X-Y Spinning LFOs

[iPassenger]

So I was reading a music tech mag the other day and it mentioned that the Jupiter 8 vsti has 2 LFOs which can be spun around by third LFO on a rotational axis. The X and Y axis determine where each LFO sends its modulation signal (output 1 (x) or output 2(y) )

See the Galaxy section here (under 'Innovative Additions'):

http://www.arturia.com/evolution/en/products/jupiter-8v/details.html

Anyway I thought this should be pretty easy to do on the Nord and have just had a bash but I am not sure if I have achieved the same effect, i think probably not. My solution seems to simplistic and I am pretty sure I am not taking into account the inversion (or negative) of the lfos etc..

So has anyone else got any better ideas on how to do it?

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Test Rotational.pch2
Description:		Download (listen)
Filename:	Test Rotational.pch2
Filesize:	1.69 KB
Downloaded:	1647 Time(s)

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[blue hell]

This is a rotator that I sometimes use for my patches, it is based on a multiplication of a vector by a rotation matrix (2D).

To make the rotation matrix a sine and a cosine function are needed, hence the use of two lfos for the rotating osc.


In this example it rotates frequency and amplitude modulation. When the amplitude changes fast the frequency changes slowly and the other way around at other times.

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rotator.pch2
Description:	A vector rotation example patch.	Download (listen)
Filename:	rotator.pch2
Filesize:	1.45 KB
Downloaded:	2394 Time(s)

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[iPassenger]

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.

[blue hell]

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 )

[fac]

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 do-able 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.

[blue hell]

[iPassenger]

Think I am going to have to go back to College!