Hardware Transfer Function Estimation
You can use adaptive filters for this task. Feed the hardware with uniform white noise and collect the output. Then feed the adaptive filter with exactly the same noise sequence and use the output of the hardware you recorded as the desired response of the adaptive filter. The filter can then be trained with standard algorithm such as LMS. Of course, you will not get the exact transfer function, but the trained adaptive filter's transfer function should be close enough to serve as model of the hardware in question.