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Fourier Synthesis

posted Dec 11, 2011, 7:54 PM by Charles Boling   [ updated Dec 11, 2011, 8:15 PM ]
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:

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