Impulse Response of a System with a Single Pole at Origin

Introduction:
In the field of signal processing and control systems, the impulse response of a system refers to the output of the system when it is subjected to an impulse input. The impulse response provides crucial information about the behavior and characteristics of the system. In this question, we are given that the system has a single pole at the origin, and we need to determine its impulse response.

Single Pole at the Origin:
A pole is a term used to describe a singularity in the system's transfer function. In this case, the pole is located at the origin, which means the transfer function of the system can be written as H(s) = 1/s, where s is the complex frequency variable.

Impulse Response:
The impulse response of a system can be obtained by taking the inverse Laplace transform of its transfer function. In this case, the transfer function H(s) = 1/s can be transformed back to the time domain using the Laplace transform table, which states that the inverse Laplace transform of 1/s is a constant function.

Explanation:
Therefore, the impulse response of a system with a single pole at the origin is a constant function. When the system is excited with an impulse input, it will produce a constant output that does not decay or change with time. This is because the pole at the origin introduces a zero-degree term in the transfer function, resulting in a constant response.

Conclusion:
In conclusion, the impulse response of a system with a single pole at the origin is a constant function. This means that when the system is subjected to an impulse input, it will produce a constant output that remains the same over time.