The literature on digital signal processing is based on four kinds of transform: Fourier transform (FT),z‐transform, Fourier series, and discrete Fourier transform (DFT). Digital implementation uses only the DFT, usually in the form of an FFT algorithm. Some popular texts attempt to describe digital results by using analog (usually FT) analysis. Some have presented analytical results for infinite length random signals and then used illustrations based on finite length periodic signals. What “windows” do and their different effects on random and periodic signals seldom are clearly identified. There are two implementations of the DFT that differ by a constant factor. Fast convolution and correlation analyses require special handling to avoid “circular” effects. The DFT treats each finite length sample from a random signal as if it were a sample from a deterministic signal. The purpose of this tutorial is to illuminate these and other potentially troublesome aspects of digital signal processing pertinent to applications in sound and vibration analysis.