The fast Fourier transform (FFT) represents one of the most important advancements in scientific and engineering computing. This is a guide to learning the FFT and the multitude of ideas and computing techniques it employs. It brings together numerous and varied ideas in a common notational framework with a unified and systematic approach. It includes discussion of many widely-applicable techniques in algorithm design and analysis, efficient numerical computation, and scientific programming.

Offers a treatment of the theory and mathematics of fuzzy automata and fuzzy languages. This title compares the different approaches used in fuzzy mathematics and automata and includes proofs of the theoretical results presented. It discusses applications in a variety of fields, including databases, learning systems, and pattern recognition.