An instantaneous system is always which of the following?

An instantaneous system is always which of the following?

• A. Non-causal
• B. Time-invariant
• C. Always causal
• D. Always unstable

Answer: (C)

An instantaneous system is one whose output at time t depends only on the input at that exact time, not on past or future samples. That means you can determine y(t) using only x(t), so you don’t need any future input to compute the present output—this is the essence of causality, and it holds for every instantaneous (memoryless) system.

However, being instantaneous does not guarantee time-invariance. If the rule for producing y(t) includes an explicit dependence on time, such as y(t) = t·x(t), the system is still memoryless, but shifting the input in time does not simply shift the output by the same amount, so the system becomes time-variant. So an instantaneous system can be causal but not necessarily time-invariant.

Stability isn’t guaranteed either. A memoryless mapping can be designed that maps a bounded input to an unbounded output if the function has a problematic behavior within the input range, so the system may be unstable in the BIBO sense.

In short, an instantaneous system is always causal, but not necessarily time-invariant or stable.