The discrete fourier transform, Part 2: Radix 2 FFT

Abstract

This paper is part 2 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on a fast implementation of the DFT, called the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). The implementation is based on a wellknown algorithm, called the Radix 2 FFT, and requires that its' input data be an integral power of two in length. Part 3 of this series of papers, demonstrates the computation of the PSD (Power Spectral Density) and applications of the DFT and IDFT. The applications include filtering, windowing, pitch shifting and the spectral analysis of re-sampling.