Development of Efficient Algorithms for Fast Computation of Discrete Transforms PDF Download
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Author: Monir Taha Hamood
Publisher:
ISBN:
Category :
Languages : en
Pages : 211
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Book Description
Author: Monir Taha Hamood
Publisher:
ISBN:
Category :
Languages : en
Pages : 211
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Book Description
Author: C. Sidney Burrus
Publisher: Lulu.com
ISBN: 1300461640
Category : Technology & Engineering
Languages : en
Pages : 256
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Book Description
This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.
Author: K.R. Rao
Publisher: Springer Science & Business Media
ISBN: 1402066295
Category : Mathematics
Languages : en
Pages : 437
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Book Description
This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
Author: Rajesh Thomas
Publisher:
ISBN:
Category : Electrical engineering
Languages : en
Pages : 0
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Book Description
Fourier transforms form an integral part of most signal processing applications and are therefore a crucial enabler of modern technology. Thus, fast and efficient algorithms to compute the Fourier transform is an area of active research. A class of algorithms called the Fast Fourier Transforms (FFTs) already exist which can compute the Discrete Fourier Transform (DFT) quite efficiently. However, these algorithms use complex arithmetic. This could be a hindrance in hardware that lacks dedicated multiplier units like low power/low performance digital signal processors and embedded microprocessors. Moreover, these algorithms are not easily vectorizable. To avoid these drawbacks, a natively-real DFT computational algorithm is presented in this dissertation. This can compute the DFT with real arithmetic using real DFT eigenvectors. Moreover, this algorithm is entirely based on linear algebra and is not as complicated as the FFT algorithms. This can be implemented in parallel processing hardware since it is easily vectorizable. It has the potential to consume less power on low performance or fixed-point hardware although it needs more number of operations than existing FFT algorithms. If the need arises, this method can be combined with FFT algorithms to reduce the number of operations. This dissertation also presents a few techniques to obtain the real and orthonormal DFT eigenvectors from the DFT projection matrices. For each of these techniques, the DFT computation error and the number of operations required are also discussed. A 2-dimensional DFT computation algorithm is also presented.
Author: Humberto Ochoa-Dominguez
Publisher: CRC Press
ISBN: 1351396471
Category : Technology & Engineering
Languages : en
Pages : 318
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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.
Author: Charles Van Loan
Publisher: SIAM
ISBN: 9781611970999
Category : Mathematics
Languages : en
Pages : 286
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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.
Author: Artyom M. Grigoryan
Publisher: CRC Press
ISBN: 1482276321
Category : Computers
Languages : en
Pages : 540
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Book Description
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
Author: K. Ramamohan Rao
Publisher: Academic Press
ISBN: 0080925340
Category : Mathematics
Languages : en
Pages : 517
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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.
Author: Richard Tolimieri
Publisher: Springer Science & Business Media
ISBN: 1475727674
Category : Technology & Engineering
Languages : en
Pages : 273
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Book Description
This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book, since these formulations highlight the data flow, which is especially important on supercomputers. Because of their importance in many applications, much of the discussion centres on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms.
Author: Richard Tolimieri
Publisher: Springer Science & Business Media
ISBN: 1468402056
Category : Technology & Engineering
Languages : en
Pages : 241
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Book Description
The main emphasis of this book is the development of algorithms for processing multi-dimensional digital signals, and particularly algorithms for multi-dimensional Fourier transforms, in a form that is convenient for writing highly efficient code on a variety of vector and parallel computers.
