APU Mixer

The NES APU mixer takes the channel outputs and converts them to an analog audio signal. Each channel has its own internal digital-to-analog convertor (DAC), implemented in a way that causes non-linearity and interaction between channels, so calculation of the resulting amplitude is somewhat involved.

The following formula calculates the audio output level within the range of 0.0 to 1.0. It is the sum of two sub-groupings of the channels:

output = pulse_out + tnd_out

pulse_out = \frac{95.88}{\frac{8128}{pulse1 + pulse2} + 100}

tnd_out = \frac{159.79}{\frac{1}{\frac{triangle}{8227} + \frac{noise}{12241} + \frac{dmc}{22638}} + 100}

The values for pulse1, pulse2, triangle, noise, and dmc are the output values for the corresponding channel. The dmc value ranges from 0 to 127 and the others range from 0 to 15. When the values for one of the groups are all zero, the result for that group should be treated as zero rather than undefined due to the division by 0 that otherwise results.

This formula can be closely approximated using an efficient lookup table, or roughly approximated with a linear formula.

To do: determine and document the low-pass and high-pass filtering applied after the mixer.