Impulsive response and step response are concepts used in signal processing and system analysis to describe the behavior of a system in response to specific input signals.
The impulse response of a system is the output produced when the system is stimulated by an impulse input. A pulse input is characterized by an infinitesimally short unit duration and amplitude. The impulse response function represents how the system reacts over time after the impulse is applied.
It provides insight into system characteristics, such as its behavior in the time domain and its ability to amplify or attenuate specific frequencies. In practical terms, the impulsive response is often obtained by applying a Dirac delta function (mathematically represented as Δ(t)) as the input signal and measuring the resulting output.
Step response, on the other hand, refers to the output of the system when excited by a step input signal. A step input signal is characterized by an abrupt change from zero to a constant value (usually unity).
The step response describes how the system adjusts to a new steady-state condition after applying the step input. It illustrates the system’s ability to transition and stabilize in response to sudden changes in input.
Step responses are commonly used to analyze and characterize dynamic systems such as electrical circuits, mechanical systems, and control systems.
Impulsive response to a step function refers to the output of a system when driven by a step function input, often represented as u(t) or θ(t), where u(t) is the function assist step function and θ(t) is the unit step function. The unit step function has a constant value of 1 for all positive time values and zero otherwise.
The impulsive response to a step function essentially captures the dynamic behavior of the system as it adjusts from its initial state to a new equilibrium state following application of the step input. It provides a time domain representation of how the output of the system changes in response to a sudden change in the input.
The main difference between unit step response and unit pulse response is the nature of the input signals they represent.
The unit impulse response describes the system’s reaction to an infinitely short impulsive input, revealing detailed information about the system’s frequency characteristics and transient response. In contrast, the unit step response characterizes the behavior of the system when subjected to a sudden change in input that remains constant thereafter. Although both responses provide valuable information about the dynamics and stability of a system, they serve different analytical purposes depending on the nature of the input stimuli applied to the system