Decimator filter based on B-splines

Abstract

The cascaded integrator-comb (CIC) filters are widely used as decimators in many applications, such as in delta sigma AD converters to decimate the sampled signal on its output. One problem with these filters is that by increasing its order to improve the signal attenuation in the stop band, worsens the passband response. In this paper we propose a so-called least-squares filters (LSF) based on B-splines to improve that response, compensating for CIC filter drop and flattening the magnitude response of the pass band. We also study the relationship between the CIC filters, otherwise called moving average, and the B-splines expanded by an integer factor. We show that the least-squares filters based on B-splines can be decomposed in CIC filters, with a higher order than the splines used, plus a compensator filter. Another important contribution of this work are the FIR approximations of anti-causal IIR filters needed to implement LSFs.