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Adding Signals - Hack Audio
https://www.hackaudio.com/digital-signal-processing/combining-signals/adding-signals/#:~:text=Digital%20signals%20can%20be%20%E2%80%9Cmixed%E2%80%9D%20or%20%E2%80%9Cblended%E2%80%9D%20by,added%20to%20the%20first%20sample%20of%20another%20signal.
Viktor T. Toth - Mixing digital audio
http://www.vttoth.com/CMS/index.php/technical-notes/68
Consider what happens if we mix another signal, $C$, to $Z$: \[T=Z+C-ZC=A+B+C-AB-AC-BC+ABC.\] In a practical implementation, the signal values are not between 0 and 1, but between 0 and some maximum integer value, such as 255 for 8-bit signals. So the equation needs to be normalized. For 8-bit audio, the normalized version looks like this:
Cheap way to mix two digital audio signals together and ...
https://www.audiosciencereview.com/forum/index.php?threads/cheap-way-to-mix-two-digital-audio-signals-together-and-output-digitally.25055/
I wonder if the audio interfaces with digital inputs and outputs do this. Why not combine the signals in your computer OS and then go digitally to DAC, like get a Focusrite Scarlet 8i6 or Motu ultralite and use the digital input for the music, then play that audio and game audio in your PC, output it through the interface digital output and then go to the DAC.
Algorithm(s) to mix audio signals without clipping ...
https://dsp.stackexchange.com/questions/3581/algorithms-to-mix-audio-signals-without-clipping
From reading around, a common method of mixing is: result = A + B - AB, where A and B are the two normalized samples being mixed, and AB is a term to ensure louder sounds are increasingly "soft-clipped". However, this introduces a distortion of the signal.
Naively mixing two (or perhaps more) audio signals ...
https://electronics.stackexchange.com/questions/103435/naively-mixing-two-or-perhaps-more-audio-signals
The simplest way to combine two signals is with two resistors as shown in the circuit diagram below. simulate this circuit – Schematic created using CircuitLab. The ground connecton is shared between both inputs and output.
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