# Statistics - (Periodicity|Periodic phenomena|Cycle)

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)

## Model

Trigonometric functions are important in modeling periodic phenomena:

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: $$f(t+T)=f(t)$$