- Dirichlet conditions: f(x) has only a finite number of discontinuities and only a finite number of extreme values (maximum and minimum).
- Functions satisfying these conditions may be called piecewise regular.

Fourier series is able to represent any piecewise regular function in the range [0,2L]

**Square wave **

- for n

**Full wave rectifier :**

- for n

**Swath wave :**

- for n