Waveshaper

In electronic music waveshaping is a type of distortion synthesis in which complex spectra are produced from simple tones by altering the shape of the waveforms.

Waveshapers are used mainly by electronic musicians to achieve an extra-abrasive sound. This effect is most used to enhance the sound of a music synthesizer by altering the waveform or vowel. Rock musicians may also use a waveshaper for heavy distortion of a guitar or bass. Some synthesizers or virtual software instruments have built-in waveshapers. The effect can make instruments sound noisy or overdriven.

In digital modeling of analog audio equipment such as tube amplifiers, waveshaping is used to introduce a static, or memoryless, nonlinearity to approximate the transfer characteristic of a vacuum tube or diode limiter.

A waveshaper is an audio effect that changes an audio signal by mapping an input signal to the output signal by applying a fixed or variable mathematical function, called the shaping function or transfer function, to the input signal (the term shaping function is preferred to avoid confusion with the transfer function from systems theory). The function can be any function at all.

Mathematically, the operation is defined by the waveshaper equation

where f is the shaping function, x(t) is the input function, and a(t) is the index function, which in general may vary as a function of time. This parameter a is often used as a constant gain factor called the distortion index. In practice, the input to the waveshaper, x, is considered on [-1,1] for digitally sampled signals, and f will be designed such that y is also on [-1,1] to prevent unwanted clipping in software.

Sin, arctan, polynomial functions, or piecewise functions (such as the hard clipping function) are commonly used as waveshaping transfer functions. It is also possible to use table-driven functions, consisting of discrete points with some degree of interpolation or linear segments.

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