Favg

Favg is a notation used in mathematics, physics, engineering, and related fields to denote the average value of a quantity F. The exact form of the average depends on the domain of integration or the sampling scheme.

Common definitions include time average, spatial average, and ensemble average. The time average over an interval [0,T] is Favg = (1/T) ∫_0^T F(t) dt. The spatial average over a region V is Favg = (1/V) ∫_V F(x) dV. The discrete version uses a finite sample set {F_i} and yields Favg = (1/N) Σ F_i. In probabilistic settings, Favg often denotes the ensemble or expected value, Favg = E[F].

In signal processing and spectroscopy, Favg is sometimes used to describe the average or centroid of a spectrum. For a continuous spectrum with density S(f), the average frequency is Favg = [∫ f S(f) df] / [∫ S(f) df], with the discrete form Favg = [Σ f_i S(f_i)] / [Σ S(f_i)].

Because Favg is not a single fixed quantity, its precise definition should be taken from the context or accompanying notation. It serves as a concise shorthand for aggregated or representative values of F in analysis and modeling.