How to find the impulse response of this system with complex roots?

1. How do you find the impulse response of a system?
2. Can impulse response be complex?
3. How do you find the impulse response of a system using Z transform?
4. How do you find impulse response from step response?

How do you find the impulse response of a system?

Key Concept: The impulse response of a system is given by the transfer function. 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).

Can impulse response be complex?

An entirely real time domain impulse function (and signal) can be complex in the frequency domain. Then, because of causality, the real and complex components of the impulse response are themselves related to each other.

How do you find the impulse response of a system using Z transform?

Remember: x[n]∗h[n]Z⟶X(z)H(z). In case the impulse response is given to define the LTI system we can simply calculate the Z-transform to obtain :math:`H(z). In case the system is defined with a difference equation we could first calculate the impulse response and then calculating the Z-transform.

How do you find impulse response from step response?

To develop this relationship, consider first the unit step response of a system. so the output is the impulse response (the derivative of the unit step response). It is important to keep in mind that the impulse response of a system is a zero state response (i.e., all initial conditions equal to zero at t=0^-).