The extended binary phase shift keying (EBPSK) transmission system with ultra narrow bandwidth has excellent BER performance, which raises many doubts with the researchers. Therefore, on the premise of the existence of a special filter that can transform the modulated phase information into amplitude information, the theoretical BER formula of EBPSK system in Additive White Gaussian Noise (AWGN) channel has been deduced. This paper gives the theoretical values of the parameters in the above BER formula and discusses the effects of parameters on BER firstly. Then the paper shows that the special impacting filter satisfies the above assumption, therefore, in the frame of binary detection theory, the excellent performance of high-efficiency EBPSK system can be explained and the correction of the theoretical BER formula can be validated.