waveform

A waveform is the mapping of a signal's amplitude (or other varying quantity) onto a temporal axis, producing a shape that encodes the signal's morphological properties. Its parameters are: the dependent variable (amplitude, pressure, voltage), the independent variable (time or spatial position), and the functional form (continuous or discrete). Waveforms persist through four mechanisms: (1) visual notation on paper or screen (oscillograms, spectrograms), (2) digital representation (sampled arrays in digital audio, vector graphics), (3) mathematical description (parametric functions like A·sin(2πft+φ)), and (4) physical transduction (needle grooves on vinyl, ink on paper chart recorders). The waveform distinguishes signal morphology from signal content — two signals with identical waveforms carry the same morphological information regardless of their physical carrier. Waveforms are classified by shape: sine (single frequency), square (abrupt transitions), sawtooth (linear ramp), triangle (symmetric ramp), pulse (brief impulse), and noise (stochastic). This classification is a human-made taxonomy; the natural world contains only electromagnetic or mechanical phenomena, not waveforms. [formal: waveform | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]