Implementing Recursive Filters with Large Ratio of Sample Rate to Bandwidth

The poles of a recursive filter shift their position when the polynomial coefficients are quantized and represented with fixed bit width approximations. This sensitivity is quite severe for high-order low-bandwidth filters. At best the root shift may cause significant deviation in spectral response, and at worst is responsible for instability in many filter designs. Narrowband filters also exhibit large numerical gain which lead to extended bit width internal registers and extended width multipliers. We address techniques to implement high order very low-bandwidth recursive lowpass filters without the brute force requirement for extended precision coefficients and registers.