# Discrete Cosine and Sine Transforms

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

Produk Detail:

• Publisher : Elsevier
• Pages : 368 pages
• ISBN : 9780080464640
• Rating : 4/5 from 21 reviews

## Discrete Cosine and Sine Transforms

• Author : Vladimir Britanak,Patrick C. Yip,K. R Rao
• Publisher : Elsevier
• Release : 28 July 2010

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

## Discrete Cosine Transform

• Author : K. Ramamohan Rao,P. Yip
• Release : 28 June 2014

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.

## Digital Television

• Author : Walter Fischer
• Publisher : Springer Science & Business Media
• Release : 18 April 2013

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.

## Discrete Cosine Transform, Second Edition

• Author : Humberto Ochoa-Dominguez,K. R. Rao
• Publisher : CRC Press
• Release : 18 April 2019

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

## Transforms and Applications Handbook

• Author : Alexander D. Poularikas
• Publisher : CRC Press
• Release : 03 September 2018

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

## Discrete Cosine & Sine Transform

• Author : Jaskeerat S. Baweja
• Publisher : Unknown Publisher
• Release : 25 May 2022

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.

## Discrete Cosine Transform, Second Edition

• Author : Humberto Ochoa-Dominguez,K. R. Rao
• Publisher : CRC Press
• Release : 18 April 2019

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

## JPEG Series

• Author : K. R. Rao,Humberto Ochoa Domínguez,Shreyanka Subbarayappa
• Publisher : River Publishers Signal, Image
• Release : 30 June 2021

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.

## Integral and Discrete Transforms with Applications and Error Analysis

• Author : Abdul Jerri
• Publisher : CRC Press
• Release : 19 November 2021

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

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

• Author : Smitha Murthy
• Publisher : Unknown Publisher
• Release : 25 May 2022

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

## Multidimensional Discrete Unitary Transforms

• Author : Artyom M. Grigoryan,Sos S. Agaian
• Publisher : CRC Press
• Release : 31 July 2003

This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm sele

## The DFT

• Author : William L. Briggs,Van Emden Henson
• Publisher : SIAM
• Release : 01 January 1995

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,

## Digital Video and Audio Broadcasting Technology

• Author : Walter Fischer
• Publisher : Springer Science & Business Media
• Release : 24 March 2010

"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

## Digital Image Processing

• Author : Jayaraman
• Publisher : Tata McGraw-Hill Education
• Release : 25 May 2022

Meant for students and practicing engineers, this book provides a clear, comprehensive and up-to-date introduction to Digital Image Processing in a pragmatic style. An illustrative approach, practical examples and MATLAB applications given in the book help in bringing the theory to life.

## Handbook of Image Engineering

• Author : Yu-Jin Zhang
• Publisher : Springer Nature
• Release : 10 December 2020

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