Introduction

Abstract

The discrete Fourier transform (DFT) is the discrete-world counterpart of the continuous Fourier transform (CFT). The DFT is widely used as a practical and efficient computing tool for calculating numerically the Fourier transform (i.e. the frequency spectrum) of functions or signals [Brigham88 pp. xiv, 1–3, 98]. In many circumstances the values of our given signal are only known on a discrete grid (for example, if the signal values have been measured at discrete intervals or obtained by a digital computer). In such cases using DFT is the natural way for computing the Fourier transform of the given data. But even when the given signal is a continuous function whose analytical expression is fully known, DFT often remains the most convenient way for getting a visual glimpse at its spectrum, especially when the analytic calculation of the continuous Fourier transform proves to be too laborious or impractical