Group delay and amplitude trade-off for equi-ripple group delay and gain-magnitude band pass filters

The increasing demand for filters to meet group delay and gain-magnitude requirements leads to a wide variety of possible solutions. Any group delay requirement can be met alongside an attenuation requirement by including some right hand plane zeros (i.e. zeros of gain or poles of the attenuation response), usually in the form of complex quartets. However certain values of ripple in the equi-ripple magnitude response match better to certain values of equi-ripple group delay. This paper explores the interrelation between gain-magnitude and group delay to suggest a link between these seemingly independently specifiable items, such that for a reasonable design it is better to loosely tie the requirements than ask for the impossible