BeginnerTopic 10 of 101Signals, Control & Comms
Causality and stability
Causal systems do not depend on future input; BIBO stable ones give bounded output for bounded input.
In depth
A causal system's output depends only on present and past inputs (h(t)=0 for t<0); all physical real-time systems are causal. BIBO stability: bounded input gives bounded output, equivalent to ∫‖h‖dt<∞ (poles in the left half-plane).
Key points
- Noncausal filters used offline
- Marginal stability
- Lyapunov alternative
ExampleA moving-average of the last 10 samples is causal and stable.
What is Causality and stability?
Causal systems do not depend on future input; BIBO stable ones give bounded output for bounded input.
Why is it important to understand causality and stability?
Causality and stability tell you whether a system can be built in real time and whether its output stays bounded, which matters for safety.
What is causality?
An output depends only on present and past inputs, which is required for any system that runs in real time.
What is BIBO stability?
A system is bounded-input bounded-output stable if every bounded input produces a bounded output.
How is Causality and stability used in practice?
Typical applications include checking that a real-time filter does not need future samples, ensuring a controller will not blow up for a bounded input and testing whether a system can be implemented in hardware without look-ahead.
What should I learn before Causality and stability?
Study "Linearity and time invariance" first (topic 9 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Causality and stability?
Noncausal filters used offline. Marginal stability. Lyapunov alternative.
Can you give an example of Causality and stability?
A moving-average of the last 10 samples is causal and stable.
What comes after Causality and stability?
The next topic is "Impulse response", which builds directly on this one.
How difficult is Causality and stability?
It is classed as Beginner in Signals, Control & Comms (topic 10 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.