I understand that the impulse response of a system is simply the systems response to applying an impulse as input. I however struggle to understand how one could determine such response in a practical situation.

As I understand it, by applying an impulse to a system we would simply destroy or destabilize the system thus have no use of the resulting response since the system would stop behaving linearly?

 

I understand that the impulse response of a system is simply the systems response to applying an impulse as input. I however struggle to understand how one could determine such response in a practical situation.

As I understand it, by applying an impulse to a system we would simply destroy or destabilize the system thus have no use of the resulting response since the system would stop behaving linearly?

Your logic is faulty. If the impulse response is finite and well behaved why would you be led to conclude the opposite?

 

In practice, the impulse response of a system can be estimated a number of ways. First, you can whack the system with as close to an impulse as you can manage and measure the response and call that your estimate of the impluse response. Second, you can apply a different input and measure the output and use your knowledge of how the response to your actual input relates to the impulse response and back the impulse response out from the actual response to the actual input.