Impulse response of a system from its step response;confusion

1. How is impulse response related to step response?
2. Is impulse response the same as step response?
3. What is the relation between step function and impulse function?
4. What is the impulse response of the system?

How is impulse response related to step response?

The impulse function in the result is easily understood. Because the step response has a discontinuity in it (i.e., a step), and the impulse response is simply the derivative of the step response, this causes an impulse function as part of the impulse response.

Is impulse response the same as step response?

They are related as follows: The step response is the integral of the impulse response. The transfer function is the Laplace transform of the impulse response.

What is the relation between step function and impulse function?

The unit step function is level in all places except for a discontinuity at t = 0. For this reason, the derivative of the unit step function is 0 at all points t, except where t = 0. Where t = 0, the derivative of the unit step function is infinite. The derivative of a unit step function is called an impulse function.

What is the impulse response of the system?

The impulse response of a system is the output of the system in response to a unit impulse input signal. This lesson introduces you convolution, which expresses the output of an LTI system as a function of its input and impulse response.