An improved stability measure for digital filter implementation

We consider the stability robustness problem of a digital filter implemented with finite word length (FWL). Based on pole modulus sensitivities, a new stability robustness related measure is derived. This measure is less conservative than that derived with the classical pole sensitivity measure. It is shown that the normal realizations are a set of optimal realizations that maximize this proposed stability robustness measure. The stability performance of the generalized direct-form II transposed (DFIIt) structure is analysed using this measure. The optimal generalized DFIIt structure problem is defined so as to identify those DFIIt structures that maximize the proposed stability measure, which is solved using an exhaustive searching method. Numerical examples are given to show the design procedure.