Numerical Noise in Fixed-Pole Parallel and Kautz Filters

In audio filtering, Kautz and fixed-pole parallel filters are commonly used, as they have the ability to approximate the frequency resolution of hearing. However, infinite impulse response filters are susceptible to numerical noise, as quantization happens in their feedback loop. This is especially severe in systems where only fixed-point arithmetic is available. In order to limit the noise to an acceptable level, several low-noise second-order structures have been developed. In this paper, the authors compare the numerical noise properties of Kautz and fixed-pole parallel filters implemented in fixed-point arithmetic. The authors present the results for two different scaling methods and show that the common Kautz realization has unacceptable noise levels. Instead, they suggest the use of better performing parallel filters for general (nonadaptive) infinite impulse response filtering and a rearranged all-pass–based Kautz structure for adaptive filtering.