Doepfer

> 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).

What a versatile principle! 

The word document would be out of my category, but maybe 
another recommendation? I would like to know more about 'general' 
properties of waves. Because as this example also demonstrates 
there are a lot of properties that are independent of the medium that 
the wave is in: air-pressure, electrons, whatever. Are there good 
books or websites on this subject? A little mathematics is ok :-) 


> 
> 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
> 
> 
> 
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