ABsin

ABsin is a term used in signal processing to describe a family of sinusoidal signals whose amplitude and instantaneous frequency are modulated independently. In this context, the abbreviation AB emphasizes separate control of the envelope and the spectral content, with sin referring to the sine-wave basis. A typical ABsin signal can be written as s(t) = A(t) · sin(∫_0^t ω(τ) dτ + φ), where A(t) is an amplitude envelope and ω(t) is the instantaneous angular frequency. The frequency is commonly defined as ω(t) = ω0 + Δω · B(t), where B(t) is a modulation function that shapes the bandwidth or frequency deviation over time.

Origins and usage: ABsin emerged in teaching materials in the 2010s as a simple framework to explore how simultaneous amplitude and frequency modulation interact in time and frequency domains. It is used as a practical model for illustrating joint modulation effects and for experiments in digital sound synthesis and communications simulations.

Applications: ABsin is employed in audio synthesis for expressive timbral control, in simulations of communications channels to study modulation effects, and in academic exercises that compare spectral outcomes under different choices of A(t) and B(t).

Variants: Variants include ABsin-Linear, ABsin-Nonlinear, and ABsin-Vector, each varying how amplitude, bandwidth, and frequency modulation are related and implemented in practice.

Limitations: As a simplified model, ABsin may not capture nonlinear distortions, hardware constraints, or complex wave shaping found in real systems, so it is primarily used as an analytical and pedagogical tool.

See also: Sine wave, Amplitude Modulation, Frequency Modulation.