The discrete fourier transform, part 3: The PSD

Abstract

This paper is part 3 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 computing the Power Spectral Density (PSD) of the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). The implementation is based on a well-known algorithm, called the decimation in time Radix 2 FFT, and requires that its' input data be an integral power of two in length. This paper demonstrates the computation of the PSD and applications of the DFT and IDFT. The applications include filtering, windowing, pitch shifting and the spectral analysis of re-sampling. © JOT, 2009.