How I reverse engineering a commercial spatial audio effect

Automated excerpt

Back while I was using a different OS, I used a program which processed the audio being played in real time and made it sound much better. Playing the impulse in the right channel allows extracting both outputs’ responses to sound played on the right, and likewise for the left. If the response to one impulse is $h$, then the response to an impulse at position $k$ is the same $h$ shifted to $k$ and scaled by $x[k]$. Adding all of those responses gives$$ $$This of course depends on the filter being a linear time-invariant filter[5].

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