Two's Complement Quantization in Two-Dimensional State-Space Digital Filters

Two-dimensional (2-D) state-space digital filters are investigated for stability with and without quantization. A sufficient condition is obtained for the stability of the linear Fornasini-Marchesini state-space model. The same model is then studied for stability when implemented using two's complement truncation quantization, and a sufficient condition for asymptotic stability of the nonlinear filter is obtained. In the process, a theorem is proved which gives a sufficient condition for the stability of a one-dimensional (1-D) state-space digital filter under the same type of quantization.