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

Time-Frequency Representations (Applied and Numerical Harmonic Analysis)

The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre dominates as questions of convergence are not considered. Our approach emphasizes the unifying role played by group structures on the development of theory and algorithms. This book consists of two main parts. The first treats Weyl-Heisenberg representations over finite abelian groups and the second deals with mul tirate filter structures over free abelian groups of finite rank. In both, the methods are dimensionless and coordinate-free and apply to one and multidimensional problems. The selection of topics is not motivated by mathematical necessity but rather by simplicity. We could have developed Weyl-Heisenberg theory over free abelian groups of finite rank or more generally developed both topics over locally compact abelian groups. However, except for having to dis cuss conditions for convergence, Haar measures, and other standard topics from analysis the underlying structures would essentially be the same. A re cent collection of papers [17] provides an excellent review of time-frequency analysis over locally compact abelian groups. A further reason for limiting the scope of generality is that our results can be immediately applied to the design of algorithms and codes for time frequency processing.

Birkhauser

This book develops theory and algorithms leading to systematic waveform design in time-frequency space. The key tool employed in the work is the Zak transform, which provides a two-dimensional image for sequences, the Fourier transform, convolution, and correlation, and allows for the design of sequences directly in Zak space. Application areas covered include pulse radars and sonars, multibeam radar and sonar imaging systems, remote dielectric material identification, and code division multiple-access communication systems. This is an excellent reference text for graduate students, researchers, and engineers in radar, sonar, and communication systems.

Ideal Sequence Design in Time-Frequency Space: Applications to Radar, Sonar, and Communication Systems (Applied and Numerical Harmonic Analysis)

Brodzik, Andrzej K.

Group Filters and Image Processing

Psypher Press

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.

See the best price to sell, buy, or rent books by An, Myoung. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by An, Myoung

See the best price to sell, buy, or rent books by An, Myoung. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

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

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

Time-Frequency Representations (Applied and Numerical Harmonic Analysis)

Ideal Sequence Design in Time-Frequency Space: Applications to Radar, Sonar, and Communication Systems (Applied and Numerical Harmonic Analysis)

Group Filters and Image Processing

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

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

Time-Frequency Representations (Applied and Numerical Harmonic Analysis)