- KVRAF
- 3426 posts since 14 Nov, 2006, from Pacific NW

joshb wrote:Can anyone give me any insight into a wavefolding algorithm? I believe it's also referred to as foldover?

Thx

Try this:

out = sinf(gain*in);

As gain gets larger, the output will start to fold back on itself. Very similar to the Serge wave multiplier, but with some nice sine curving, instead of the triangle wave folding found in the Serge circuit.

- KVRist
- 305 posts since 21 Jun, 2013

- KVRist
- 76 posts since 13 Apr, 2016

Wow, thank you. That's very cool. Both the demo animation and the actual function.

"apply triangle"...is that a known function? Never heard of it and it really beats the hell out of the 18 ugly lines of code I threw together:

"apply triangle"...is that a known function? Never heard of it and it really beats the hell out of the 18 ugly lines of code I threw together:

- Code: Select all
`float fold(float x)`

{

float sign = 1.0f;

if(x < 0.0f)

sign = -1.0;

x *= sign;

if(x > threshold)

{

const float remainder = std::fmod(x, threshold);

const int numFolds = (int)std::floor(x / threshold);

float y;

if(numFolds % 2 == 0)

y = remainder;

else

y = threshold - remainder;

return y * sign;

}

return x * sign;

}

- KVRAF
- 4979 posts since 11 Feb, 2006, from Helsinki, Finland

Oh... that round() trick is really neat, saves some remapping when compared to using fmod(). Have to try to remember it.

<- plugins | forum

- KVRist
- 305 posts since 21 Jun, 2013

mystran wrote:Oh... that round() trick is really neat, saves some remapping when compared to using fmod(). Have to try to remember it.

- Code: Select all
`//Range (-0.5,0.5)`

__m128 fold(__m128 x)

{

__m128i int_round = _mm_cvtps_epi32(x);

__m128 frac = _mm_sub_ps(x,_mm_cvtepi32_ps(int_round));

return _mm_xor_ps(frac,_mm_castsi128_ps(_mm_slli_epi32(int_round,31)));

}

Here's another. Not plain C, but i guess you know sse2

- KVRist
- 305 posts since 21 Jun, 2013

joshb wrote:"apply triangle"...is that a known function? Never heard of it and it really beats the hell out of the 18 ugly lines of code I threw together:

Have a look at:

https://en.wikipedia.org/wiki/Triangle_wave

- KVRist
- 132 posts since 10 Oct, 2014

Polynomial integration/differentiation can be used to limit aliasing.

With this method, instead of using a punctual sample, you get a mean value over a sampling interval.

This method can be combined with x2 oversampling.

Here is a simplified code snippet from an Axoloti object.

With this method, instead of using a punctual sample, you get a mean value over a sampling interval.

This method can be combined with x2 oversampling.

Here is a simplified code snippet from an Axoloti object.

- Code: Select all
`//init code`

float x0 = 0, x1 = 0, y0 = 0, y1 = 0;

//sample rate code

x1 = x0; y1 = y0;

x0 = input * drive; // input drive

float f0 = x0+16.5f;

int i0 = (int)f0; //rounding

if(i0 & 1){

f0 = 2 * (f0 - i0) - 1.0f; //wavefold segment

y0 = 0.25f*(f0*f0-1); // and its smooth integral

} else {

f0 = -2 * (f0 - i0) + 1.0f; //wavefold segment

y0 = -0.25f*(f0*f0-1); // and its smooth integral

}

float x1_x0 = x1 - x0;

if(fabs(x1_x0) > 0.001f){ // if the interval is large enough,

out = (y1 - y0) / (x1_x0); // we differentiate

}else{ // else we take the

out = f0; // direct value

}

- KVRAF
- 11941 posts since 7 Dec, 2004

While there is a very narrow focus on abs(), it is important to recognize that abs() is merely one possible non-linear function, while any non-linear function can be used to create this effect.

http://xhip.net/effects/?p=Multiplier

https://soundcloud.com/xhip/multiplier

abs() is an infinite order non-linearity while it is also possible to use low order (2nd, 3rd) to approximate it very well. These can be trivially anti-aliased because they generate a limited number of harmonics. (N^2 = at most 2x the bandwidth.)

The famous "Serge wave multiplier" used a diode clamp (NOT APPROXIMATED BY TANH()!) as the non-linear function.

Search for past threads on the topic, I'm not going to go into detail just repeating what has already been said.

http://xhip.net/effects/?p=Multiplier

https://soundcloud.com/xhip/multiplier

abs() is an infinite order non-linearity while it is also possible to use low order (2nd, 3rd) to approximate it very well. These can be trivially anti-aliased because they generate a limited number of harmonics. (N^2 = at most 2x the bandwidth.)

The famous "Serge wave multiplier" used a diode clamp (NOT APPROXIMATED BY TANH()!) as the non-linear function.

Search for past threads on the topic, I'm not going to go into detail just repeating what has already been said.

Free plug-ins for Windows, MacOS and Linux. Xhip Synthesizer v8.0 and Xhip Effects Bundle v6.7.

- KVRist
- 76 posts since 13 Apr, 2016

The algorithm that 2DaT most generously gave:

is really close to what I'm trying to do. But I played around with this in Logic:

and was hoping to achieve that. I played around with that really elegant algorithm, but couldn't get there.

Any help would be greatly appreciated.

- Code: Select all
`out = 4.0 * (std::abs(0.25 * in + 0.25 - std::round(0.25 * in + 0.25)) - 0.25);`

is really close to what I'm trying to do. But I played around with this in Logic:

and was hoping to achieve that. I played around with that really elegant algorithm, but couldn't get there.

Any help would be greatly appreciated.

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- KVRAF
- 11941 posts since 7 Dec, 2004

- Code: Select all
`float sign = x > 0 ? 1.0f : -1.0f;`

float y = abs(x);

while (y >= 1.0f || y < 0.0f) {

if (y > 0.0f) {

y = 1.0f - y;

} else {

y = -y;

}

}

return sign * y;

Just off the top of my head. If it doesn't work right, figure it out and fix it.

Free plug-ins for Windows, MacOS and Linux. Xhip Synthesizer v8.0 and Xhip Effects Bundle v6.7.

- KVRAF
- 11941 posts since 7 Dec, 2004

Just a tip: give up on DSP and do something else with your time.

Free plug-ins for Windows, MacOS and Linux. Xhip Synthesizer v8.0 and Xhip Effects Bundle v6.7.

- KVRAF
- 11941 posts since 7 Dec, 2004

Although that wraps at 1/2 which is a major problem.

A simple solution is to scale the input/output like so:

https://www.desmos.com/calculator/f9cedeyybp

Noting of course that these operations can be applied to the bits of the float value far more efficiently using some mask magic. I know it can be done trivially as an optimization but I won't get in to it: anyone in need of the performance boost can invest that time themselves.

Unfortunately nothing will cure the atrocious aliasing resulting from such an implementation; you're limited to over-sampling and 6 dB per power of 2.

Better functions are like this:

https://www.desmos.com/calculator/yay1rwvk2w

Which is only third order and so can be perfectly anti-aliased with only 3x over-sampling.

Since this example uses 3 stages it requires a 3^3 (27x) over-sample, but it may make sense to go for 8x, 12x or other values for optimization purposes. Practically speaking such a wave-multiplier has little benefit on super-sonic partials anyway so pre-filtering the input can make a lot of sense to decrease over-sampling needs.

It's also possible to apply dynamic range processing (limiter or compressor) to set the maximum depth of the effect so as to ensure the bandwidth is limited far below the absolute maximum of the function. In many cases an expander and limiter combination (inverted compansion) can make the depth effect more exponential (DX series FM-like) and limit the maximum bandwidth with minimal processing expense compared to over-sampling methods.

A simple solution is to scale the input/output like so:

https://www.desmos.com/calculator/f9cedeyybp

Noting of course that these operations can be applied to the bits of the float value far more efficiently using some mask magic. I know it can be done trivially as an optimization but I won't get in to it: anyone in need of the performance boost can invest that time themselves.

Unfortunately nothing will cure the atrocious aliasing resulting from such an implementation; you're limited to over-sampling and 6 dB per power of 2.

Better functions are like this:

https://www.desmos.com/calculator/yay1rwvk2w

Which is only third order and so can be perfectly anti-aliased with only 3x over-sampling.

Since this example uses 3 stages it requires a 3^3 (27x) over-sample, but it may make sense to go for 8x, 12x or other values for optimization purposes. Practically speaking such a wave-multiplier has little benefit on super-sonic partials anyway so pre-filtering the input can make a lot of sense to decrease over-sampling needs.

It's also possible to apply dynamic range processing (limiter or compressor) to set the maximum depth of the effect so as to ensure the bandwidth is limited far below the absolute maximum of the function. In many cases an expander and limiter combination (inverted compansion) can make the depth effect more exponential (DX series FM-like) and limit the maximum bandwidth with minimal processing expense compared to over-sampling methods.

Free plug-ins for Windows, MacOS and Linux. Xhip Synthesizer v8.0 and Xhip Effects Bundle v6.7.