Eigenfilter design of higher-order digital differentiators

An effective approach is proposed for designing higher order differentiators by the eigenfilter method. By minimizing a quadratic measure of the error in the frequency band, an eigenvector of an appropriate matrix is computed to get the filter coefficients. This method is not only simple and fast, but also optimal in the least-squares sense. Comparison to the McClellan-Parks algorithm for minimax equiripple filters shows that both are optimal in the sense of different minimum norms of the error function, but much better performance is obtained with the proposed approach in most of the frequency band, except in the narrowband region near the cutoff edge