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2-D maximally flat diamond-shaped half-band linear phase FIR digital filters are used in sampling structure conversion. In some cases, this filter is expected to have different filter order for each dimension. However, the conventional methods can realize such filters only if difference between each order is 2, 4 and 6. In this paper, we proposed a closed-form transfer function of 2-D low-pass maximally flat diamond-shaped half-band FIR digital filters with arbitrary filter orders. The constraints to treat arbitrary filter orders are firstly proposed. Then, a closed-form transfer function is achieved by using Bernstein polynomial.

Two-dimensional (2-D) linear phase maximally flat finite impulse response (FIR) digital filters have flat passbands and stopbands. Conventionally, there are only fan-shaped or diamond-shaped. In this paper, we propose a method for designing 2-D low-pass maximally flat FIR digital filters that can realize various passband shapes. The proposed transfer function is achieved as a closed-form expression, and various passband shapes can be created by changing the filter order or flatness degree.