they include the Fresnel propagation in free space, propagation in graded-index media, passage through thin lenses, and arbitrary concatenations of any number of these, including anamorphic, astigmatic, nonorthogonal elements. Such computation is accomplished by representing the physical system with a general mathematical framework of integrations against kernels and then distilling the entire system into one input-output relationship that can be represented by a linear integral transform. The underlying mathematical integral transforms can be applied to a wider field of signal processing where they are known as the linear canonical transform (LCT) of a signal. Conventional numerical integration methods have a computational complexity of O(N^2) where N is the space-bandwidth product of the sampling scheme, e.g. the number of pixels in the field for an optical system. The algorithms described here yield a complexity of only O(Nlog N). The key is the use of different decompositions (or factorizations) of a given input/output relationship into simpler ones. Instead of following the general physical subparts in cascaded systems and computing input-output relations separately, these algorithms use the simplest possible decompositions to represent the entire system in terms of least possible number of steps. The algorithms are Fast Fourier Transform (FFT) based methods and the only essential deviation from exactness arises from approximating a continuous Fourier transform (FT) with the discrete Fourier transform (DFT). Thus the algorithms work with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy. Unlike conventional techniques these algorithms also track and control the space-bandwidth products, in order to achieve information that is theoretically sufficient but not wastefully redundant.

Fast Algorithms for the Digital Computation of Linear Canonical Transforms

Author : Aykut Koc
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (712 download)

DOWNLOAD NOW!

Book Synopsis Fast Algorithms for the Digital Computation of Linear Canonical Transforms by : Aykut Koc

Download or read book Fast Algorithms for the Digital Computation of Linear Canonical Transforms written by Aykut Koc and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Although it is straightforward to determine the relationship between the in-focus image and the object of a simple optical system such as a lens, it is far more challenging to compute the input/output relationships of general first-order and astigmatic optical systems. Such optical systems are known as quadratic-phase systems (QPS) and they include the Fresnel propagation in free space, propagation in graded-index media, passage through thin lenses, and arbitrary concatenations of any number of these, including anamorphic, astigmatic, nonorthogonal elements. Such computation is accomplished by representing the physical system with a general mathematical framework of integrations against kernels and then distilling the entire system into one input-output relationship that can be represented by a linear integral transform. The underlying mathematical integral transforms can be applied to a wider field of signal processing where they are known as the linear canonical transform (LCT) of a signal. Conventional numerical integration methods have a computational complexity of O(N^2) where N is the space-bandwidth product of the sampling scheme, e.g. the number of pixels in the field for an optical system. The algorithms described here yield a complexity of only O(Nlog N). The key is the use of different decompositions (or factorizations) of a given input/output relationship into simpler ones. Instead of following the general physical subparts in cascaded systems and computing input-output relations separately, these algorithms use the simplest possible decompositions to represent the entire system in terms of least possible number of steps. The algorithms are Fast Fourier Transform (FFT) based methods and the only essential deviation from exactness arises from approximating a continuous Fourier transform (FT) with the discrete Fourier transform (DFT). Thus the algorithms work with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy. Unlike conventional techniques these algorithms also track and control the space-bandwidth products, in order to achieve information that is theoretically sufficient but not wastefully redundant.

Linear Canonical Transforms

Author : John J. Healy
Publisher : Springer
ISBN 13 : 1493930281
Total Pages : 463 pages
Book Rating : 4.4/5 (939 download)

DOWNLOAD NOW!

Book Synopsis Linear Canonical Transforms by : John J. Healy

Download or read book Linear Canonical Transforms written by John J. Healy and published by Springer. This book was released on 2015-11-26 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

Fast Algorithms for Digital Signal Processing

Author : Richard E. Blahut
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 464 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Fast Algorithms for Digital Signal Processing by : Richard E. Blahut

Download or read book Fast Algorithms for Digital Signal Processing written by Richard E. Blahut and published by Addison Wesley Publishing Company. This book was released on 1985 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to abstract algebra. Fast algorithms for short convolutions. Fast algorithms for the discrete Fourier transform. Number theory and algebraic field theory. Computation in surrogate fields. Fast algorithms and multidimensional convolutions. Fast algorithms and multidimensional transforms. Architecture of filters and transforms. Fast algorithms based on doubling strategies. Fast algorithms for solving Toeplitz systems. Fast algorithms for Trellis and tree search. A collection of cyclic convolution algorithms. A collection of Winograd small FFT algorithms.

Fast Fourier Transform and Convolution Algorithms

Author : H.J. Nussbaumer
Publisher : Springer Science & Business Media
ISBN 13 : 3662005514
Total Pages : 260 pages
Book Rating : 4.6/5 (62 download)

DOWNLOAD NOW!

Book Synopsis Fast Fourier Transform and Convolution Algorithms by : H.J. Nussbaumer

Download or read book Fast Fourier Transform and Convolution Algorithms written by H.J. Nussbaumer and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra. This section is limited to the basic concepts as they apply to other parts of the book. Thus, we have restricted our discussion of number theory to congruences, primitive roots, quadratic residues, and to the properties of Mersenne and Fermat numbers. The section on polynomial algebra deals primarily with the divisibility and congruence properties of polynomials and with algebraic computational complexity. The rest of the book is focused directly on fast digital filtering and discrete Fourier transform algorithms. We have attempted to present these techniques in a unified way by using polynomial algebra as extensively as possible. This objective has led us to reformulate many of the algorithms which are discussed in the book. It has been our experience that such a presentation serves to clarify the relationship between the algorithms and often provides clues to improved computation techniques. Chapter 3 reviews the fast digital filtering algorithms, with emphasis on algebraic methods and on the evaluation of one-dimensional circular convolutions. Chapters 4 and 5 present the fast Fourier transform and the Winograd Fourier transform algorithm.

Information Optics and Photonics

Author : Thierry Fournel
Publisher : Springer Science & Business Media
ISBN 13 : 144197380X
Total Pages : 281 pages
Book Rating : 4.4/5 (419 download)

DOWNLOAD NOW!

Book Synopsis Information Optics and Photonics by : Thierry Fournel

Download or read book Information Optics and Photonics written by Thierry Fournel and published by Springer Science & Business Media. This book was released on 2010-11-01 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will address the advances, applications, research results, and emerging areas of optics, photonics, computational approaches, nano-photonics, bio-photonics, with applications in information systems. The objectives are to bring together novel approaches, analysis, models, and technologies that enhance sensing, measurement, processing, interpretation, and visualization of information. The book will concentrate on new approaches to information systems, including integration of computational algorithms, bio-inspired models, photonics technologies, information security, bio-photonics, and nano-photonics. Applications include bio-photonics, digitally enhanced sensing and imaging systems, multi-dimensional optical imaging and image processing, bio-inspired imaging, 3D visualization, 3D displays, imaging on nano-scale, quantum optics, super resolution imaging, photonics for biological applications, microscopy, information optics, and holographic information systems.

Fast Fourier Transforms

Author : C. Sidney Burrus
Publisher : Lulu.com
ISBN 13 : 1300461640
Total Pages : 256 pages
Book Rating : 4.3/5 (4 download)

DOWNLOAD NOW!

Book Synopsis Fast Fourier Transforms by : C. Sidney Burrus

Download or read book Fast Fourier Transforms written by C. Sidney Burrus and published by Lulu.com. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Frameworks for the Fast Fourier Transform

Author : Charles Van Loan
Publisher : SIAM
ISBN 13 : 9781611970999
Total Pages : 286 pages
Book Rating : 4.9/5 (79 download)

DOWNLOAD NOW!

Book Synopsis Computational Frameworks for the Fast Fourier Transform by : Charles Van Loan

Download or read book Computational Frameworks for the Fast Fourier Transform written by Charles Van Loan and published by SIAM. This book was released on 1992-01-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most comprehensive treatment of FFTs to date. Van Loan captures the interplay between mathematics and the design of effective numerical algorithms--a critical connection as more advanced machines become available. A stylized Matlab notation, which is familiar to those engaged in high-performance computing, is used. The Fast Fourier Transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing.

Fast Transforms Algorithms, Analyses, Applications

Author : Douglas F. Elliott
Publisher : Elsevier
ISBN 13 : 0080918069
Total Pages : 448 pages
Book Rating : 4.0/5 (89 download)

DOWNLOAD NOW!

Book Synopsis Fast Transforms Algorithms, Analyses, Applications by : Douglas F. Elliott

Download or read book Fast Transforms Algorithms, Analyses, Applications written by Douglas F. Elliott and published by Elsevier. This book was released on 1983-03-09 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it.

Fourier-related Transforms, Fast Algorithms, and Applications

Author : Okan K. Ersoy
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 550 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Fourier-related Transforms, Fast Algorithms, and Applications by : Okan K. Ersoy

Download or read book Fourier-related Transforms, Fast Algorithms, and Applications written by Okan K. Ersoy and published by Prentice Hall. This book was released on 1997 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting an introduction to all Fourier-related transforms, this work includes a number of applications in the different markets. The accompanying disk provides C and Fortran routines that can be implemented.

The Regularized Fast Hartley Transform

Author : Keith Jones
Publisher : Springer Science & Business Media
ISBN 13 : 9048139171
Total Pages : 232 pages
Book Rating : 4.0/5 (481 download)

DOWNLOAD NOW!

Book Synopsis The Regularized Fast Hartley Transform by : Keith Jones

Download or read book The Regularized Fast Hartley Transform written by Keith Jones and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most real-world spectrum analysis problems involve the computation of the real-data discrete Fourier transform (DFT), a unitary transform that maps elements N of the linear space of real-valued N-tuples, R , to elements of its complex-valued N counterpart, C , and when carried out in hardware it is conventionally achieved via a real-from-complex strategy using a complex-data version of the fast Fourier transform (FFT), the generic name given to the class of fast algorithms used for the ef?cient computation of the DFT. Such algorithms are typically derived by explo- ing the property of symmetry, whether it exists just in the transform kernel or, in certain circumstances, in the input data and/or output data as well. In order to make effective use of a complex-data FFT, however, via the chosen real-from-complex N strategy, the input data to the DFT must ?rst be converted from elements of R to N elements of C . The reason for choosing the computational domain of real-data problems such N N as this to be C , rather than R , is due in part to the fact that computing equ- ment manufacturers have invested so heavily in producing digital signal processing (DSP) devices built around the design of the complex-data fast multiplier and accumulator (MAC), an arithmetic unit ideally suited to the implementation of the complex-data radix-2 butter?y, the computational unit used by the familiar class of recursive radix-2 FFT algorithms.

Lecture Notes on Wavelet Transforms

Author : Lokenath Debnath
Publisher : Birkhäuser
ISBN 13 : 3319594338
Total Pages : 220 pages
Book Rating : 4.3/5 (195 download)

DOWNLOAD NOW!

Book Synopsis Lecture Notes on Wavelet Transforms by : Lokenath Debnath

Download or read book Lecture Notes on Wavelet Transforms written by Lokenath Debnath and published by Birkhäuser. This book was released on 2017-09-05 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India.

Fast Fourier Transform and Convolution Algorithms

Author : Henri J Nussbaumer
Publisher :
ISBN 13 : 9783642818981
Total Pages : 292 pages
Book Rating : 4.8/5 (189 download)

DOWNLOAD NOW!

Book Synopsis Fast Fourier Transform and Convolution Algorithms by : Henri J Nussbaumer

Download or read book Fast Fourier Transform and Convolution Algorithms written by Henri J Nussbaumer and published by . This book was released on 1982-09-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Photon Management

Author :
Publisher :
ISBN 13 :
Total Pages : 514 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Photon Management by :

Download or read book Photon Management written by and published by . This book was released on 2004 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inside the FFT Black Box

Author : Eleanor Chu
Publisher : CRC Press
ISBN 13 : 9781420049961
Total Pages : 346 pages
Book Rating : 4.0/5 (499 download)

DOWNLOAD NOW!

Book Synopsis Inside the FFT Black Box by : Eleanor Chu

Download or read book Inside the FFT Black Box written by Eleanor Chu and published by CRC Press. This book was released on 1999-11-11 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.

Discrete Cosine and Sine Transforms

Author : Vladimir Britanak
Publisher : Elsevier
ISBN 13 : 9780080464640
Total Pages : 368 pages
Book Rating : 4.4/5 (646 download)

DOWNLOAD NOW!

Book Synopsis Discrete Cosine and Sine Transforms by : Vladimir Britanak

Download or read book Discrete Cosine and Sine Transforms written by Vladimir Britanak and published by Elsevier. This book was released on 2010-07-28 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Loéve transform (KLT), with the emphasis on fast algorithms (one-dimensional and two-dimensional) and integer approximations of DCTs and DSTs for their efficient implementations in the integer domain. DCTs and DSTs are real-valued transforms that map integer-valued signals to floating-point coefficients. To eliminate the floating-point operations, various methods of integer approximations have been proposed to construct and flexibly generate a family of integer DCT and DST transforms with arbitrary accuracy and performance. The integer DCTs/DSTs with low-cost and low-powered implementation can replace the corresponding real-valued transforms in wireless and satellite communication systems as well as portable computing applications. The book is essentially a detailed excursion on orthogonal/orthonormal DCT and DST matrices, their matrix factorizations and integer aproximations. It is hoped that the book will serve as a valuable reference for industry, academia and research institutes in developing integer DCTs and DSTs as well as an inspiration source for further advanced research. Presentation of the complete set of DCTs and DSTs in context of entire class of discrete unitary sinusoidal transforms: the origin, definitions, general mathematical properties, mutual relationships and relations to the optimal Karhunen-Loéve transform (KLT) Unified treatment with the fast implementations of DCTs and DSTs: the fast rotation-based algorithms derived in the form of recursive sparse matrix factorizations of a transform matrix including one- and two-dimensional cases Detailed presentation of various methods and design approaches to integer approximation of DCTs and DSTs utilizing the basic concepts of linear algebra, matrix theory and matrix computations leading to their efficient multiplierless real-time implementations, or in general reversible integer-to-integer implementations Comprehensive list of additional references reflecting recent/latest developments in the efficient implementations of DCTs and DSTs mainly one-, two-, three- and multi-dimensional fast DCT/DST algorithms including the recent active research topics for the time period from 1990 up to now

Digital Signal Processing Algorithms

Author : Hari Krishna
Publisher :
ISBN 13 : 9781351454957
Total Pages : pages
Book Rating : 4.4/5 (549 download)

DOWNLOAD NOW!

Book Synopsis Digital Signal Processing Algorithms by : Hari Krishna

Download or read book Digital Signal Processing Algorithms written by Hari Krishna and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences. Digital Signal Processing Algorithms examines three of the most common computational tasks that occur in digital signal processing; namely, cyclic convolution, acyclic convolution, and discrete Fourier transformation. The application of number theory to deriving fast and efficient algorithms for these three and related computationally intensive tasks is clearly discussed and illustrated with examples. Its comprehensive coverage of digital signal processing, computer arithmetic, and coding theory makes Digital Signal Processing Algorithms an excellent reference for practicing engineers. The authors' intent to demystify the abstract nature of number theory and the related algebra is evident throughout the text, providing clear and precise coverage of the quickly evolving field of digital signal processing."--Provided by publisher.