Fourier integral representations The *Fourier integral* is the continuous analogue of a Fourier series. This formulas can be derived from the Fourier series expansion of the function on interval as . The substitution of and into the integral gives the following Fourier integral formulas: The first definition can be rewritten in exponential form, leading to exponential direct and inverse Fourier transforms: If the function is absolutely integrable on the real axis, you have the following equality: |