Design of optimal non-separable 2-D half-band filters

Based on a polyphase decomposition, the problem of designing 2-D finite impulse response (FIR) half-band filters is reduced to its lowest complexity. Curves of approximation errors versus the relative transition width are reported for a large set of optimal non-separable half-band filters. For a 1-D half-band filter, the optimal approximation error only depends upon two parameters, which are the filter length and the transition width