A closed-form transfer function of 2-D maximally flat half-band FIR digital filters with arbitrary filter orders

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.