This document explains the spectrum of a pulsed signal in two quite different ways: first, in terms of a conceptually simple but powerful analytical tool, called the Fourier series,1 and second, in terms of what physically takes place when a radio frequency signal passes through a lossless narrowband filter. For those readers who have some familiarity with calculus, the essence of both explanations is presented in more precise, mathematical terms–the Fourier transform.