Original: The Fourier transform is also defined for such a function. As we increase the length of the interval on which we calculate the Fourier series, then the Fourier series coefficients begin to look like the Fourier transform and the sum of the Fourier series of Æ 'begins to look like the inverse Fourier transform.
Simplified: The Fast Fourier Transform is a way of calculating a Fourier transform much faster with a computer.