A Primer on the Discrete Fourier Transform

Abstract

.There are several methods available to neurophysiologic technologists for the analysis of EEGs. Visual analysis is a technique that is comfortable and familiar to us. We use it to describe the EEG contents in terms of frequencies, amplitudes, phases, and unique waveforms as they evolve over time. The compressed spectral array (CSA) and the fast Fourier transform (FFT) are alternative analysis techniques that are becoming more common for monitoring in intensive care units and in the operating room. Additionally, with the advent of digital EEG, FFTs are available on some newer instruments. My own problems in trying to comprehend the relationship between the visual analysis of the EEG and the FFT has been my inability to get my hands on the FFT in a practical sense. I was comfortable with the general concept of transforms, but I really wanted to make small models for myself to explore the FFT. In the process of searching for methods of making small models, I began to read about the discrete Fourier transform (DFT) and realized that by using trigonometry and the DFT you can bridge the gap between the visual analysis and FFT analysis of the EEG. My reasons for selecting the DFT instead of the FFT are twofold. First, the DFT and the FFT yield the same numeric results. Secondly the DFT is simpler to understand for limited calculations. Admittedly the FFT is computationally more efficient than the DFT.