Improved narrowband low-pass IIR filters in fixed-point systems [DSP Tips & Tricks]

Due to their resistance to quantized-coefficient errors, traditional second-order infinite impulse response (IIR) filters are the fundamental building blocks in computationally efficient high-order IIR digital filter implementations. However, when used in fixed-point number systems, the inherent properties of quantized-coefficient second-order IIR filters do not readily permit their use in narrowband low-pass filtering applications. Narrowband low- pass IIR filters have traditionally had a bad reputation; for example, MATLAB\´s Signal Processing Toolbox documentation warns: "All classical IIR low-pass filters are ill conditioned for extremely low cutoff frequencies." This article presents a neat trick that can be used to overcome the shortcomings of narrowband second-order low- pass IIR filters, with no increase in filter coefficient bit widths and no increase in the number of filter multiplies per output sample.