Sparse optimal and suboptimal realizations
A linear system of order n can be modelled by its transfer function using 2n + 1 parameters. In state space representations, the so-called direct forms, also called canonical forms, such as the controllable and observable forms are also parametrized with 2n + 1 parameters. These forms have the advantage of a simple implementation structure and hence of high computational speed. However, we have seen in our previous chapters, both theoretically and through a range of simulations, that these realizations usually yield poor performance when implemented with FWL coefficients and arithmetics. To overcome this performance degradation, optimal FWL design problems have been formulated and solved. This has been thoroughly studied in the previous chapters.
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