Appendix A: Discrete Fourier Transform

Abstract

The discrete Fourier transform (DFT) is the algorithm of choice to implement a sampled version of the Fourier transform. The DFT can be interpreted as a sampled version of the discrete time Fourier transform (DTFT). The DFT is normally implemented in practice using the famous fast Fourier transform (FFT) algorithm. The FFT is an efficient way to implement the DFT and is not a transform in and of itself. The apparent loss of amplitude in the DFT when the input signal frequency does not match the DFT sample frequency is called straddle loss. Straddle loss can be mitigated by zero padding the FFT algorithm to increase the sample frequency and applying a weighting function to the data to degrade the resolution.