Which are the two defining properties of a linear time-invariant system?

• A. Causality and stability.
• B. Linearity and causality.
• C. Linearity and time invariance.
• D. Time invariance and causality.

Answer: (C)

Two properties characterize a linear time-invariant system. First, linearity means the system follows the superposition principle: if you input a1 times one signal plus a2 times another, the output is the same weighted combination of the individual outputs. In practical terms, doubling an input doubles the output, and adding two inputs produces the sum of their respective outputs.

Second, time invariance means the system’s behavior does not depend on when an input is applied. If you shift the input in time, the output shifts by the same amount. Mathematically, delaying the input by t0 results in the output being delayed by t0 as well. This leads to a consistent representation of the system’s response, often described by the impulse response h(t) and the output being the convolution y(t) = x(t) * h(t).

Causality and stability are important properties in practice, but they do not define an LTI system. A system can be linear and time-invariant yet noncausal or unstable, so those traits aren’t the defining pair.