FFT, a Powerful Tool for Modern Science and Technology

Abstract

In 1965, a five-page paper titled "An Algorithm for the Machine Calculation of Complex Fourier Series" by James W. Cooley and John W. Tukey was published in an American Mathematical Society journal—Mathematics of Computation.(1) That paper laid out a scheme that sped up one of the most common activities in scientific and engineering practice: the computation of the Fourier transform. The algorithm is called the Fast Fourier Transform— often referred to as FFT. It has become a standard analysis module because it is handy and powerful, especially with the aid of computer technology. The popularity of the FFT is evidenced by the wide variety of application areas. In addition to conventional radar, communications, sonar, and speech signal-processing applications, current fields of FFT usage include biomedical engineering, imaging, analysis of stock market data, spectroscopy, metallurgical analysis, nonlinear system analysis, mechanical analysis, geophysics analysis, simulation, music synthesis, and determining weight variation in the production of paper from pulp. It is considered "the most valuable numerical algorithm in our life . "M) To understand why the Fast Fourier Transform has had such a profound influence first requires some appreciation of the Fourier transform itself.