answer:You regard a function of time as if it were a periodic wave, representing the superposition of multiple sine waves. Each sine wave has a different frequency, amplitude, and phase shift, so the whole mixture is a kind of “recipe” for re-creating the original function. For actual periodic waves it’s called Fourier analysis, where there are discrete frequencies called overtones or harmonics. Fourier transforms, on the other hand, can handle an arbitrary function (especially one of finite time duration) using continuous rather than discrete frequencies. Thus a function of time is Fourier-transformed into a function of frequency, representing the unique mix of sine waves that, all superimposed together, forms the original time-domain function. It’s pretty remarkable. Here “domain” is in the sense of the x-coordinate of a mathematical function y = f(x). In time domain (what you see on an oscilloscope, for instance) the horizontal axis is time. In frequency domain the horizontal axis is frequency. There is a symmetric duality between time domain and frequency domain—they are flip sides of the same function. Engineering problems sometimes are more easily solved by working the frequency domain instead of the time domain. Imagine an audio engineer setting EQ on a recording—that frequency-domain stuff. The only catch is that Fourier transforms are usually complex numbers with both real and imaginary components, requiring an extra dimension to visualize. So often the frequency-domain representation shows only the magnitude or power of each frequency, discarding some of the phase information.