Fourier Transform

We know from Chap.  3 that any piecewise continuous periodic function f(x) can be expanded into a Fourier series. One may ask if a similar expansion can be constructed for a function which is not periodicNon-periodic functions? The purpose of this chapter is to address this very question. We shall show that for non-periodic functions f(x) an analogous representation of the function exists, but in this case the Fourier series is replaced by an integral, called Fourier integral.