A new study on the synthesis of 2D state-space digital filters with minimum roundoff noise

Some results reported by Hinamoto et al. (IEEE Trans. Circuits Syst., Vol. 35, pp. 1037-1042, Aug 1988) and W. S. Lu and A. Antoniou (IEEE Trans. Circuits Syst., Vol. 37, pp. 1424-1425, Nov. 1990) concerning 2-D state-space digital filters with minimum roundoff noise are discussed. If 2D first order transfer functions can be realized by a minimal Roesser (or Fornasini-Marchesini (F-M)) model, there are two distinct Roesser (or F-M) structure groups, and the structure in one group cannot be transformed to a structure in the other group by the block-diagonal (or general, not block-diagonal, for F-M model) similarity transformation matrix. The two distinct F-M structure groups have different minimum roundoff noise properties. 2-D transfer functions may be realized by an F-M model with lower dimension than the Roesser model in some cases, for those transfer functions that do not admit absolutely minimal realizations in the Roesser model. The minimum roundoff noise produced by minimal F-M realizations may be smaller than that produced by nonminimal Roesser realizations