Optimizing Order to Minimize Low-Pass Filter Lag

Abstract

This paper develops a tool kit for designing low-pass filters to exhibit the smallest possible phase drop. Based solely on the stopband requirements, it is thus possible to find the best order for a filter to be employed in a feedback loop. That is shown for two much-used filter families, Butterworth and Bessel, in cases where the filter is specified to have a minimum attenuation above a certain frequency. It is argued that the phase drop can be represented by an equivalent filter delay. Design tools are then developed, which do not depend on the precise dynamics of the application process. The tools comprise not only the means for determining the optimal filter order and bandwidth, but also formulae and tables useful for obtaining the resulting filter delay. A simple approximation is subsequently developed, which links the minimum obtainable delay directly to said requirements. The filter order need not be known to apply this expression, and the filter family is represented in it by no more than a single constant. This rule of thumb is finally adapted to the area of anti-aliasing filters and there briefly compared to approximative formulae found in existing literature.