The world of flatness

In the published literature on circuit theory and signal processing, the maximally flat FIR filters are commonly attributed to O. Herrmann. It is the purpose of this paper to elucidate the status of these filters before and after Herrmann's paper. Our survey shows that both the formula and the shape of the magnitude response of these filters had been known to actuaries and mathematicians before the publication of Herrmann's paper. We provide a broad outline of the contributions made by actuaries and mathematicians on this class and other related FIR filters. Some recent developments and extensions are also reviewed.