Design of optimal 2-D FIR differentiators with quadrantally symmetric properties using the L1-method

Abstract

In this paper the design of 2-dimensional finite impulse response (2-D FIR) digital differentiator (DD) with quadrantally odd symmetric impulse response is presented. The L1-method is developed to design the 2-D system and minimize the L1-error. The design problem of 2-D FIR-DD is formulated as an optimization problem in order to compute the system coefficients with quadrantally odd symmetric properties. Finally, the design examples of 2-D differentiator of different order is demonstrated and analyzed in terms of the L1-error and elapsed time. The proposed 2-D FIR L1-DD is also compared with the existing 2-D differentiators designed using metaheuristic techniques and is observed to yield least L1-error.