Butterworth transfer function with the equalised group delay response in the maximally flat sense

An effective method for the design of the continuous-time all-pass network for the low-pass filter group delay response equalisation is presented in this Letter. Since the method is derived from the maximally flat conditions at the origin of the group delay response's rational function, the cascade connection of the designed all-pass network and low-pass filter exhibits a constant group delay response at the origin in the flat sense. Illustrative examples regarding group delay equalisation of the Butterworth filters are given.