A Practical Method for Determining Coefficient Word Length in Digital Filters

This correspondence presents a new method for assessing the sensitivity of recursive digital filters to changes in their coefficients, and is particularly aimed at real-time control applications where continuous filters are being emulated in digital form. The method described enables sensitivity factors to be derived which directly relate the accuracy of the digital filter coefficients to the parameters of the continuous filter. By this means, for a particular percentage accuracy requirement in the parameters of the continuous filter, it is possible to determine directly the percentage accuracy (and hence word length) for the coefficients of the digital filter. Application of the method to typical examples is given, and the sensitivity predictions are confirmed by simulations of the digital filters in response to step inputs. An overview of its use in a design sense is also included.