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

• 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.

Square wave 

for n_max=15

Full wave rectifier :

for n_max=14

Swath wave :

for n_max=15