The Fourier Transform equation

The Fourier Transform of a function x(t) can be shown to be:

This equation is called the Fourier Transform equation.

(As a convention, we generally use capital letters to denote the Fourier transform)

Obviously not in all cases are we guaranteed that the integral on right hand side will converge.

We'll next discuss the conditions for the Fourier Transform of an aperiodic signal to exist.