Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms

Features Bridges the gap between textbooks and the literature Teaches up-to-date computational techniques relevant to the FFT-systematically reviews, explains, and unifies FFT ideas Provides more detail on the algorithmic aspects of the FFT than any other book on the market Serves as a self-teaching guide for learning not only the FFT, but also many widely applicable techniques in algorithm design and analysis, efficient numerical computation, and scientific programming Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.