Novel differentiator designs with applications to system simulation

Novel designs for FIR (finite impulse response) digital differentiators are used in the computation of the impedance and impulse response for an electrical system. The differentiators have linear phase and are maximally linear. Their design is optimal in terms of integrated energy for the passband and stopband. The impedance and impulse response are determined from partial knowledge of the system step response. Initially, the step response is represented in digital form. After some finite time, it can be described analytically. The derivative of the digital representation for the step response must be accurately determined and matched with the derivative of the analytic function continuation. An example is provided which demonstrates the effectiveness of this technique