Discrete Fourier Transforms and their Applications,

This text is designed to be a practial handbook on the evaluation and application of one of the major techniques for discrete signal processing. Knowledge of the discrete Fourier transform (DFT) and the ability to construct alogorithms based on the techniques of fast Fourier analysis are essential prerequisites for communications and cybernetics engineers. These methods are also of inestimable value to applied scientists in many other fields. The treatment given here is aimed specifically at such experimentalists and practitioners, and includes only such mathematical development as is necessary to give a feel for the significance of the methods, and to promote proficiency in its use. An introductory discourse on the general theory of Fourier series and transforms is followed by a thorough review of the properties and means of computation of the DFT. The fast Fourier transform is presented as a particularly efficient algorithm for DFT evaluation, and is described in some detail. Some applications of DFT's are discussed, and the book is rounded off with an introduction to discrete Hilbert transforms. Examples are provided throughout the text, and a full bibliography provides the basis for further study of the mathematical theory and specific areas of application.