A novel approach to frequency domain design of three-dimensional digital filters via decomposition

The authors propose an efficient frequency domain design method for three-dimensional (3-D) digital filters. The proposed method decomposes a given 3-D magnitude specification into 1-D magnitude specifications with small error. To design 3-D digital filters applicable to real-time video signal processing, a novel approach is presented to approximation of negative magnitude specifications given by the decomposition with causal infinite impulse response (IIR) filters in a temporal direction and with linear phase non-causal IIR filters in spatial directions. Numerical examples show that the approximation error of the proposed design method is very small