You are demonstrating what I really like about QQ in that its a highly intelligent/ educated/ hard nosed / one eyed audience and you actually pay attention to detail. The rest of the HIFi media really have no idea and just repeat the sales waffle from types like me.
You are probing way back into the bowels of my early concepts of Involve when I was examining all sorts of decode techniques including QS, SQ, Ambiosonics. As someone else observed SQ is a different and mind rapping beast but it does require the phase shifting to be done prior to the summations, see below:
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this is because it sums combined in phase and 90 degree phase shift signals, eg the A' signal is Mix of L(-0.71 SHIFTED -90) + R(INVERTED X 0.71), just summing L + R in the right ratios and post phase shifting is not the same.
QS is different
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As you can see all the summations are with the in shifted L/ R signals and we are NOT MIXING in phase and 90 degree shifted components. As such the phase shifts into L, L(-90), R, R(-90) can be done prior to the additions and produce the same answer.
Here is a snapshot of our 90 degree shift networks prior to the DSP:
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Showing all 4 components going into the DSP.
The advantage of this was that I was making provision for future developments in case SQ were onto a good idea and it enabled me to frig with the maths of the shifted components if an idea hit me (it did not). As you know, I resisted incorporating SQ into the blue eyed monster (as I hate it) , but you guys can be very "persuasive". This meant it was a change that we could do without complicated hardware changes.
As you are stalking the patents, have you looked at my personal favorites "Sweet spot" and Intelligent encode? I have attached them below and I will ask questions later! Note the encoder had to be split into 2 patents as the passive version discovery of the wonders of the 0.21 ratio mix had to be covered