System memory, causality, stability

1. How do you know if a system is causal or stable?
2. Can a memoryless system be causal?
3. What are the conditions for stability and causality of an LTI system?
4. Can a causal system have memory?

How do you know if a system is causal or stable?

Hence, the system is causal. A system is said to invertible if the input of the system appears at the output. The system is said to be stable only when the output is bounded for bounded input. For a bounded input, if the output is unbounded in the system then it is said to be unstable.

Can a memoryless system be causal?

If a system is memoryless, it is also causal. However, being causal does not necessarily imply that a system is memoryless. In fact, most causal systems do have memory.

What are the conditions for stability and causality of an LTI system?

LTI System Properties

An LTI system is called causal if the output signal value at any time t depends only on input signal values for times less than t. It is easy to see from the convolution integral that if h(t) = 0 for t < 0, then the system is causal.

Can a causal system have memory?

In fact, most causal systems have memory. Input x(t) bounded produces bounded output. , where y(t) is output.