“most of the time, you can take apart a continuous signal into the sum of a bunch of sine waves. The fourier transform tells you how tall and how shifted each o

“most of the time, you can take apart a continuous signal into the sum of a bunch of sine waves. The fourier transform tells you how tall and how shifted each of those sine waves are for a given signal, for as many of those sine wave components as you care to calculate. If you want those summed sine waves to usefully model your input, you’ll need to add up sine waves that are wiggling at least two times as fast as the most rapidly changing feature you want to capture is. “