Fourier Series and the Discrete Fourier Transform: Quick Primer

The Fourier Series (FS) and the Discrete Fourier Transform (DFT) should be thought of as playing similar roles for periodic signals in either continuous time (FS) or discrete time (DFT). Both analyze signals into amplitude, phases, and frequencies of complex exponentials; both synthesize signals by linearly combining complex exponentials with appropriate amplitude, phase, and frequency. Finally, both transforms have aspects that are extremely important to remember and other aspects that are important, but can be adjusted as necessary. As we work through some of the details, we’ll identify these very important and the not so important aspects.