Digital filters with maximally flat amplitude and delay characteristics

An analytical solution is obtained for the transfer function of a digital filter which exhibits an optimum maximally flat amplitude characteristic and a maximally flat delay characteristic simultaneously. Explicit values for the multipliers are given for the direct realization in terms of the degree of the network and an arbitrary bandwidth scaling factor. Finally, it is concluded that this type of filter is useful in the area where the degree of a non‐recursive filter becomes excessive to fulfil an amplitude requirement (e.g. narrow bandwidth) and where recursive filters designed solely on an amplitude basis are too dispersive.