> 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
>
>
>
>
>
> Yahoo! Groups Links
>
>
>
>
>
>
>