On digital filter failure due to an underflow and overflow dilemma caused by the nonrecursive filter coefficient
Robert K. Otnes, Lawrence P. McNamee · IEEE Transactions on Audio and Electroacoustics · 1972
Butterworth low-pass filters implemented on fixed-point computers can become useless for small passband designs because of underflow or overflow caused by the size of the nonrecursive terms. Curves are provided that show where the filters become unusable for various computer word lengths as a function of bandwidth and the size of the nonrecursive coefficient.