New design of full band differentiators based on Taylor series

The classical central difference approximations of the derivative of a function based on Taylor series are the same as type III maximally linear digital differentiators for low frequencies. A new finite difference formula is derived which can be implemented as a full band type IV maximally linear differentiator. The differentiator is compared with type III maximally linear and type IV equiripple minimax differentiators. A modification is proposed in the design to minimise the region of inaccuracy near the Nyquist frequency edge