Optimizing the Numerical Noise of Parallel Second-Order Filters in Fixed-Point Arithmetic

Infinite impulse response (IIR) filters are widely used in audio signal processing. but they are sensitive to numerical effects especially when only fixed-point arithmetic is available. The numerical problems can be reduced by converting the filter to parallel second-order sections. This is, however. often not sufficient in audio signal processing, as a filter with logarithmic pole distribution leads to poles near the unit circle generating unacceptable amount of numerical noise. This can be avoided by implementing these problematic sections by specialized filter structures. In this paper various second-order structures are systematically analyzed. including the common direct-form structures and the Gold & Rader, Kingsbury, Zolzer, and optimized warped IIR structure. The paper also proposes an extension to the Chamberlin state variable filter so that it can be used as a general IIR filter and shows that exactly this filter has the best noise performance among the tested structures for the problematic low pole frequencies. A simulation example demonstrates that by using the generalized Chamberlin structure for the lowest poles, a significant signal-to-noise ratio improvement can be achieved compared to a filter using direct form I sections only.