Analytic closed-form matrix for designing higher order digital differentiators using eigen-approach

The eigenfilter method has 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. We present simple analytic 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 design time is reduced greatly for designing long filters.