Multiple-shift sequences in digital filter design

In the realization of a digital filter the finite number of bits used introduces essentially three types of errors: quantization, coefficient, and roundoff errors. Analysis based on the state-variable formulation is given for both the conventional and multiple-shift digital filters. Sensitivity results for the two configurations are compared with the help of charts. A digital filter can be designed for a prescribed accuracy and, in certain situations, multiple-shift sequences can result in substantial improvements. Experimental results using digital computer simulation show close agreement with the theoretical conclusions.