One factorization technique for 2-D digital transfer matrices
The analysis and implementation oi a 2-D digital filter can be considerably simplified when the filter transfer matrix is separable. This simplification can be achieved since the filter is actualiy a cascade connection ot two .l-D filters. Then the analysis and impiementation of the 2-0 filter i§ reduced to those of 1-D filters and the well-established techniques for 1-D filters can be applied. Thus it is of great interest to check if a given 2-D filter is factorizabie into a cascade of two 1-D filters. In thls contribution, we develop a techniouc lor 2-D rational matrix factoriratian. In ~~~ ~~ . ... ~~ ~ ~~ l i l l b d;;ilipmenl we consiaer both singular and nonsingLiar tlansfer matrices. by extendin the conceDt. 01 m h m a i cascaoe seoaration 09 2-D square muwinput multi-butput (MiMO) matrix to the case ot sinoular matrices. Based on this ~~ ~~~~ ~ ~ ~~~ ~~~ technique,^ we <resent a method that can be used to check whether a given 2-D MiMO filter 1s minimay separable into a cascade of two 1-D tilter?..