An instantaneous system is always which of the following?

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

Answer: (C)

The main idea is that an instantaneous system forms its output strictly from the input at the same moment in time. Because the output at time t depends only on x(t) (and not on any future samples x(t′) with t′ > t), it cannot look ahead to future inputs. This guarantees causality, since the system never relies on information that hasn’t happened yet.

That’s why an instantaneous system is always causal. It can still vary with time in how it maps x(t) to y(t) (for example, y(t) = a(t) x(t) uses a time-varying factor a(t)), so it isn’t necessarily time-invariant. It also isn’t inherently unstable or stable—the stability depends on the specific instantaneous rule, not on the fact that it uses only the current input. The key point is the dependence on the present input ensures causality.