All electrical signals can be described either as a function of time or of frequency. When we observe signals as a function of time they are called the time domain measurements. Sometimes, we observe the frequencies present in signals, in which case they are called the frequency domain measurements. The word spectrum refers to the frequency content of any signal. When signals are periodic, time and frequency are simply related; namely, one is the inverse of the other. Then we can use the Fourier series to find the spectrum of the signal. For non-periodic signals, a Fourier transform is used to get the spectrum. This chapter provides an overview of fast Fourier transform (FFT) techniques, as applied to dynamic signal analysers (or FFT analysers) or DSOs where spectrum components of a time varying signal are to be displayed. In addition, the essential principles and applications of swept-tuned spectrum analysers are discussed, because spectrum observations of higher frequency signals, such as those used in communications systems, are still beyond the capability of FFT analysers.