wavesthat

Wavesthat is a term used in digital audio and signal processing to denote a family of parameterized waveforms whose shape is defined by a set of controllable components. The concept emphasizes families of related waveforms rather than a single fixed signal and is used when discussing waveform design, synthesis methods, and timbre analysis.

Construction and representation: A wavesthat is typically described as a sum of basis waveforms with adjustable amplitudes, phases, and possibly time-varying parameters. A common mathematical form is W(t) = sum_i A_i(t) · w_i(t + phi_i(t)), where w_i are fixed basis shapes and A_i, phi_i encode modulation. In practice, wavesthat can be created by additive synthesis, by phase or frequency modulation, or by neural-network-based mapping from feature vectors to waveform samples.

Relationships to other concepts: Wavesthat are related to wavetable synthesis, additive synthesis, and granulized waveform design. Unlike a single oscillator, wavesthat describe a family allow dynamic timbre changes within notes or across performances.

Applications: In sound design, wavesthat enable flexible timbre modeling, interpolation between timbres, and rapid exploration of sonic textures. In research, they aid in parametric analysis of timbre, compression schemes, and perceptual studies of harmonic content.

Examples and variants: A simple wavesthat might interpolate between sine, triangle, and square waves by adjusting the weight coefficients of a selected basis set. More complex implementations may use learned bases from data or use nonstationary parameters to simulate evolving spectra.

Limitations and terminology: Because wavesthat is not a standardized term, its exact meaning can vary between authors. Clear definitions typically specify the basis set, modulation rules, and the intended application to avoid ambiguity.