A NOVEL NONNEGATIVE DECOMPOSITION METHOD AND ITS APPLICATION TO 2-D DIGITAL-FILTER DESIGN

In designing two-dimensional (2-D) digital filters in the frequency do main, an efficient technique is to first decompose the given 2-D frequ ency domain design specifications into one-dimensional (1-D) ones, and then approximate the resulting 1-D magnitude specifications using the well-developed 1-D filter design techniques. Finally, by interconnect ing the designed 1-D filters one can obtain a 2-D digital filter. Howe ver, since the magnitude responses of digital filters must be nonnegat ive, it is required that the decomposition of 2-D magnitude specificat ions result in nonnegative 1-D magnitude specifications. We call such a decomposition the nonnegative decomposition. This paper proposes a n onnegative decomposition method for decomposing the given 2-D magnitud e specifications into 1-D ones, and then transforms the problem of des igning a 2-D digital filter into that of designing 1-D filters. Conseq uently, the original problem of designing a 2-D filter is significantl y simplified.