Fourier Transform

Fourier Transform does mathematically what our ears do physically: resolve a signal into component frequencies. FT is a method to determine the simple wave components of a mixed wave. The method is theoretically based on calculus, but is actually carried out computationally using numerical analysis.

The signal output from an NMR instrument is called a Free Induction Decay (FID) and looks like the image on the left, which is intensity of the signal versus time. A fourier transform algorithm is applied to the signal which converts it to intensity versus frequency and looks like the image on the right:

A good way to see the method in action is to use excel and a simple dataset of times and intensities. A description of how to use excel to do FT is given here, but I will summarize it in case this link disappears: