An Alternative Derivation of the Al-Alaoui Operator

It is shown in this letter that the well-known class of first-order digital differentiators and integrators can be simply derived from a classical continuous-time approximate differentiator by using the bilinear transformation. The result obtained represents a simple and alternative method of deriving the Al-Alaoui operator (also known as Al-Alaoui´s differentiator, integrator, transform).