Impulse response and step response are both mathematical representations of how a system responds to a sudden change or input. Impulse response represents the output of a system when presented with an impulse input, while step response represents the output when presented with a step input.
The step response can be obtained by integrating the impulse response, and the impulse response can be obtained by differentiating the step response. This means that the two are mathematically related and can be used interchangeably to analyze a system's behavior.
To calculate the impulse response from the step response, you can use the integration function in a mathematical software or perform the integration manually using calculus. The resulting function will be the impulse response of the system.
Impulse response is widely used in signal processing to analyze and characterize systems such as filters, amplifiers, and communication channels. By studying the impulse response, engineers can gain insights into the behavior and performance of these systems and make improvements or adjustments as needed.
One limitation is that these responses are only valid for linear time-invariant (LTI) systems. This means that the system's behavior must be the same regardless of when the input is applied. Additionally, these responses may not accurately represent the behavior of a system if it has nonlinear or time-varying components.
