A monitoring device is arranged to receivea time-dependent measurement signal (d(n)) from a pressuresensor in a fluid containing system, which is associatedwith a first pulse generator and a second pulse generator.The pressure sensor is arranged in the fluid containingsystem to detect a first pulse originating from the firstpulse generator and a second pulse originating from thesecond pulse generator. The monitoring device is configuredto process the measurement signal (d(n)) to removethe first pulse. In this process, the monitoring devicereceives (201) the measurement signal (d(n)), obtains (202) afirst pulse profile (u(n)) which is a predicted temporal signalprofile of the first pulse, and filters (203) the measurementsignal (d(n)) in the time-domain, using the first pulseprofile (u(n)), to essentially eliminate the first pulse whileretaining the second pulse. The fluid containing systemmay include an extracorporeal blood flow circuit, e.g. aspart of a dialysis machine, and a blood circuit of a humanpatient.