Dirichlet Conditions

Dirichlet Conditions

Condition 1.

Over any period $[t,t+T],\,f(t)$ must have the property: $\int _{t}^{t+T}\mid f(t)\mid dt<\infty$

In other words, $f(t)$ is abosolutely integrable. The result of this property is that each of the Fourier coefficients $c_{n}$ is finite.

Condition 2.

Over any period of the signal, there must be only a finite number of minima and maxima. in other words, functions like $\sin \left({\frac {1}{t}}\right)$ are excluded. These functions are known as bounded variations.

Condition 3.

Over any period, $f\,(t)$ can have only a finite number of discontinuities.