Introduction

• If you've ever used modular systems, or digital sound design, you've probably heard about waveshaping and wavefolding.

Both techniques take an input signal and transform it into a new one, harmonically rich, distorted sound with new timbre.

What is a Waveshaper?

At it's core, a waveshaper is an algorithm that reshapes an audio signal based on a transfer function. It takes the input signal's amplitude and outputs a new amplitude according to the waveshaper's curve.

Here's a simple example of linear case, where output signal is equal to the input signal:

y = n

 or

 output = input

The straight line in the picture represents linearity. When we bend that line, we introduce nonlinearity.

In nonlinear processing the input signal is not equal to the output signal (because of the bend).

Here is the simplest nonlinear case - an exponential curve:

y = pow(x,2)

or

output = input (increasing to the pow of 2)

In a waveshaper, we define a threshold (usually between -1,1) for y(output). Any input signal x, that exceeds this range is compressed to fit within those limits.

In the picture, the shown waveshapers are:

• tanh() - purple
• arctan() - blue

y = tanh(x * k) -> where k is defining the knee of the waveshaping curve

What is a Wavefolder?

A wavefolder is a specific type of waveshaper, where when the input signal's waveform gets too big, it doesn't get compressed, but it gets folds back.

When the signal exceeds a certain threshold (positive or negative) the wavefolder inverts it. Then the part that would go above the limit gets flipped upside down and folded back in.

The more drive gets added to the input, the more folds are introduced.

Wavefolding generates a lot of new harmonics in the high-end, creating bright, metallic sound texture.

Besides being used in distortion/saturator algorithms, they are widely used in sound synthesis and became famous in West Coast Systhesis.

Wavefolders are harmonically dense, bright and can be harsh if the input signal is too big.

When we use them?

We've showen the basic examples of how a waveshaper and wavefolder work. These simple concepts can be used in various scenarios:

• When creating distortion/saturation plugins
• When designing compressor plugins
• When we use them as modulation sources in audio synthesis of simple waveforms (triangle, sine etc.)

Summary

Waveshapers and wavefolders are both nonlinear algorithms that reshape signals in different ways. A waveshaper bends the signal according to a transfer curve, adding controlled distortion and warmth. A wavefolder, on the other hand, folds the signal back when it passes a limit, creating complex harmonics and bright, metallic textures.