Exploring the fundamentals of fast Fourier transform technique and its elementary applications in physics

Abstract

Fast Fourier transform (FFT) is a powerful and versatile tool used in engineering science. As expected, papers related to the methods and applications of FFT are galore in literature. However, most of them are too advanced for comprehension by the undergraduates. In this work, the nitty-gritty of FFT algorithm is discussed in a manner so as to equip the reader with this ubiquitous computational tool with less time investment. The target readers of the paper are students pursuing physics at the high school or introductory undergraduate level. The aim is to illustrate the use of FFT technique as a simulation tool in physics and motivate the students to use it with ease for solving realistic problems, that often lack analytical solutions. Most of the scientific computing softwares available today have ready to use built-in FFT modules. Broadly speaking, most of these modules are known to be developed on the basis of a common FFT algorithm which was first proposed by Cooley et al (1969 IEEE Trans. Educ. 12 27–34; 1987 Mikrochim. Acta 93 33–45). An attempt is made to simplify the explanation of this not-so-straightforward algorithm. The built-in FFT module of SCILAB (2012 Scilab: Free and Open Source Software for Numerical Computation) (an open source software for scientific computation) has been used to simulate some simple problems from introductory undergraduate level topics like oscillations and wave optics.