Impulse response of a system in z domain

1. What is the impulse response of Z-transform?
2. How do you find the impulse response of LTI system using Z-transform?
3. How do you find the impulse response of a system?

What is the impulse response of Z-transform?

The impulse response of the discrete-time filter is expressed by the z transform function as: H ( z ) = 1 − z − 1 1 + 0.5 z − 1.

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

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 the impulse response of a system?

Given the system equation, you can find the impulse response just by feeding x[n] = δ[n] into the system. If the system is linear and time-invariant (terms we'll define later), then you can use the impulse response to find the output for any input, using a method called convolution that we'll learn in two weeks.