periodisitet

Periodisitet is the property of repeating at regular intervals in time or space. It appears in mathematics, physics, chemistry, and computer science.

In mathematics, a function f is periodic if there exists a nonzero number T such that f(x+T) = f(x) for all x in its domain. T is the period; the smallest positive T is the fundamental period. Examples: sine and cosine have period 2π; a complex exponential e^{iωx} has period 2π/ω. A discrete sequence is periodic if it repeats after a fixed number of terms; for example, a_n = a_{n+N}.

In signal processing, many signals are modeled as periodic; Fourier analysis decomposes periodic signals into sums of sines and cosines. In physics, waves exhibit periodicity in time and space; periodic boundary conditions are used in simulations to model repeating environments.

In chemistry, periodicity refers to recurring trends in properties of elements across the periodic table, such as atomic radius, ionization energy, and electronegativity, reflecting the structure of periods and groups.

Some phenomena are quasi-periodic or almost periodic, meaning they repeat with approximate regularity or with multiple incommensurate frequencies; true non-periodicity occurs when no fixed period exists.

Related terms include the period (the actual length of the repeating interval), angular frequency ω = 2π/T, Fourier series, and periodic boundary conditions.