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Anyone know the transfer functions for MultiSin & MultiT

 
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CharlesFerraro
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PostPosted: Tue Feb 21, 2017 8:11 am    Post subject: Anyone know the transfer functions for MultiSin & MultiT Reply with quote

The MultiSin and MultiTri settings in the Amp of MMT are waveshapers as you can tell from their nonlinear response. Sending a saw through either will have it transform into the designated waveform and then produce an octave higher version when more gain is applied. I have not checked either transformation through an oscilloscope yet which will probably prove illuminating.

Off hand would anyone happen to know what the transfer function graph looks like for both modes? I have gotten approximate results from toying around but knowing the real answer would be nice.
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voip
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PostPosted: Tue Feb 21, 2017 8:04 pm    Post subject: Reply with quote

The transfer functions for several waveshape types are depicted in the user manual Synth Parameters section.

http://www.korg.com/us/support/download/product/1/197/

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CharlesFerraro
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PostPosted: Wed Feb 22, 2017 3:27 am    Post subject: Reply with quote

Thanks for the reply voip. Unfortunately those aren't the transfer functions, those are the results of the waveshapers as seen through an oscilloscope. The transfer functions themselves are static. ie the graph doesn't change depending on the gain level.
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voip
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PostPosted: Wed Feb 22, 2017 8:07 am    Post subject: Reply with quote

Strictly speaking the transfer function is a mathematical description of the input-output relationship so you're really after the transfer curve. Because of the way the output breaks into harmonics, a single simple x-y plot does not suffice. In the user manual, the input is shown as the leftmost graphic, so visualise it as the x-axis, and the possible output relationships are shown to the right. There will be a transition zone between the two behaviours.

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CharlesFerraro
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PostPosted: Wed Feb 22, 2017 9:43 am    Post subject: Reply with quote

voip wrote:
Strictly speaking the transfer function is a mathematical description of the input-output relationship so you're really after the transfer curve. Because of the way the output breaks into harmonics, a single simple x-y plot does not suffice. In the user manual, the input is shown as the leftmost graphic, so visualise it as the x-axis, and the possible output relationships are shown to the right. There will be a transition zone between the two behaviours.

.


Yes of course I'm looking for the curve but I don't see why "a single simple x-y plot does not suffice". Maybe there's something you understand about waveshaping that I don't... but the transfer curve itself should be shown as a single plot. Naturally the input/output relationship changes the final waveform depending on gain.

I think you were just pointing out why the manual shows what it does... which I perfectly understood already. But that still doesn't tell me what the transfer curve itself looks like.
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voip
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PostPosted: Wed Feb 22, 2017 1:09 pm    Post subject: Reply with quote

OK, so consider this. The shape of the plot depends on the depth of the effect. Taking the MultiSin transfer curve as an example. At depth = 0 the transfer curve x vs y is a straight line. At depth = 64 the transfer curve becomes essentially a single sine curve. At depth = 127 it becomes two sine curves. To understand the transfer relationship more fully, it would be better if it were depicted by a family of curves, one for each depth value (I think these are treated internally within the Radias as integer values). From this, it would be possible to see, for any given depth value and input signal amplitude, what the output should look like.

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OpAmp
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PostPosted: Wed Feb 22, 2017 11:18 pm    Post subject: Reply with quote

Hi,

For the Multi.tri function, IMHO it can be modeled using a transfer function. I looked using a scope at it (on mKXL).
It is something like this: multiply the incoming signal by a factor, which is the gain that you can set.
Push this to a transfer function, which consist of 3 periods of a triangular wave centered around x = 0.
The wave starts at the most negative x value with a falling slope at y = 0. This makes you get a rising slope around x = 0.
When no gain is set the factor is 1 and the transfer function will then move over the rising slope of the middle period of the triangular wave.
by gradually increasing, the resulting waveform grows and suddenly at the rising edge of original saw, the change in slope direction of the triangle wave appears, but still with a disrupt transition. When the gain is further increased at some point (68 ) you get a complete triangular wave, but it is not clean. Due to internal roundings you still see some blur where the original swa has its rising edge. Further increasing the gain makes it going to the doubling of the frequency, but again disrupt transitions, till some point and so on...

For Multi.sin (yet) it is the same principle. Take 3 sinewave periods centered around 0. Look at a sine wave. Basically if you take this formula: sin(saw). If the amplitude of saw is small enough, the sine wave sin(x) can be approximated to x or sin(saw) = saw. Increasing the amplitude of the saw will gradually result in the sine wave. Of course only at discrete values of the gain the resulting sine wave will look like a sine. On other gain settings, it looks like an oscillator which is hard synced by a faster oscillator. I confirmed this on a scope.

Have fun.
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voip
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PostPosted: Thu Feb 23, 2017 10:36 pm    Post subject: Reply with quote

This link might be of interest. It's a spreadsheet that will help to visualise the effects of the depth and level parameters on a triangular wave passing through the MultiSin WaveShape type Amplifier function, and could be used to plot the transfer curve(s).

https://app.box.com/s/x2pio9qmz3dedixoso3t1o7bkrtj2fjo

The results model the actual behaviour of this WaveShaper reasonably closely. As the depth parameter value is increased, the initial triangle wave output becomes first a sine at the same frequency then, as the depth parameter is increased further, passes through three further transitions, where sinewaves are generated at 3x, 5x and then 7x the fundamental frequency.

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OpAmp
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PostPosted: Fri Feb 24, 2017 10:44 pm    Post subject: Reply with quote

The spreadsheet is well done. It's what I had in mind.
I saw you modelled/curve fitted the depth parameter so that values from 0-127 result in the correct amplification of the wave before pushing it through the sine. I did not look into that.

Anyway the same approach can be taken for the MultiTri. Unfortunately there is no arithmetic function for a triangular wave. Use a look-up-table or a variant of following formula
triangle = abs(x - rounddown(x) - 0.5) - 0.25 (This gives a triangle wave with a period of 1.)

Have fun
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