Fixed-point design of generalised comb filters: a statistical approach

This study is concerned with the problem of designing computationally efficient generalised comb (GC) filters. Basically, GC filters are anti-aliasing filters that guarantee superior performance in terms of selectivity and quantisation noise rejection compared to classical comb filters, when used as decimation filters in multistage architectures. Upon employing a partial polyphase (PP) architecture proposed in a companion study, the authors develop a sensitivity analysis in order to investigate the effects of the coefficients´ quantisation on the frequency response of the designed filters. The authors show that the sensitivity of the filter response to errors in the coefficients is dependent on the particular split of the decimation factor between the two sub-filters constituting the PP architecture. The sensitivity analysis is then used for developing a fixed-point implementation of a sample filter from the class of GC filters, used as reference filter throughout the study. Finally, the authors present computer simulations in order to evaluate the performance of the designed fixed-point filters.