Floating-point roundoff noise analysis of second-order state-space digital filter structures

A parametric approach is used to determine the roundoff noise in all real second-order floating-point state-space realizations of a transfer function having complex conjugate poles. The parametric roundoff noise analysis is then verified by experimental measurements. The output noise variance is shown to be proportional to the input signal variance, resulting in a constant signal-to-noise ratio. It is found that floating-point roundoff noise is independent of filter scaling, allowing floating-point realizations that require two fewer multiples than comparable fixed-point realizations. Realizations with low fixed-point roundoff noise are found to have low floating-point roundoff noise, and vice versa. Therefore, the design techniques that have been developed for efficient low-noise fixed-point realizations are also applicable to the design of floating-point realizations