Minimum-deadband design of digital filters

A design rule for digital filters minimizing their deadbands is derived here by observing and comparing the widths, and thus the severity of the effect, of deadbands that occur in different realizations of the same filter. It is asserted that, normally, the parallel realization is better than the direct realization. The caseade realization is comparable to the parallel realization, and would be better or worse depending on how the sections are cascaded.