When networked control systems (NCSs) are stable with any constant time delays, they are called delay-independently stable (DIS). For delay-independently stable networked control systems (DIS-NCSs), 'staircase phenomenon' in its dynamic response has been discovered and proven to be an intrinsic problem, which can only be eliminated by changing the system's traditional feedback structure. Recent research proves that the introduction of scattering transformation into DIS-NCS can effectively eliminate the 'staircase phenomenon'. But new problems appear, as the DIS-NCS with scattering transformation displays another undesired 'periodically-active phenomenon' in its dynamic response, which literally means that the system's dynamic response is active periodically. In this article, the definition and certain examples of 'periodically-active phenomenon' are given at the beginning, which show that the phenomenon is indeed a problem and may bring unexpected results. Then the analysis of the reason for its appearance is provided. To eliminate it, this article proceeds to propose a simple but effective method: inserting certain filters into the system. The needed theoretical proof of this method is given. Simulation is provided in the end.