A monitoring device operates on a pressure signal from a blood processing apparatus which has an extracorporeal blood circuit for pumping blood through a dialyzer, and a treatment fluid supply system for pumping a treatment fluid through the dialyzer. The monitoring device has a first input block for obtaining a first pressure signal, and a second input block for obtaining a second pressure signal. An emulation block generates, as a function of the second pressure signal, an emulated first pressure signal which emulates a concurrent signal response of the first pressure sensor, and a filtering block generates a filtered signal as a function of the first pressure signal and the emulated first pressure signal, so as to suppress, in the filtered signal compared to the first pressure signal, signal interferences originating from the treatment fluid supply system. A pulse detection block processes the filtered signal for detection of subject pulses.