Analytic closed forms for designing higher order digital differentiators by eigen-approach

The eigenfilter method has recently been proposed for designing higher-order differentiators very effectively. The design method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The elements of this matrix are usually evaluated by very time-consuming numerical integration. In the present work, the authors present simple analytical closed-form formulas to compute these matrix-elements very efficiently. Hence, the eigenfilter approach for differentiators becomes much easier and more accurate than before, and the design time is reduced greatly with the larger filter length. Several design examples are used to illustrate the effectiveness of this approach