Adder errors versus multiplier errors in floating-point digital filters:

One of the most important criteria for comparing digital filters is based on the effects of finite word lengths. Although the errors originated by multipliers have been discussed in detail in the technical literature, very few contributions concern the adders in the floating-point implementation. In the paper, the use of the sensitivity of the the transfer function of the digital filter, with respect to the multiplier coefficients for characterising the effects in floating-point implementation, is extended to the adders by introducing the concept of the `equivalent multiplier¿ The validity of this extension is illustrated by examples.