<p>“If the computer is going to do all the math for you, then why do they want you to have a background in Fourier transforms?”</p>
<p>There are computer programs that do all kinds of things: finite element programs that calculate stresses, optical programs that ray trace, signal processing programs that do autocorrelation calculations etc. There is an old saying: “garbage in = garbage out”. You just can’t hit the bottom and get the right answer. With fft routines, you have to rearrange the elements in the array, you need to make certain that your sampling is correct. If you don’t set things up correctly, you will get all kinds of bizarre results and when you show them to your boss, he’ll realize that you don’t know what you’re doing and you’ll be fired.</p>