Simultaneous flat approximations of the ideal low-pass attenuation and delay for recursive digital, distributed, and lumped filters

Transmittances approximating with a Taylor norm flat delay and attenuation at the origin are studied. By using appropriate characterization of their properties, closed forms are deduced. Equal emphasis nonreciprocal transmittances are recognized as Padé approximants. Using new recurrence relations, closed forms of reciprocal nonminimum phase transmittances are derived. Moreover, the chosen characterization simplifies the computation of transmittances having constraints on attenuation and delay at the origin as well as specifications in the stophand. The results apply to distributed filters and to recursive digital filters. Lumped transmittances are obtained by a limiting process.