Design of arbitrary cutoff 2-D diamond-shaped FIR filters using the Bernstein polynomial

In this paper, we propose a design of two-dimensional (2-D) linear-phase, diamond-shaped (DS) finite impulse response (FIR) filters by using Bernstein polynomials. Although the one-dimensional (1-D) FIR filter designed by the Bernstein polynomials has been well investigated, this approach has not been broadly applied to 2-D filter design yet. We present a novel method of designing the 2-D FIR DS filter. In order to be approximated by a 2-D Bernstein polynomial, the 2-D symmetrical frequency response is transformed into a new domain. The key observation is that the region of support of the transformed frequency response is not diamond-shaped. The boundary of the new region of support represents an ellipse, a circle, or a line, and is analytically derived. The resultant magnitude responses are flat in the passband and stopband.