Mathematics Of Multidimensional Fourier Transform Alogrithms

Mathematics of Multidimensional Fourier Transform Algorithms

The Fourier transform of large multidimensional data sets is an essen tial computation in many scientific and engineering fields, including seismology, X-ray crystallography, radar, sonar and medical imaging. Such fields require multidimensional arrays for complete and faithful modelling. Classically, a set of data is processed one dimension at a time, permitting control over the size of the computation and calling on well-established I-dimensional programs. The rapidly increasing availability of powerful computing chips, vector processors, multinode boards and parallel machines has provided new tools for carrying out multidimensional computations. Multidimensional processing offers a wider range of possible implementations as compared to I-dimensional the greater flexibility of movement in the data in processing, due to dexing set. This increased freedom, along with the massive size data sets typically found in multidimensional applications, places intensive demands on the communication aspects of the computation. The writ ing of code that takes into account all the algorithmic possibilities and matches these possibilities to the communication capabilities of the tar get architecture is an extremely time-consuming task. A major goal of this text is to provide a sufficiently abstra

Mathematics of Multidimensional Fourier Transform Alogrithms

Fast Fourier Transform - Algorithms and Applications

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.