Some Applications of the Fast Fourier Transform

Abstract

Examples of applications of Fourier transforms are chosen from a variety of topics. Roughly, those topics can be classified in a few categories: problems that lead to partial differential equations and can be solved by certain methods of separation of variables; other problems that lead to ordinary differential equations or systems of such equations with constant coefficients, which are solved by subjecting the equations to Fourier analysis; and finally, many processes which become more intelligible to us if we study them not as functions of time but as functions of frequency. All these problems were previously attacked by standard Fourier analysis. Special emphasis is placed on pointing to the modifications brought about by the introduction of the fast Fourier transform. As far as physical subject matter is concerned, the applications are chosen largely from the field of ship design and ship operation.