Design of two-dimensional FIR filters with quadrantally symmetric properties using the 2D L1-method

Abstract

The mathematical formulation of the two-dimensional (2D) -method for designing of the 2D-finite impulse response (FIR) filter is introduced in this study. It features the 2D-FIR filter with narrow transition width and flatter passband and stopband response. The 2D complexity is reduced using the quadrant symmetricity concept for the reduction of filter coefficients to be evaluated. Here, the unique features of the 2D -method are exploited for the efficient design of the 2D-FIR filter. To study the effectiveness of the 2D-FIR filter using the proposed method, its performance is compared with other existing 2D-FIR filter methods. Simulation results for five design example of 2D lowpass, highpass, bandpass, bandstop filters and 2D differentiator are presented to prove the efficacy of the proposed design in terms of passband ripple, stopband ripple, passband error, stopband error and magnitude response.