Fourier transforms of large multidimensional data sets arise in many fields --ranging from seismology to medical imaging. The rapidly increasing power of computer chips, the increased availability of vector and array processors, and the increasing size of the data sets to be analyzed make it both possible and necessary to analyze the data more than one dimension at a time. The increased freedom provided by multidimensional processing, however, also places intesive demands on the communication aspects of the computation, making it difficult to write code that takes all the algorithmic possiblities into account and matches these to the target architecture. This book develops algorithms for multi-dimensional Fourier transforms that yield highly efficient code on a variety of vector and parallel computers. By emphasizing the unified basis for the many approaches to one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimizing implementations. This book will be of interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing. Topics covered include: tensor products and the fast Fourier transform; finite Abelian groups and their Fourier transforms; Cooley- Tukey and Good-Thomas algorithms; lines and planes; reduced transform algorithms; field algorithms; implementation on Risc and parallel

Mathematics of Multidimensional Fourier Transform Algorithms (Signal Processing and Digital Filtering)

Science & Math

Tolimieri, Richard

An, Myoung

Lu, Chao

Mathematics

Springer

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.

Algorithms for Discrete Fourier Transform and Convolution (Signal Processing and Digital Filtering)

Computers & Technology

Computer Science

Developing algorithms for multi-dimensional Fourier transforms, this book presents results that yield highly efficient code on a variety of vector and parallel computers. By emphasising the unified basis for the many approaches to both one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimising implementations. It will thus be of great interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing.

This book investigates in detail production scheduling technology in different kinds of shop environment to achieve sustainability manufacturing. Studies on shop scheduling have attracted engineers and scientists from various disciplines, such as electrical, mechanical, automation, computer, and industrial engineering. Pursuing a holistic approach, the book establishes a fundamental framework for this topic, while emphasizing the importance of intelligent optimization and the significant influence of production scheduling in the manufacturing systems. The book is intended for undergraduate and graduate students who are interested in intelligent optimization technology, shop scheduling, and green manufacturing systems or other scheduling applications.

Intelligence Optimization for Green Scheduling in Manufacturing Systems (Engineering Applications of Computational Methods, 18)

Business & Money

Gao, Liang

Li, Xinyu

Yin, Lvjiang

Management & Leadership

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