Difference Between Impulse Response and Excitation Function
The terms impulse response and excitation function are related but refer to different concepts in system analysis (signals and systems, control systems, vibration analysis).
1. Excitation Function (Input)
An excitation function is the input signal or force applied to a system to stimulate or excite it.
- It can be any signal: step, impulse, sinusoid, random noise, etc.
- It is something you apply to the system.
- Also called the input, forcing function, or driving function.
Examples:
- A hammer strike on a structure
- A voltage applied to a circuit
- A sinusoidal force applied to a spring-mass system
y(t) = System { x(t) }
Here, x(t) is the excitation function.
2. Impulse Response (System Property)
The impulse response is the output of a system when the excitation is an impulse (Dirac delta function δ(t)).
- It describes the intrinsic behavior of the system.
- It is a characteristic property of a Linear Time-Invariant (LTI) system.
- Usually denoted as h(t).
h(t) = System { δ(t) }
Once you know the impulse response, you can determine the output for any input using convolution:
y(t) = x(t) * h(t)
Key Differences
| Aspect | Excitation Function | Impulse Response |
|---|---|---|
| What it is | Input applied to system | Output due to impulse input |
| Role | Causes system behavior | Describes system behavior |
| Depends on | User choice | System characteristics |
| Symbol | x(t) | h(t) |
| Type | Any signal | Specific response to δ(t) |
Simple Analogy
Think of a bell:
- Excitation function = how you strike it (hard, soft, single hit, repeated hits).
- Impulse response = the sound the bell naturally produces when struck once sharply.
The bell's ringing pattern (impulse response) is a property of the bell itself, while how you strike it is the excitation.