Design of 3-D noncausal filters with small roundoff noise and no overflow oscillations

The contribution of this paper consists of two parts. First, an invertible mapping technique is presented for 3-D digital system design, and it is applied to approximate 3-D noncausal filters in the spatial domain. Secondly, an algorithm is proposed for obtaining a structure for 3-D IIR filters with small roundoff noise and no overflow oscillations. The design of noncausal filters can be carried out by three steps: (1) a given noncausal impulse response is transformed into the first cubic using the proposed 3-D invertible mapping technique; (2) the transformed impulse response in the first cubic is approximated by balanced model reduction of 3-D separable denominator systems; (3) the resultant 3-D IIR filter is transformed back to the original coordinates.