Asymptotic behavior of block floating-point digital filters

The asymptotic behavior of block floating-point and floating-point digital filters is analyzed. As a result, mantissa wordlength conditions are derived guaranteeing the absence of limit cycles in the regular dynamic range. Explicitly, the requirements are given for block floating-point state space filters with different quantization formats. Although these conditions are only sufficient, examples are given in which they are also necessary. In most cases the conditions are easily satisfied.