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Two-dimensional (2-D) maximally flat finite impulse response (FIR) digital filters have flat characteristics in both passband and stopband. 2-D maximally flat diamond-shaped half-band FIR digital filter can be designed very efficiently as a special case of 2-D half-band FIRfilters. In some cases, this filter would require the reduction of the filter lengths for one of the axes while keeping the other axis unchanged. However, the conventional methods can realize such filters only if difference between each order is 2, 4 and 6. In this paper, we propose a closed-form frequency response 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. key words: 2-D diamond-shaped filter, maximally flat, half-band filter, arbitrary different filter orders, closed-form expression

ieice transactions on fundamentals of electronics, communications and computer sciences/ieice transactions on fundamentals of electronics, communications and computer science

A Closed-Form of 2-D Maximally Flat Diamond-Shaped Half-Band FIR Digital Filters with Arbitrary Difference of the Filter Orders