Quasisine

Quasisine is a term used in mathematics and signal processing to describe a waveform that is nearly, but not exactly, a sine wave. There is no universally accepted formal definition; the term is largely descriptive and context-dependent.

In many usages, a quasisine refers to a sine wave whose amplitude or phase is slowly modulated, or to a waveform whose spectrum is dominated by the fundamental sine and has only small higher harmonics or sidebands. This captures the idea of a signal that remains visually or audibly close to a pure sine while incorporating controlled deviations.

Common mathematical representations include f(t) = A(t) sin(φ(t)) with A(t) close to a constant and φ(t) = ω0 t plus a small perturbation, or f(t) = ∑ a_k cos(k ω0 t + φ_k) with a_1 much larger than a_k for k > 1, or f(t) = sin(ω0 t) + ε g(t) with small ε. These forms reflect near-periodicity and limited spectral complexity.

Key properties typically cited are near-periodicity, low total harmonic distortion, and robustness to mild perturbations; the exact criteria depend on the application. In practice, deviations are often quantified using measures such as total harmonic distortion or spectral content.

Applications occur in signal generation, audio synthesis, communications, and instrumentation, where a nearly sinusoidal carrier or tone is desirable but some controlled deviation is useful for signaling or modeling realistic phenomena.

See also: sine wave, quasi-periodic, modulation, Fourier series.