Instability thresholds in digital filters due to coefficient rounding
Robert K. Otnes, Lawrence P. McNamee · IEEE Transactions on Audio and Electroacoustics · 1970
Asymptotic expressions are developed to determine the threshold frequency at which sine and tangent Butterworth digital low-pass recursive filters become unstable because of coefficient rounding. Both floating point and fixed point arithmetic is considered. The theoretical threshold values are compared with those obtained through actual operation of the filter on data.