Design of 2-D variable fractional delay FIR filter using 2-D differentiators

In this paper, the design of two-dimensional (2-D) variable fractional delay FIR filter using 2-D differentiators is presented. First, the Taylor series expansion is used to transform the specification of a 2-D variable fractional delay filter into the one of a 2-D differentiator. This transform makes the design problem of a 2-D fractional delay filter reduce to the design of 2-D differentiators with different orders. Then, a simple window method is proposed to design the 2-D differentiators. Also an analysis of the design error is provided. Finally, examples are demonstrated to illustrate the effectiveness of this new design approach.