2-D state-space digital filters with fewer multipliers

It is shown that as many as [m(m-1) + n(n-1)]/2 multiplications can be eliminated in a local state-space realization of a 2-D digital filter of order (m,n) by applying an appropriate transformation from the class of orthogonal similarity transformations. Further, it is demonstrated that the class of similarity transformations can be enlarged so that one can either introduce m+n free parameters in the sensitivity function, which may be chosen to reduce the sensitivity of the filter or to eliminate m+n additional multiplications while keeping the filter free of overflow oscillations. A numerical example is then given to illustrate the various techniques.