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Discrete Cosine and Sine Transforms

Discrete Cosine and Sine Transforms
General Properties, Fast Algorithms and Integer Approximations

by Vladimir Britanak,Patrick C. Yip,K. R Rao

  • Publisher : Elsevier
  • Release : 2010-07-28
  • Pages : 368
  • ISBN : 9780080464640
  • Language : En, Es, Fr & De
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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

Discrete Cosine Transform, Second Edition
A Book

by Humberto Ochoa-Dominguez,K. R. Rao

  • Publisher : CRC Press
  • Release : 2019-04-18
  • Pages : 358
  • ISBN : 1351396471
  • Language : En, Es, Fr & De
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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.

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

Hardware Implementation of Windowed Discrete Cosine and Discrete Sine Transforms in VHDL
A Book

by Smitha Murthy

  • Publisher : Unknown Publisher
  • Release : 2004
  • Pages : 126
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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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 & Sine Transform

Discrete Cosine & Sine Transform
1-D, 2-D & 3-D

by Jaskeerat S. Baweja

  • Publisher : Unknown Publisher
  • Release : 2000
  • Pages : 266
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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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.

Data Compression with Discrete Cosine-sine Transform, Discrete Cosine Transform, and Wavelet Transforms

Data Compression with Discrete Cosine-sine Transform, Discrete Cosine Transform, and Wavelet Transforms
Application to ECG Data Compression

by Feng Zou

  • Publisher : Unknown Publisher
  • Release : 19??
  • Pages : 143
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Digital Television

Digital Television
A Practical Guide for Engineers

by Walter Fischer

  • Publisher : Springer Science & Business Media
  • Release : 2013-04-18
  • Pages : 394
  • ISBN : 3662054299
  • Language : En, Es, Fr & De
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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.

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

Hardware Implementation, Design Synthesis and Analysis of Odd Discrete Cosine Transform and Odd Discrete Sine Transform Using Verilog HDL
A Book

by Sanskruti Mainkar

  • Publisher : Unknown Publisher
  • Release : 2007
  • Pages : 170
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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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.

Transforms and Applications Handbook

Transforms and Applications Handbook
A Book

by Alexander D. Poularikas

  • Publisher : CRC Press
  • Release : 2018-09-03
  • Pages : 911
  • ISBN : 1420066536
  • Language : En, Es, Fr & De
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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.

Discrete Cosine Transform, Second Edition

Discrete Cosine Transform, Second Edition
A Book

by Humberto Ochoa-Dominguez,K. R. Rao

  • Publisher : CRC Press
  • Release : 2019-04-18
  • Pages : 358
  • ISBN : 135139648X
  • Language : En, Es, Fr & De
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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.

Linear Difference Equations with Discrete Transform Methods

Linear Difference Equations with Discrete Transform Methods
A Book

by A.J. Jerri

  • Publisher : Springer Science & Business Media
  • Release : 2013-03-09
  • Pages : 442
  • ISBN : 1475756577
  • Language : En, Es, Fr & De
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This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv ing, primarily, ordinary linear difference equations. Examples from various fields are presented clearly in the first chapter, then discussed along with their detailed solutions in Chapters 2-7. The book is in tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the di rect use of the discrete Fourier transforms for solving boundary value problems associated with difference equations represents an added new feature compared to other existing books on the subject at this introductory level. This means that in addition to the familiar meth ods of solving difference equations that are covered in Chapter 3, this book emphasizes the use of discrete transforms. It is an attempt to introduce the methods and mechanics of discrete transforms for solv ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the opera tional (integral) calculus of Laplace and Fourier transforms to solve differential equations. As in the continuous case, discrete operational methods may not solve problems that are intractable by other meth ods, but they can facilitate the solution of a large class of discrete initial and boundary value problems. Such operational methods, or what we shall term "operational sum calculus," may be extended eas ily to solve partial difference equations associated with initial and/or boundary value problems.

Computational Frameworks for the Fast Fourier Transform

Computational Frameworks for the Fast Fourier Transform
A Book

by Charles Van Loan

  • Publisher : SIAM
  • Release : 1992
  • Pages : 273
  • ISBN : 9781611970999
  • Language : En, Es, Fr & De
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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.

Discrete Cosine Transform

Discrete Cosine Transform
Algorithms, Advantages, Applications

by K. Ramamohan Rao,P. Yip

  • Publisher : Academic Press
  • Release : 2014-06-28
  • Pages : 512
  • ISBN : 0080925340
  • Language : En, Es, Fr & De
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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.

Multidimensional Discrete Unitary Transforms

Multidimensional Discrete Unitary Transforms
Representation: Partitioning, and Algorithms

by Artyom M. Grigoryan,Sos S. Agaian

  • Publisher : CRC Press
  • Release : 2003-07-31
  • Pages : 544
  • ISBN : 1482276321
  • Language : En, Es, Fr & De
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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

DSP for MATLAB and LabVIEW: Fundamentals of discrete frequency transforms

DSP for MATLAB and LabVIEW: Fundamentals of discrete frequency transforms
A Book

by Forester W. Isen

  • Publisher : Morgan & Claypool Publishers
  • Release : 2009
  • Pages : 217
  • ISBN : 1598298933
  • Language : En, Es, Fr & De
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This book is Volume II of the series DSP for MATLABâ„¢ and LabVIEWâ„¢. This volume provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z -Transform (including definition and properties, the inverse z -transform, frequency response via z-transform, and alternate filter realization topologies (including Direct Form, Direct Form Transposed, Cascade Form, Parallel Form, and Lattice Form), and the Discrete Fourier Transform (DFT) (including Discrete Fourier Series, the DFT-IDFT pair, DFT of common signals, bin width, sampling duration and sample rate, the FFT, the Goertzel Algorithm, Linear, Periodic, and Circular convolution, DFT Leakage, and computation of the Inverse DFT). The entire series consists of four volumes that collectively cover basic digital signal processing in a practical and accessible manner, but which nonetheless include all essential foundation mathematics. As the series title implies, the scripts (of which there are more than 200) described in the text and supplied in code form (available via the internet at http://www.morganclaypool.com/page/isen) will run on both MATLABâ„¢ and LabVIEWâ„¢. The text for all volumes contains many examples, and many useful computational scripts, augmented by demonstration scripts and LabVIEWâ„¢ Virtual Instruments (VIs) that can be run to illustrate various signal processing concepts graphically on the user's computer. Volume I consists of four chapters that collectively set forth a brief overview of the field of digital signal processing, useful signals and concepts (including convolution, recursion, difference equations, LTI systems, etc), conversion from the continuous to discrete domain and back (i.e., analog-to-digital and digital-to-analog conversion), aliasing, the Nyquist rate, normalized frequency, sample rate conversion and Mu-law compression, and signal processing principles including correlation, the correlation sequence, the Real DFT, correlation by convolution, matched filtering, simple FIR filters, and simple IIR filters. Chapter 4 of Volume I, in particular, provides an intuitive or "first principle" understanding of how digital filtering and frequency transforms work, preparing the reader for the present volume (Volume II). Volume III of the series covers digital filter design (FIR design using Windowing, Frequency Sampling, and Optimum Equiripple techniques, and Classical IIR design) and Volume IV, the culmination of the series, is an introductory treatment of LMS Adaptive Filtering and applications.

Digital Image Processing

Digital Image Processing
A Book

by Jayaraman

  • Publisher : Tata McGraw-Hill Education
  • Release : 2009
  • Pages : 723
  • ISBN : 9780070144798
  • Language : En, Es, Fr & De
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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.

Fast Transform Methods in Digital Signal Processing

Fast Transform Methods in Digital Signal Processing
A Book

by Leonid Yaroslavsky

  • Publisher : Bentham Science Publishers
  • Release : 2011-09-09
  • Pages : 119
  • ISBN : 1608052303
  • Language : En, Es, Fr & De
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"This ebook covers fast transform algorithms, analyses, and applications in a single volume. It is the result of the collaboration by the author with others in the world wide university community and has been accumulated over the author's working lifetime "

Digital Image Processing

Digital Image Processing
An Algorithmic Introduction Using Java

by Wilhelm Burger,Mark J. Burge

  • Publisher : Springer
  • Release : 2016-03-25
  • Pages : 811
  • ISBN : 1447166841
  • Language : En, Es, Fr & De
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This revised and expanded new edition of an internationally successful classic presents an accessible introduction to the key methods in digital image processing for both practitioners and teachers. Emphasis is placed on practical application, presenting precise algorithmic descriptions in an unusually high level of detail, while highlighting direct connections between the mathematical foundations and concrete implementation. The text is supported by practical examples and carefully constructed chapter-ending exercises drawn from the authors' years of teaching experience, including easily adaptable Java code and completely worked out examples. Source code, test images and additional instructor materials are also provided at an associated website. Digital Image Processing is the definitive textbook for students, researchers, and professionals in search of critical analysis and modern implementations of the most important algorithms in the field, and is also eminently suitable for self-study.

Handbook of Image Engineering

Handbook of Image Engineering
A Book

by Yu-Jin Zhang

  • Publisher : Springer Nature
  • Release : 2021
  • Pages : 129
  • ISBN : 9811558736
  • Language : En, Es, Fr & De
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A Hardware Implementation and Analysis of the Discrete Cosine Transform Update Algorithms

A Hardware Implementation and Analysis of the Discrete Cosine Transform Update Algorithms
A Book

by Hazem Bassam Alassaly

  • Publisher : Unknown Publisher
  • Release : 2005
  • Pages : 480
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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This work can be divided into three main objectives. The first objective is to implement hardware circuits that are capable of computing the Discrete Cosine Transform (DCT) coefficients and the Discrete Sine Transform (DST) coefficients in an efficient and optimized way (conventional mode of operation). Those circuits are built using a hybrid design that combines the butterfly flow-graph and the matrix-vector multiplication method. The hybrid design helps solving the problem of global communications that are necessary to implement the traditional butterfly flow-graph. An optimum size of 8 data points is used to implement the hybrid design. The second objective is to incorporate hardware circuits that are capable of updating both the DCT coefficients and the DST coefficients simultaneously using moving window of size 8 and step size of 1 and 4 (update mode of operation). This mode of operation aids in recalculating the DCT and DST coefficients in their entirety (i.e. updated) based on receiving a number of data points that is smaller than the size of the window. By having both modes of operation implemented together, the capability of switching between the two modes becomes available which can be exercised in some specific cases. Finally, the third objective is to investigate the possibilities of speeding-up the architecture along with reducing the power requirements.

Cosine-/Sine-Modulated Filter Banks

Cosine-/Sine-Modulated Filter Banks
General Properties, Fast Algorithms and Integer Approximations

by Vladimir Britanak,K. R. Rao

  • Publisher : Springer
  • Release : 2017-08-02
  • Pages : 645
  • ISBN : 3319610805
  • Language : En, Es, Fr & De
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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.