The digital filter which is constructed by Lebesgue spectrum analysis of ergodic theory, is shown to achieve a 15% gain of the number of simultaneous accessible users of asynchronous CDMA communication systems at the same BER (Bite Error Rate) compared to the Gold sequence and random sequence. According to the simulation of asynchronous CDMA communication systems with spreading sequences at the spreading factor of 127, it is shown that the performance gain caused by the digital filter called Lebesgue spectrum filter (LSF) is independent on the nature of spreading sequences.