Due to phantom center phenomenon, when sound is panned to the ‘center’ and listened to from speakers, the sound will appear to be coming from between the two speakers, but not the ‘center’. True center can only be achieved by listening on headphones.
Pan controls could more closely emulate real-life movement of sound if they also control phase/doppler effects, reverb, and filtering.
Pan control law would be optimized to send -6dB to each channel (L/R) if the output channels will be combined to a mono signal. -3dB is the optimization if the output channels will be set to be stereo and not changed. In the case that the output channels might move between mono and stereo, -4.5dB would be the optimal pan control law setting.
Linear Amplitude Panning:
As one channel is moved from a signal 1. to 0. the other is moving from 0. to 1. When the pan is in the center, .5 signal is being sent to both channels. This type of panning causes a dip in intensity when panned to the center because two speakers at -6dB does not have the same perceived loudness as one speaker at 0dB.
Constant Power Panning:
The loss of intensity when panned to the center doesn’t happen when you begin to add up to 3dB as you move toward the center. To do this, you can take square root of each channels signal to measure amplitude instead of intensity. This way, center panning of signal intensity of .5 will equal .707 after the square root operation, which is a 3dB increase.
Constant Power Panning using table lookup:
Because taking the square root of two signals can be computationally intensive, looking up the first quarter of the sine and cosine for an angle and adding it to a 0 Hz cycle~ as an offset, can achieve the same panning results while saving on CPU.