A general structure of type-III FIR filters with derivative constraints

In this paper, a general structure of type-III FIR filters with derivative constraints is proposed. It consists of a linear combinations of basic sub-filters, called cardinal filters, with weighting coefficients equal to derivatives of the target frequency response at ω = 0. Closed-form expressions for these cardinal filters are derived and their filter coefficients are shown to have a simple recursive relation. Numerical experiments confirm that the proposed design is much more numerically stable than the solution obtained by solving the derivative constraints.