An example circuit includes: a filter configured to process a digital signal through at least one stage; and a coefficient generator circuit configured to generate coefficients for the at least one stage of the filter. The coefficient generator circuit includes: a lookup-table (LUT) configured to output a differential sequence; an up-sampling holder circuit configured to up-sample and hold the differential sequence to generate an up-sampled differential sequence; and an accumulator configured to integrate the up-sampled differential sequence to generate the coefficients.