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Periodic phenomena such as:

• sound and light waves,
• the position and velocity of harmonic oscillators,
• sunlight intensity and day length,
• and average temperature variations throughout the year. See Time Serie - Seasonality (Cycle detection)

Articles Related

Model

Trigonometric functions are important in modeling periodic phenomena:

• Trigonometry - (Sine|Sinus)

See wiki/Periodic_function

All periodic functions can be exactly represented by Fourier Series

A function is periodic, with fundamental period T, if the following is true for all t: <MATH> f(t+T)=f(t) </MATH>