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 lowpass 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."