This paper shows several data processing operations used to improve and interpret spectrum analysis results of real-world data. The material shows how to overcome typical problems with time-domain data when using the Fast Fourier Transform (FFT), such as time sample values riding on a high-level “DC” bias, time sequence lengths not an integer power of two needed by the FFT, and determining spectral peak locations that reside between FFT bin centers. The mathematical content is kept at a sensible level while maintaining useful signal processing information.