Fourier Series of Locally Stable Periodic Signals

A periodic signal is neither stable nor of finite energy unless it is almost everywhere null, and therefore, the theory of the preceding Chapter is not applicable. The relevant notion is that of Fourier series. (Note that Fourier series were introduced before Fourier transforms, in contrast with the order of appearance chosen in this text.) The elementary theory of Fourier series of this section is parallel to the elementary theory of Fourier transforms of the previous section. The connection between Fourier transforms and Fourier series is made by the Poisson sum formula, of which we present a weak (yet useful) version in this chapter.