Asymptotic behavior of digital filters with block floating point arithmetic

The paper analyzes the asymptotic response behavior of direct form block floating point digital filters. The analysis is valid independent of the order or the quantization scheme used. Absolute bounds on the quantization error are derived and conditions for the existence of certain response types, the corresponding bounds on the output, and criteria for zero convergence are derived. Using sufficiently long block mantissa registers, the limit cycle amplitude can be made arbitrarily small by choosing the block exponent register length large enough