Which statement defines a causal system?

Which statement defines a causal system?

• A. The output depends on future input values.
• B. The output does not depend on future values of the input.
• C. The output is the integral of the input.
• D. The output is independent of input.

Answer: (B)

Causality means the output at any time can depend only on the input values at the present and in the past, not on future input. That necessity—no peeking into the future—is what defines a causal system. The statement that the output does not depend on future values of the input matches this idea exactly: it asserts the output relies only on past and present input, which is the essence of causality.

For context, real-time signal processing uses current and past samples to compute the current output. An example is y[n] = x[n] + 0.5x[n-1], which is based on the current and one past sample, not on any future sample. In contrast, a system that uses x[n+1] or x[n+2] would be non-causal because it requires knowledge of future inputs. The other descriptions are either ambiguous or describe a specific operation that isn’t by itself the definition of causality (an integral could be causal depending on the limits, and “independent of input” describes no relationship at all, which isn’t a useful system).