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iPassenger
Joined: Jan 27, 2007 Posts: 1051 Location: Sheffield, UK
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Blue Hell
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Joined: Apr 03, 2004 Posts: 22289 Location: The Netherlands, Enschede
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iPassenger
Joined: Jan 27, 2007 Posts: 1051 Location: Sheffield, UK
Audio files: 5
G2 patch files: 78

Posted: Tue May 13, 2008 12:47 pm Post subject:



That link makes no sense to me whatsoever, I should have stayed at School for higher physics and maths.
Your patch makes a lot of sense (as I had originally tried the multipliers and given up). Is it easy to explain why you use only one inverter on the sine instead of one on both the sine and cosine? No worries if not, i'll just take it as red (Clavia red).
Cheers Blue.
R. _________________ iP (Ross)
 http://ipassenger.bandcamp.com
 http://soundcloud.com/ipassenger 

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Blue Hell
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Joined: Apr 03, 2004 Posts: 22289 Location: The Netherlands, Enschede
Audio files: 212
G2 patch files: 319

Posted: Tue May 13, 2008 1:18 pm Post subject:



This might be a better link ... the derivation given there under "complex plane" is one of the shortest possible answers to your question as to why the sine is negated and the cosine is not ... but it involves some higher math again.
I'm sure it all boils down to symmetry considerations in the end, but can't come up with an intuitive example. Maybe someone else can?
Wofram research has some pics illustrating what happens to a vector when a rotation matrix is applied to it .. it erm .. rotates the vector ( http://mathworld.wolfram.com/RotationMatrix.html ) _________________ Jan 

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fac
Joined: Dec 08, 2007 Posts: 162 Location: Mexico
G2 patch files: 1

Posted: Tue May 13, 2008 3:12 pm Post subject:



I have no clue what you guys are talking about but I know something about affine transformations (the class of geometric transformations to which rotations belong).
So, let's suppose you have two signals X(t) and Y(t), which may as well be LFO's, oscillators, or whatever. Let's consider a point in 2D given by [X(t), Y(t)]. If you want to rotate that point by A radians, you would so something like:
X'(t) = X(t) * cos(A)  Y(t) * sin(A)
Y'(t) = X(t) * sin(A) + Y(t) * cos(A)
where [X'(t), Y'(t)] is the rotated point (or the rotated pair of signals, if you like).
Now, the stuff above can be easily implemented in the G2 if A is constant, but let's suppose A can change over time, so we actually have another signal A(t) (e.g., the third LFO). This time, we get something like
X'(t) = X(t) * cos(A(t))  Y(t) * sin(A(t))
Y'(t) = X(t) * sin(A(t)) + Y(t) * cos(A(t))
I guess this should be also doable in the G2: the multiplications are done with level amplifiers, the sums and differences with mixers. The problem is with sin(A(t)) and cos(A(t)). I think those could be implemented with the phase modulation oscillator, which should do something like
cos(wt + I(t))
where w is the oscillator's frequency and I(t) is the modulating signal. Now, if I(t) = A(t)  wt, you would get precisely cos(A(t)).
And wt can be more or less obtained with a sawtooth oscillator at frequency w.
So, I would try doing this: place a phase modulation oscillator (Osc1) at a fixed frequency, and then take the signal A(t) and add an inverted saw (with the same frequency as Osc1), and send the resulting signal to the modulation input of Osc1. That should result in something similar to cos(A(t)).
Ok, so maybe this doesn't made any sense, but I think someone should try it because it sounds interesting. 

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Blue Hell
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Joined: Apr 03, 2004 Posts: 22289 Location: The Netherlands, Enschede
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iPassenger
Joined: Jan 27, 2007 Posts: 1051 Location: Sheffield, UK
Audio files: 5
G2 patch files: 78


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