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Discrete Cosine And Sine Transforms

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Discrete Cosine and Sine Transforms

Discrete Cosine and Sine Transforms Book
Author : Vladimir Britanak,Patrick C. Yip,K. R Rao
Publisher : Elsevier
Release : 2010-07-28
ISBN : 9780080464640
Language : En, Es, Fr & De

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Book Description :

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

Discrete Cosine and Sine Transforms

Discrete Cosine and Sine Transforms Book
Author : Vladimir Britanak,Patrick C Yip,K R Rao
Publisher : Academic Press
Release : 2006-11-26
ISBN : 9781493301034
Language : En, Es, Fr & De

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Book Description :

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-Loeve 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. Key Features - 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-Loeve 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."

Discrete Cosine Transform Second Edition

Discrete Cosine Transform  Second Edition Book
Author : Humberto Ochoa-Dominguez,K. R. Rao
Publisher : CRC Press
Release : 2019-04-18
ISBN : 135139648X
Language : En, Es, Fr & De

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Book Description :

Many new DCT-like transforms have been proposed since the first edition of this book. For example, the integer DCT that yields integer transform coefficients, the directional DCT to take advantage of several directions of the image and the steerable DCT. The advent of higher dimensional frames such as UHDTV and 4K-TV demand for small and large transform blocks to encode small or large similar areas respectively in an efficient way. Therefore, a new updated book on DCT, adapted to the modern days, considering the new advances in this area and targeted for students, researchers and the industry is a necessity.

Discrete Cosine Transform

Discrete Cosine Transform Book
Author : K. Ramamohan Rao,P. Yip
Publisher : Academic Press
Release : 2014-06-28
ISBN : 0080925340
Language : En, Es, Fr & De

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Book Description :

This is the first comprehensive treatment of the theoretical aspects of the discrete cosine transform (DCT), which is being recommended by various standards organizations, such as the CCITT, ISO etc., as the primary compression tool in digital image coding. The main purpose of the book is to provide a complete source for the user of this signal processing tool, where both the basics and the applications are detailed. An extensive bibliography covers both the theory and applications of the DCT. The novice will find the book useful in its self-contained treatment of the theory of the DCT, the detailed description of various algorithms supported by computer programs and the range of possible applications, including codecs used for teleconferencing, videophone, progressive image transmission, and broadcast TV. The more advanced user will appreciate the extensive references. Tables describing ASIC VLSI chips for implementing DCT, and motion estimation and details on image compression boards are also provided.

Digital Television

Digital Television Book
Author : Walter Fischer
Publisher : Springer Science & Business Media
Release : 2013-04-18
ISBN : 3662054299
Language : En, Es, Fr & De

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Book Description :

Digital Television closely examines all present-day TV transmission methods. These include MPEG, DVB, ATSC and ISDB-T. DVD is also discussed. The text covers these subjects in a practical-minded manner. Although mathematical formulations are used, they are in most cases only utilized to supplement the text. The book also contains chapters dealing with basic concepts such as digital modulation or transformations into the frequency domain. A major emphasis is placed on the measuring techniques used on these various digital TV signals. Practical examples and hints concerning measurement are provided. The book starts with analog TV base and signal, continues with MPEG-2 data stream, digital video, and digital audio, and then moves on to compression methods. After an excursion into the digital modulation methods, all the mentioned transmission methods are discussed in detail.

JPEG Series

JPEG Series Book
Author : K.R. Rao,Humberto Ochoa Domínguez
Publisher : CRC Press
Release : 2022-09-01
ISBN : 100079296X
Language : En, Es, Fr & De

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Book Description :

While the JPEG image standard was developed more than 25 years ago, it is still dominant in terms of image formation, manipulation and transmission over the internet and other media. As technology advances, new demands have arisen for the efficient transmission and storage of images causing other formats to emerge. Over the years, several extensions such as, JPEGLS, JPEG2K, JPEGXT, JPEGXR, JPEGXS and JPEG Pleno, have been added, constructing a series of standards for the compression and transmission of images. This book is the first to bring together most of the series of JPEG standards in a book. This book covers the descriptions of the JPEG standards and gives the reader an overview of the latest advances in the standards of the Joint Photographic Experts Group. Topics discussed include: • JEPG;• JPEG XR;• JPEG XT;• JPEG 2000;• JPEG XS;• JPEG Pleno;• JPEG AIC;• JPEG LS;• JPEG XL;• JPSearch;• JPEG Systems;• JBIG

Transforms and Applications Handbook

Transforms and Applications Handbook Book
Author : Alexander D. Poularikas
Publisher : CRC Press
Release : 2018-09-03
ISBN : 1420066536
Language : En, Es, Fr & De

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Book Description :

Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.

Integral and Discrete Transforms with Applications and Error Analysis

Integral and Discrete Transforms with Applications and Error Analysis Book
Author : Abdul Jerri
Publisher : CRC Press
Release : 2021-11-19
ISBN : 1000147525
Language : En, Es, Fr & De

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Book Description :

This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.

Discrete Cosine Transform

Discrete Cosine Transform Book
Author : Humberto Ochoa-Dominguez,K. R. Rao
Publisher : CRC Press
Release : 2019
ISBN : 9781138304727
Language : En, Es, Fr & De

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Book Description :

Revised edition of: Discrete cosine transform: algorithms, advntages, applications / K.R. Rao, P. Yip. 1990.

The Transform and Data Compression Handbook

The Transform and Data Compression Handbook Book
Author : Kamisetty Ramam Rao,Patrick C. Yip
Publisher : CRC Press
Release : 2018-10-03
ISBN : 1420037382
Language : En, Es, Fr & De

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Book Description :

Data compression is one of the main contributing factors in the explosive growth in information technology. Without it, a number of consumer and commercial products, such as DVD, videophone, digital camera, MP3, video-streaming and wireless PCS, would have been virtually impossible. Transforming the data to a frequency or other domain enables even more efficient compression. By illustrating this intimate link, The Transform and Data Compression Handbook serves as a much-needed handbook for a wide range of researchers and engineers. The authors describe various discrete transforms and their applications in different disciplines. They cover techniques, such as adaptive quantization and entropy coding, that result in significant reduction in bit rates when applied to the transform coefficients. With clear and concise presentations of the ideas and concepts, as well as detailed descriptions of the algorithms, the authors provide important insight into the applications and their limitations. Data compression is an essential step towards the efficient storage and transmission of information. The Transform and Data Compression Handbook provides a wealth of information regarding different discrete transforms and demonstrates their power and practicality in data compression.

Digital Video and Audio Broadcasting Technology

Digital Video and Audio Broadcasting Technology Book
Author : Walter Fischer
Publisher : Springer Science & Business Media
Release : 2010-03-24
ISBN : 3642116124
Language : En, Es, Fr & De

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Book Description :

"Digital Video and Audio Broadcasting Technology – A Practical Engineering Guide" deals with all the most important digital television, sound radio and multimedia standards such as MPEG, DVB, DVD, DAB, ATSC, T-DMB, DMB-T, DRM and ISDB-T. The book provides an in-depth look at these subjects in terms of practical experience. In addition it contains chapters on the basics of technologies such as analog television, digital modulation, COFDM or mathematical transformations between time and frequency domains. The attention in the respective field under discussion is focussed on aspects of measuring techniques and of measuring practice, in each case consolidating the knowledge imparted with numerous practical examples. This book is directed primarily at the specialist working in the field, on transmitters and transmission equipment, network planning, studio technology, playout centers and multiplex center technology and in the development departments for entertainment electronics or TV test engineering. Since the intire field of electrical communications technology is traversed in a wide arc, those who are students in this field are not excluded either. The third edition of this well established reference work includes the new formats MPEG-4 und IPTV, and it already gives an outlook to the newest standards like DVB-SH and DVB-T2.

Digital Image Processing

Digital Image Processing Book
Author : Wilhelm Burger,Mark J. Burge
Publisher : Springer Science & Business Media
Release : 2012-01-19
ISBN : 9781846283796
Language : En, Es, Fr & De

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Book Description :

Written as an introduction for undergraduate students, this textbook covers the most important methods in digital image processing. Formal and mathematical aspects are discussed at a fundamental level and various practical examples and exercises supplement the text. The book uses the image processing environment ImageJ, freely distributed by the National Institute of Health. A comprehensive website supports the book, and contains full source code for all examples in the book, a question and answer forum, slides for instructors, etc. Digital Image Processing in Java is the definitive textbook for computer science students studying image processing and digital processing.

Computational Frameworks for the Fast Fourier Transform

Computational Frameworks for the Fast Fourier Transform Book
Author : Charles Van Loan
Publisher : SIAM
Release : 1992-01-01
ISBN : 9781611970999
Language : En, Es, Fr & De

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Book Description :

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.

The DFT

The DFT Book
Author : William L. Briggs,Van Emden Henson
Publisher : SIAM
Release : 1995-01-01
ISBN : 0898713420
Language : En, Es, Fr & De

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Book Description :

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.

Handbook of Image Engineering

Handbook of Image Engineering Book
Author : Yu-Jin Zhang
Publisher : Springer Nature
Release : 2020-12-10
ISBN : 9811558736
Language : En, Es, Fr & De

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Book Description :

Image techniques have been developed and implemented for various purposes, and image engineering (IE) is a rapidly evolving, integrated discipline comprising the study of all the different branches of image techniques, and encompassing mathematics, physics, biology, physiology, psychology, electrical engineering, computer science and automation. Advances in the field are also closely related to the development of telecommunications, biomedical engineering, remote sensing, surveying and mapping, as well as document processing and industrial applications. IE involves three related and partially overlapping groups of image techniques: image processing (IP) (in its narrow sense), image analysis (IA) and image understanding (IU), and the integration of these three groups makes the discipline of image engineering an important part of the modern information era. This is the first handbook on image engineering, and provides a well-structured, comprehensive overview of this new discipline. It also offers detailed information on the various image techniques. It is a valuable reference resource for R&D professional and undergraduate students involved in image-related activities.

Cosine Sine Modulated Filter Banks

Cosine  Sine Modulated Filter Banks Book
Author : Vladimir Britanak,K. R. Rao
Publisher : Springer
Release : 2017-08-02
ISBN : 3319610805
Language : En, Es, Fr & De

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Book Description :

This book covers various algorithmic developments in the perfect reconstruction cosine/sine-modulated filter banks (TDAC-MDCT/MDST or MLT, MCLT, low delay MDCT, complex exponential/cosine/sine-modulated QMF filter banks), and near-perfect reconstruction QMF banks (pseudo-QMF banks) in detail, including their general mathematical properties, matrix representations, fast algorithms and various methods to integer approximations being recently a new transform technology for lossless audio coding. Each chapter will contain a number of examples and will conclude with problems and exercises. The book reflects the research efforts/activities and achieved results of the authors in the time period over the last 20 years.

Fractional Fourier Transform Techniques for Speech Enhancement

Fractional Fourier Transform Techniques for Speech Enhancement Book
Author : Prajna Kunche,N. Manikanthababu
Publisher : Springer Nature
Release : 2020
ISBN : 3030427463
Language : En, Es, Fr & De

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Book Description :

This book explains speech enhancement in the Fractional Fourier Transform (FRFT) domain and investigates the use of different FRFT algorithms in both single channel and multi-channel enhancement systems, which has proven to be an ideal time frequency analysis tool in many speech signal processing applications. The authors discuss the complexities involved in the highly non- stationary signal processing and the concepts of FRFT for speech enhancement applications. The book explains the fundamentals of FRFT as well as its implementation in speech enhancement. Theories of different FRFT methods are also discussed. The book lets readers understand the new fractional domains to prepare them to develop new algorithms. A comprehensive literature survey regarding the topic is also made available to the reader. Analyzes FRFT techniques in speech enhancement applications; Presents new approaches for speech enhancement using FRFT; Suggests the future directions of research in this emerging area.

D oh Fourier Theory Applications And Derivatives

D oh  Fourier  Theory  Applications  And Derivatives Book
Author : Mark S Nixon
Publisher : World Scientific
Release : 2022-03-10
ISBN : 1800611129
Language : En, Es, Fr & De

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Book Description :

D'oh! Fourier introduces the Fourier transform and is aimed at undergraduates in Computer Science, Mathematics, and Applied Sciences, as well as for those wishing to extend their education. Formulated around ten key points, this accessible book is light-hearted and illustrative, with many applications. The basis and deployment of the Fourier transform are covered applying real-world examples throughout inductively rather than the theoretical approach deductively.The key components of the textbook are continuous signals analysis, discrete signals analysis, image processing, applications of Fourier analysis, together with the origin and nature of the transform itself. D'oh! Fourier is reproducible via MATLAB/Octave and is supported by a comprehensive website which provides the code contained within the book.

Excursions in Harmonic Analysis Volume 4

Excursions in Harmonic Analysis  Volume 4 Book
Author : Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Publisher : Birkhäuser
Release : 2015-10-20
ISBN : 3319201883
Language : En, Es, Fr & De

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Book Description :

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Introduction to Orthogonal Transforms

Introduction to Orthogonal Transforms Book
Author : Ruye Wang
Publisher : Cambridge University Press
Release : 2012-03-08
ISBN : 0521516889
Language : En, Es, Fr & De

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Book Description :

A systematic, unified treatment of orthogonal transform methods that guides the reader from mathematical theory to problem solving in practice.