# Discrete Cosine And Sine Transforms

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## Discrete Cosine and Sine Transforms

Author | : Vladimir Britanak,Patrick C. Yip,K. R Rao |

Publsiher | : Elsevier |

Total Pages | : 368 |

Release | : 2010-07-28 |

ISBN | : 9780080464640 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Discrete Cosine and Sine Transforms 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

## Discrete Cosine Transform Second Edition

Author | : Humberto Ochoa-Dominguez,K. R. Rao |

Publsiher | : CRC Press |

Total Pages | : 358 |

Release | : 2019-04-18 |

ISBN | : 1351396471 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Discrete Cosine Transform Second Edition Book Excerpt:**

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.

## Digital Television

Author | : Walter Fischer |

Publsiher | : Springer Science & Business Media |

Total Pages | : 394 |

Release | : 2013-04-18 |

ISBN | : 3662054299 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Digital Television Book Excerpt:**

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.

## Discrete Cosine Transform Second Edition

Author | : Humberto Ochoa-Dominguez,K. R. Rao |

Publsiher | : CRC Press |

Total Pages | : 358 |

Release | : 2019-04-18 |

ISBN | : 135139648X |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Discrete Cosine Transform Second Edition Book Excerpt:**

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

Author | : Humberto Ochoa-Dominguez,K. R. Rao |

Publsiher | : CRC Press |

Total Pages | : 358 |

Release | : 2019 |

ISBN | : 9781138304727 |

Category | : Discrete cosine transforms |

Language | : EN, FR, DE, ES & NL |

**Discrete Cosine Transform Book Excerpt:**

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

## Discrete Cosine Sine Transform

Author | : Jaskeerat S. Baweja |

Publsiher | : Unknown |

Total Pages | : 266 |

Release | : 2000 |

ISBN | : 1928374650XXX |

Category | : Algorithms |

Language | : EN, FR, DE, ES & NL |

**Discrete Cosine Sine Transform Book Excerpt:**

The goals of this thesis are the following: to provide a tutorial in the field of discrete cosine transforms and discrete sine transforms in one, two, and three dimensions; to show how these transforms can be used in the field of image processing; and finally to compare their image coding capabilities.

## Transforms and Applications Handbook

Author | : Alexander D. Poularikas |

Publsiher | : CRC Press |

Total Pages | : 911 |

Release | : 2018-09-03 |

ISBN | : 1420066536 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Transforms and Applications Handbook Book Excerpt:**

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.

## Hardware Implementation of Windowed Discrete Cosine and Discrete Sine Transforms in VHDL

Author | : Smitha Murthy |

Publsiher | : Unknown |

Total Pages | : 126 |

Release | : 2004 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Hardware Implementation of Windowed Discrete Cosine and Discrete Sine Transforms in VHDL Book Excerpt:**

This study is to investigate the hardware implementation of the digital signal processing algorithms namely Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) for image compression and image updating. A typical approach when processing a signal or an image using Discrete Cosine Transform (DCT) or Discrete sine Transform (DST) is to extract a portion of the signal by windowing it and then applying DCT or DST of the window contents. The entire signal is processed by shifting the window point by point over the signal, hence limiting the updating algorithms (of DCT & DST) to a single point step between successive windows. In this thesis an algorithm developed to simultaneously update DCT and DST to reflect inclusion of r where 1[less than or equal to] r [less than or equal to] N-1. Additional points and removal of r old points from the signal is implemented in Very High-Speed Integrated Hardware Description Language (VHDL). The algorithm is derived for use with split triangular (trapezoidal) window; in this way the results are extended to handle larger step sizes. This thesis involves the hardware implementation using distributed arithmetic method of implementing DCT and DST in VHDL.

## Discrete Cosine Transform

Author | : K. Ramamohan Rao,P. Yip |

Publsiher | : Academic Press |

Total Pages | : 512 |

Release | : 2014-06-28 |

ISBN | : 0080925340 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Discrete Cosine Transform Book Excerpt:**

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.

## Integral and Discrete Transforms with Applications and Error Analysis

Author | : Abdul Jerri |

Publsiher | : CRC Press |

Total Pages | : 848 |

Release | : 2021-11-19 |

ISBN | : 1000147525 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Integral and Discrete Transforms with Applications and Error Analysis Book Excerpt:**

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.

## Digital Image Processing

Author | : Wilhelm Burger,Mark J. Burge |

Publsiher | : Springer Science & Business Media |

Total Pages | : 565 |

Release | : 2012-01-19 |

ISBN | : 9781846283796 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Digital Image Processing Book Excerpt:**

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.

## Digital Video and Audio Broadcasting Technology

Author | : Walter Fischer |

Publsiher | : Springer Science & Business Media |

Total Pages | : 800 |

Release | : 2010-03-24 |

ISBN | : 3642116124 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Digital Video and Audio Broadcasting Technology Book Excerpt:**

"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.

## Computational Frameworks for the Fast Fourier Transform

Author | : Charles Van Loan |

Publsiher | : SIAM |

Total Pages | : 286 |

Release | : 1992-01-01 |

ISBN | : 9781611970999 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Computational Frameworks for the Fast Fourier Transform 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.

## Hardware Implementation Design Synthesis and Analysis of Odd Discrete Cosine Transform and Odd Discrete Sine Transform Using Verilog HDL

Author | : Sanskruti Mainkar |

Publsiher | : Unknown |

Total Pages | : 170 |

Release | : 2007 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Hardware Implementation Design Synthesis and Analysis of Odd Discrete Cosine Transform and Odd Discrete Sine Transform Using Verilog HDL Book Excerpt:**

This objective of this work is to address the hardware implementation of Odd Discrete Cosine Transform (ODCT) and Odd Discrete Sine Transform (ODST) by utilizing the ODCT/ODST coefficients obtained from the conventional algorithms. The Discrete Cosine Transform (DCT) is a Fourier-related transform similar to the Discrete Fourier Transform (DFT), but using a purely real representation. The DCT Algorithm is widely used due to its autocorrelation properties, bandwidth reduction and energy compaction efficiency and is used extensively in the field of data and image compression, audio-visual, communication and speech enhancement techniques. The Discrete Sine Transform (DST) is equivalent to a DFT of real and odd functions. It is equivalent to the imaginary part of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample. In this thesis, the digital hardware implementations of these two transforms are achieved using a hybrid design process by modifying the traditional butterfly flow-graph. This is achieved by combining the butterfly flow-graph and the matrix-vector multiplication method. A set of 4 data points is used to implement the hybrid design, but the study can be extended to larger data sets in case of more data points with minor modifications, due to the symmetry in the basic butterfly.

## Handbook of Image Engineering

Author | : Yu-Jin Zhang |

Publsiher | : Springer Nature |

Total Pages | : 1967 |

Release | : 2020-12-10 |

ISBN | : 9811558736 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Handbook of Image Engineering Book Excerpt:**

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.

## Data Compression with Discrete Cosine sine Transform Discrete Cosine Transform and Wavelet Transforms

Author | : Feng Zou |

Publsiher | : Unknown |

Total Pages | : 143 |

Release | : 19?? |

ISBN | : 1928374650XXX |

Category | : Data compression (Computer science) |

Language | : EN, FR, DE, ES & NL |

**Data Compression with Discrete Cosine sine Transform Discrete Cosine Transform and Wavelet Transforms Book Excerpt:**

## Cosine Sine Modulated Filter Banks

Author | : Vladimir Britanak,K. R. Rao |

Publsiher | : Springer |

Total Pages | : 645 |

Release | : 2017-08-02 |

ISBN | : 3319610805 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Cosine Sine Modulated Filter Banks Book Excerpt:**

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

Author | : Prajna Kunche,N. Manikanthababu |

Publsiher | : Springer Nature |

Total Pages | : 110 |

Release | : 2020 |

ISBN | : 3030427463 |

Category | : Algorithms |

Language | : EN, FR, DE, ES & NL |

**Fractional Fourier Transform Techniques for Speech Enhancement Book Excerpt:**

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.

## Excursions in Harmonic Analysis Volume 4

Author | : Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou |

Publsiher | : Birkhäuser |

Total Pages | : 428 |

Release | : 2015-10-20 |

ISBN | : 3319201883 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Excursions in Harmonic Analysis Volume 4 Book Excerpt:**

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.

## The Transform and Data Compression Handbook

Author | : Kamisetty Ramam Rao,Patrick C. Yip |

Publsiher | : CRC Press |

Total Pages | : 408 |

Release | : 2018-10-03 |

ISBN | : 1420037382 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**The Transform and Data Compression Handbook Book Excerpt:**

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.