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Design of 3D Nonseparable Mth Band Eigenfilters with the 48-Hedral Symmetry

Abstract We present a design method for designing 3D Mth band eigenfilters with 48-hedral symmetry, along with their application to sampling structure conversion of 3D signals defined on the face centered cubic (FCC) or body centered cubic (BCC) lattice to cartesian cubic (CC) lattice. While we present experimental results for FCC and BCC lattices, since these are commonly used 3D lattices, the design formulations we present are valid for other 3D lattices with 48-hedral symmetry as well. The sampling structure conversion of a signal sampled on FCC (or BCC) lattice to the CC lattice is a 3D interpolation problem, with the upsampling operation defined using the FCC (or BCC) lattice. In the design formulation for 3D eigenfilters, we impose the Mth band constraint, the so-called zero direct component (DC) leakage constraint, and the 48-hedral symmetry of the 3D filter impulse response. The Mth band constraint ensures that the original input samples are preserved at the output and the zero DC leakage results in the suppression of the zero (DC) frequency in the aliases due to the upsampling operation, thus improving the quality of the interpolated output. The symmetry results in the reduction of independent parameters in the filter design.