On optimal equalization of an analog antialiasing filter with a nonrecursive digital system

A cascade connection of an analog system with a nonrecursive digital one is designed such that this combination works as an optimum prefilter in front of the system for the intended digital processing. As such, it has to minimize the aliasing error, measured in the mean squared sense, as well as the approximation error inside the passband. For the latter a complex error function has to be introduced if both the magnitude and the phase distortion are of importance. The solution we are interested in is characterized by an equal ripple behaviour of the magnitude of this error function combined with a minimum aliasing error.