The step response is the output of a system when a unit step input is applied. It shows how the system responds over time. The impulse response, on the other hand, is the output of a system when a single impulse (or Dirac delta) input is applied. It shows how the system responds instantaneously.
The step response is the integral of the impulse response. This means that the step response can be derived from the impulse response and vice versa. The impulse response can also be used to calculate the step response of a system by convolving it with the unit step function.
The impulse response is important because it provides a complete characterization of a linear system. It can be used to determine the stability, frequency response, and other important properties of a system. It is also useful in designing and analyzing filters and control systems.
The shape of the impulse response can reveal important information about a system, such as its order, stability, and frequency response. A long and slow decaying impulse response indicates a system with many poles, while a short and fast decaying response suggests a system with fewer poles. The frequency content of the impulse response can also provide insights into the frequency response of the system.
No, the step response and impulse response are only applicable for linear systems. Non-linear systems do not exhibit a linear relationship between the input and output, so the concept of impulse and step responses does not apply. However, the concept of impulse and step functions can be extended to non-linear systems by using the idea of generalized functions or distributions.
