Waveshaping synthesis passes a signal through a nonlinear shaping function, and input amplitude controls spectral brightness

Waveshaping (nonlinear distortion) synthesis generates harmonically rich tones by passing an input signal — usually a sine wave — through a fixed nonlinear transfer function stored in a table. The key musical property is amplitude sensitivity: unlike a linear amplifier, a nonlinear shaping function produces a different output spectrum depending on how large the input is. Driving the function with a low-amplitude signal touches only its gentle central region (near-linear, few harmonics); a large-amplitude signal reaches its extremes (strong distortion, many harmonics). So an amplitude envelope on the input directly sculpts a time-varying spectrum at the output — mimicking how acoustic instruments brighten when played harder (a strummed guitar, a blown sax). This makes waveshaping efficient: one precomputed shaping table yields a whole family of timbres just by scaling the input. Chebyshev polynomial shaping functions let a designer specify an exact harmonic mix. A drawback is that output loudness varies with input amplitude, so amplitude normalization is usually needed to separate timbre from level.

Examples

A sine driven through a soft-clipping curve at low level stays nearly pure; raise its amplitude and odd harmonics bloom — the classic overdrive brightening. Using Chebyshev T2 as the shaping table turns a cosine into its second harmonic.

Assessment

Explain why increasing the amplitude of the input sine to a waveshaper makes the tone brighter rather than merely louder, and name one acoustic phenomenon this models. Then state why amplitude normalization is typically added.