Sine-Law Panning

A third type of panning function is Sine-Law Panning. As the name suggests, this type of panning is based on the sine function.

Similar to linear and square-law panning, an amplitude value for the left channel and right channel of a stereo signal can be calculated based on the sine-law panning functions. Then a mono signal can be converted to a stereo signal by multiplying by the amplitude value for each channel.

Just as before, the relationship between an amplitude, $x$ , and a pan knob value, $p$ , is:

$x = \frac{p}{200} + 0.5$

For Sine-Law panning, the amplitude of the right channel and left channel can be calculated:

$R = \sin{(x \cdot \frac{\pi}{2})}$

$L =\sin{((1-x) \cdot \frac{\pi}{2})}$

Sine-law panning is similar to square-law panning in that it maintains equal-combined power across both channels, but does not maintain equal-combined amplitude.

One interesting use of panning functions is to create the stereo auto-pan effect. This effect uses many of the same concepts as the mono tremolo effect.