Absolute error bounds for block floating-point direct-form digital filters

摘要

Provides an asymptotic response analysis of digital filters, which are implemented in block floating-point format. Using absolute bounds on the quantization error, conditions for the existence of certain response types and the corresponding bounds on the output are derived. It is demonstrated that by using sufficiently long block mantissa registers, the limit cycle amplitude can be made arbitrarily small by choosing the block exponent register length sufficiently high.