Best error propagation properties for state space structures of digital systems

The numerical properties of finite wordlength implementation of state-space structures of a digital system are analysed. We investigate how error due to both roundoff noise and coefficient quantization propagates. Some sufficient conditions to obtain low noise structures are established. These conditions are more general than those given in the literature. Also, we have shown that the criteria given in previous work for optimal finite wordlength (FWL) design cannot be used as a measure of performances to compare the implementation of different realizations. On the other hand, our work have unified several concepts that have been heretofore treated independently. A numerical example is given to illustrate the effectiveness of the analysis and synthesis method proposed here.