I am working on a medical engineering project that involves processing signals received from a human body. We use a sensor to record the blood pressure, $B(t)$.
However, if you put your finger on many parts of your skin, you can notice your heartbeat. Accordingly, the recorded signal also has some weak heartbeat signal added, $A'(t)$. To obtain accurate blood pressure signal, we have a sensor that records the heartbeat signal, $A(t)$. However, $A'(t)$ is a delayed and weak version of $A(t)$, where the phase lag is unknown.
Knowing $A(t)$, how can we find accurate $B(t)$?