Over 80% of all DSP applications require some form of frequency domain processing and there are many techniques for performing this kind of operation. This two part paper will serve as an introduction to frequency domain signal processing. In this first in a two paper series, we will cover the theory behind Fourier Transforms and frequency domain processing, while the second half will look at specific frequency domain techniques from an application perspective and show how frequency domain techniques can often provide information that is difficult or sometimes impossible to realise in the time domain. Topics discussed in this paper include: continuous and discrete Fourier transforms and FFTs; How the FFT works; The complex exponential; Windowing equations and effects.