Fourier Synthesis

Post date: Dec 12, 2011 3:54:50 AM

This is the idea that any waveform can be built by combinations of other waves. Any basic shape can be synthesized by combining a sine wave of the same primary frequency with varying amplitudes of its harmonics. Not all shapes contain all harmonics; for example, triangle and square waves only contain even harmonics, whereas a sawtooth is an example of a shape that does contain all harmonics. The more a shape varies from a sine (think sharp corners!) the more energy it has in the harmonics. This is why the the "flat-topping" or "splatter" that occurs when over-modulating an AM signal is bad; it creates a flat areas with squarish corners, and radiates significant energy on bands other than the one intended!

Here is a pictoral example of how adding more harmonics of the proper amplitude approximates a sawtooth wave:

(pictures extracted from http://en.wikipedia.org/wiki/File:Synthesis_sawtooth.gif)