A monitoring device (7) operates on a pressure signal from a blood processing apparatus, e.g. a dialysis machine, which has an extracorporeal blood circuit connected to a vascular system of a subject for pumping blood through a dialyzer, and a treatment fluid supply system for pumping a treatment fluid through the dialyzer. The monitoring device (7) has a first input block (50) for obtaining a first pressure signal (y) from a first pressure sensor (6a) in the extracorporeal blood circuit, and a second input block (51) for obtaining a second pressure signal (w) from a second pressure sensor (6b) in the treatment fluid supply system. An emulation block (56) generates, as a function of the second pressure signal (w), an emulated first pressure signal (y) which emulates a concurrent signal response of the first pressure sensor (6a), and a filtering block (53) generates a filtered signal (y) as a function of the first pressure signal (y) and the emulated first pressure signal (y), so as to suppress, in the filtered signal (}y) compared to the first pressure signal (y), signal interferences originating from the treatment fluid supply system (lb). A pulse detection block (54) processes the filtered signal (y f ) for detection of subject pulses originating from the subject.