Almost periodic function
Article
An almost periodic function is a function that repeats its values with arbitrary accuracy, although it may not have one exact period. It generalises the idea of periodicity to signals formed from several frequencies whose periods may not share a common multiple.
Harald Bohr introduced one of the best-known definitions using translations of a function. For every desired accuracy, there must be many shifts that make the translated function uniformly close to the original.
Finite sums of sinusoidal functions are important examples. When their frequencies are incommensurable, the result is not exactly periodic but can still be almost periodic.
Almost periodic functions are used in harmonic analysis, differential equations, dynamical systems, quantum mechanics, and the study of oscillations with several interacting timescales.
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- Source / publisher: Wikipedia
- URL type: WWW
- Credits: Wikipedia
- URL: https://en.wikipedia.org/wiki/Almost_periodic_function