Recursive digital filters with low coefficient sensitivity

This paper describes a technique for designing IIR digital filters to a desired magnitude-squared frequency response with auxiliary constraints to control coefficient quantization sensitivity. The procedure can be used to design IIR filters for direct form implementation with a reasonable number of bits, e.g., 12 or 16, in contrast to standard IIR filters which usually require parallel or cascade form realization because of quantization sensitivity. The method will design filters with response characteristics that provide a continuous link between conventional IIR and FIR filters. The relative control simplicity associated with the direct form is shown to have advantages in special-purpose hardware implementations of low-sensitivity IIR filters using LSI arithmetic function circuits. A design example and its 12-bit hardware realization are described.