Doepfer

> the so called 'difference tone'. If you combine two sine waves f1 and
> f2, that are far enough apart in frequency, you will be able to hear a
> 'difference tone' f1 - f2. Does anybody on the list have enough
> physics background to tell if this is basically the same thing going
> on? Or is this something else? Or is it too off topic :)

That's one of the basic principles of the frequency shifter. I have a word
document that explains all the trigonometric formulas behind the RM/FS
(sorry the words are in German). If anybody's interested I can send him the
file (excerpt from the A-126 service manual).

These are the most important formulas (a and b are the two inputs)

1. For RM only:

·	sin a x sin b = cos(a-b) - cos(a+b)
or
·	cos a x cos b = cos(a-b) + cos(a+b)

Sine and cosine have a phase shift of 90 degree (in other words: shifting a
sine signal by 90 degrees leads to the cosine). But one cannot hear the
difference between sine and cosine as long as no phase-fixed reference
signal is available. Consequently you will hear the sum cos(a+b) and
difference cos(a-b) in the RM output. As each audio signal can be treated as
a sum of sine signals (Fourier analysis) any audio signals can be used.

The multiplications (sin a x sin b and the same with cosine) are realized
with the RM (four quadrant multiplier).


2. For additional frequency shifting:

·	sum of the above formulas: sina sinb + cosa cosb = 2 cos(a-b)
·	difference of the above formulas: sina sinb - cosa cosb = -2 cos(a+b)

That's how in principle the frequency shifter works (2 RM for the sine and
cosine and a simple adder and subtractor).
For frequency shifting "b" is a sine/cosine oscillator (so-called quadrature
oscillator) that generates sine and cosine simultaneously. "a" is the audio
signal to be frequency-shifted. To obtain the cosine of this signal a
so-called dome filter is required that generates a 90 degree phase shift of
the signal over a wide frequency range (~ 60Hz - 12kHz for the A-126). This
is because sine and cosine have a phase shift of 90 degree.

I hope that's not too much mathematics for the weekend - but you have been
asking ....


Best wishes
Dieter Doepfer