Normally you create a filter math. model that takes in same random input (or actual expected signal) to produce reference output that need be compared with design data captured in some way.
You will need to be familiar with bit accurate modelling.
As a short cut for FIR, you may pass just an impulse input then you should get your coeffs out.
The impulse input is one sample at high value with zeros after it. You need to repeat that from time to time and check your outputs. The coeffs will be scaled out depending on your sample value. This is a good test but is not best. Best is a random data.