The impulse response of an LTI system can be obtained by

The correct answer is: A. Differentiating the unit ramp response.

The impulse response of an LTI system is the response of the system to a unit impulse input. The unit ramp response is the response of the system to a unit ramp input. The derivative of the unit ramp response is the unit impulse response.

Here is a more detailed explanation of each option:

• Option A: Differentiating the unit ramp response. This is the correct answer. The impulse response of an LTI system is the response of the system to a unit impulse input. The unit ramp response is the response of the system to a unit ramp input. The derivative of the unit ramp response is the unit impulse response.
• Option B: Differentiating the unit step response. This is incorrect. The unit step response is the response of the system to a unit step input. The derivative of the unit step response is the unit impulse response. However, the impulse response of an LTI system is not the derivative of the unit step response.
• Option C: Integrating the unit ramp response. This is incorrect. The unit ramp response is the response of the system to a unit ramp input. The integral of the unit ramp response is the unit step response. However, the impulse response of an LTI system is not the integral of the unit ramp response.
• Option D: Integrating the unit step response. This is incorrect. The unit step response is the response of the system to a unit step input. The integral of the unit step response is the unit ramp response. However, the impulse response of an LTI system is not the integral of the unit step response.