Narrowband recursive filters with error spectrum shaping

Errors due to finite wordlength can in general be quite large in narrowband recursive digital filters. It has been shown that the mean squared roundoff error may be considerably reduced by using a technique known as error spectrum shaping (ESS), which utilizes quantizer feedback. In this paper it is shown that ESS can also significantly reduce the amplitude of zero input limit cycle oscillations. A more complete analysis of the MSE is then presented, which is useful for design purposes.