How Does This Fourier Grapher Work?

Question

A friend sent me this link: http://toxicdump.org/stuff/FourierToy.swf. I am not very versed in fourier series. I know the basic definitions and some convergence stuff, what you'd learn in a basic real analysis course. Would someone explain to me what this thing is doing? What do the various numbers at the bottom represent? Thanks.

Answer 1

The core concept of the Fourier series is that any wave form can be transformed into a series of (co)sin waves. In general you can represent any wave form in the following way. $$ f(x) = \sum_{i=0}^{\infty}a_i \cos(ix) $$

All you have to do is pick the right values for $a_0, a_1, a_2, ...$

The boxes on that page each represent a harmonic of the wave. The left most is the first harmonic or the fundamental. The numbers along the bottom are the amplitudes of each of these harmonics; the $a_i$ values in the equation above.

You can play around with these values and you will see you can use it to generate other wave forms. For example 1, 0.5, 0.25, 0.125 ... will get you a sawtooth looking wave.