[music-dsp] stereo-wide pan law?

[Theo Verelst]

 > left = cos 0 * Re - sin 0 * Im = Re
 > right = sin theta * Re + cos theta * Im

It sometimes amazes me where people learn all this ..., though I 
partially know the answer.

How can you take the Real and imaginary part of a general audio signal, 
really, will somebody *with* a proper Electrical Engineering background 
try to explain that to themselves, that should be good for a few laughs.

Seriously, a Hilbert space has to do with the mathematical Fourier (not 
necessarily the Fast FF) transform (beginning of the 19th century, so 
hardly the pinnacle of contemporary mathematics, which would be more in 
the field of the Fock transform), and a transform as such will probably 
refer to the some variation on the important Fourier Theory. But, 
people, the head directionality approximation and thereflectivity of 
audio sounds, and even the strengths and relative distances of various 
frequencies emanating from small speakers have not directly to do with 
this transform, and the idea of the real and imaginary part in 
electrical signals has more to do with the three phases of wires 
carrying sinusoidal signals coming from an electricity generator than 
any sensible audio signal, unless it concerns an extremely specialistic 
subclass.

Just saying.

Ir. Theo Verelst