Narrow-band recursive filters with error spectrum shaping

Earrrs due to Finite wordlength can be quite large in narrowband recursive digital filters. It has been shown that these errors may be considerably reduced by using a technique known as error spectrum shaping (ESS), which utilizes quantizer feedback. In this letter we first derive closed-formn bounds on the amplitude of zero-input limit cycles in ESS filters. An expression is then derived for the mean squared roundoff error (MSE) in a inultiplierless ROM/ACC type implementation, including the effects of scaling and finite wordlength ROM.