phase modulation phasor animation

Hey, here's an animation showing how phase modulation works in the phasor picture. Specifically, this shows phase modulation with a sinusoidal modulation waveform and a modulation depth of π/4 radians. The blue line segments represent the phasors at the carrier and the harmonics of the modulation frequency.

The stationary horizontal blue line segment represents the carrier. Ordinarily, it would be spinning around the phasor diagram very quickly--at whatever the carrier frequency is. The phasor picture is more useful, though, if we choose a "co-moving reference frame" in which the carrier is stationary. The upper sidebands of the carrier then appear to move clockwise while the lower sidebands rotate anti-clockwise.

The next two blue line segments (after the carrier) are the first-order sidebands. Notice how they are phased such that their sum is always perpendicular to the carrier, and, thus, to first order, they don't change the amplitude of the resultant phasor. For big modulation depths, such as here, they do change the amplitude a little, so the 2nd and higher order sidebands are needed to correct this.

some things that would be cool:
* re-implement in javascript (processing.js?)
* add an interactive modulation-depth slider
* allow user to try out other modulation waveforms

matlab source: https://gist.github.com/1015769