How to get the difference equation from impulse response?

1. What is the difference equation for impulse response?
2. How do you find the difference equation?
3. How do you find the transfer function from impulse response?

What is the difference equation for impulse response?

Given the system equation, you can find the impulse response just by feeding x[n] = δ[n] into the system.

How do you find the difference equation?

A first-order difference equation only contains the first difference of a variable between two consecutive periods, like y(t + 1) − y(t). A second-order difference equation also contains the second difference in a variable between every two successive time periods, like y(t + 2) − y(t).

How do you find the transfer function from impulse response?

If the transfer function of a system is given by H(s), then the impulse response of a system is given by h(t) where h(t) is the inverse Laplace Transform of H(s). A less significant concept is that the impulse response is the derivative of the step response.