Design of 2-D interpolation/decimation filters using a general 2-D digital allpass filter

Two-dimensional (2-D) interpolation/decimation digital filters are widely used for sampling rate conversion. A general structure consisting of a 2-D recursive digital allpass filter (DAF) and a 2-D pure delay block is presented for designing 2-D recursive interpolation/decimation filters. We utilize a 2-D DAF with symmetric half-plane (SHP) support for its filter coefficients to comply with the symmetry possessed by 2-D interpolation/decimation filters. The structure also possesses a preferable doubly complementary half-band (DC-HB) property that reduces the number of required independent coefficients for designing 2-D interpolation/decimation filters. We appropriately formulate the design problem to obtain a simple linear optimization problem that minimizes the phase error of the 2-D recursive SHP DAF in the pth norm (Lp) sense. Simulation results are provided for illustration and comparison.