BeginnerTopic 11 of 101Signals, Control & Comms
Impulse response
The output for an impulse input characterises an LTI system.
In depth
The impulse response h(t) is the output when the input is δ(t). For LTI systems it contains all information about the system: any output follows by convolution y=x*h. Measured by exciting a system with a short pulse or noise.
Key points
- Step response is integral of h
- Laplace transform of h is H(s)
- Finite vs infinite impulse response
ExampleA room's acoustic impulse response captured with a clap gives its reverberation.
What is Impulse response?
The output for an impulse input characterises an LTI system.
Why is it important to understand impulse response?
The impulse response completely describes an LTI system, so measuring it lets you predict the output for any input.
Why is the impulse response so powerful?
For an LTI system, any input can be written as a sum of shifted impulses, so the response to each impulse gives the total output.
How do I measure an impulse response in practice?
Use a short pulse or a swept sine input and compute the impulse response from the measured output, often with correlation or deconvolution.
How is Impulse response used in practice?
Typical applications include measuring the impulse response of a room to design an echo correction, estimating the ringing of a structure from a hammer test and identifying the dynamics of a process by applying a short pulse.
What should I learn before Impulse response?
Study "Causality and stability" first (topic 10 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Impulse response?
Step response is integral of h. Laplace transform of h is H(s). Finite vs infinite impulse response.
Can you give an example of Impulse response?
A room's acoustic impulse response captured with a clap gives its reverberation.
What comes after Impulse response?
The next topic is "Convolution", which builds directly on this one.
How difficult is Impulse response?
It is classed as Beginner in Signals, Control & Comms (topic 11 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.