Design of efficient fir digital differentiators of second and higher degrees by using universal weights

We propose in this paper an efficient design of FIR digital differentiators of degree k, k= 1, 2, 3,…, and their implementation in a novel structure which allows the order to be varied without having to alter the weights used in it. More precisely, we show that by using these ‘universal weights’ in a structure of order N_max, the order can be varied from N= 3 to N_max while keeping the weights fixed and retaining the optimality of performance. Mathematical formulae have been derived for these ‘universal weights’ for differentiators performing in the low- or midband-frequency ranges.