On the roundoff noise in 2-D state-space digital filtering

The output roundoff noise variance and the scaling of the internal registers are associated with two impulse response sequences. Furthermore, two Lyapunov equations are established, corresponding to those which have been already used for the noise analysis and optimal structure synthesis in the 1-D case. An analytic formula is given for the solution of the Lyapunov equations. Thus the known techniques from the 1-D filters can be directly extended.