A monitoring device is arranged to receive a time-dependent measurement signal from a pressure sensor in a fluid containing system, which is associated with a first pulse generator and a second pulse generator. The pressure sensor is arranged in the fluid containing system to detect a first pulse originating from the first pulse generator and a second pulse originating from the second pulse generator. The monitoring device is configured to process the measurement signal to remove the first pulse. In this process, the monitoring device receives the measurement signal, obtains a first pulse profile which is a predicted temporal signal profile of the first pulse, and filters the measurement signal in the time-domain, using the first pulse profile, to essentially eliminate the first pulse while retaining the second pulse. The fluid containing system may include an extracorporeal blood flow circuit and a blood circuit of a human patient.