Design of linear phase FIR filters using fractional derivative constraints

In this paper, the designs of linear phase FIR filters using fractional derivative constraints are investigated. First, the definition of fractional derivative is reviewed briefly. Then, the linear phase FIR filters are designed by minimizing integral squares error under the constraint that the ideal response and actual response have several same fractional derivatives at the prescribed frequency point. Next, the fractional maximally flat FIR filters are designed by letting the number of fractional derivative constraints be equal to the number of filter coefficients. Finally, numerical examples are demonstrated to show that the proposed method has larger design flexibility than the conventional integer derivative constrained methods.

► This is a research branch of fractional calculus and digital filter design.
► Fractional derivative constraints have been used to improve the accuracy of the linear phase FIR filter design.
► Fractional maximally flat FIR filter design has been studied in this paper.
► Performance comparison with conventional integer derivative constrained method has been demonstrated.