Which statement describes a non-linear system?

Which statement describes a non-linear system?

• A. It obeys the superposition principle.
• B. It does NOT obey the superposition principle.
• C. It is always time-invariant.
• D. It has a defined impulse response.

Answer: (B)

The key idea is linearity and superposition. In a linear system, the output follows both additivity and homogeneity: if you feed in two signals separately and sum their outputs, you get the same result as feeding in their sum, and if you scale the input, the output scales by the same factor. A non-linear system does not satisfy these rules, so the response to a sum of inputs isn’t simply the sum of the individual responses, and scaling the input doesn’t guarantee proportional output.

That’s why describing a non-linear system as one that does not obey the superposition principle is the correct way to characterize it. Time-invariance and impulse response are concepts that align with linear (often time-invariant) systems; a non-linear system can be time-varying, and even the idea of a single impulse response doesn’t fully describe a non-linear system.