Which statement best defines a distortionless system?

Which statement best defines a distortionless system?

• A. The output is the input scaled and time-delayed with y(t) = K x(t - t0).
• B. The output is identical to the input with no gain or delay.
• C. The output is the input convolved with a non-flat frequency response.
• D. The output is the input plus added noise.

Answer: (A)

Distortionless means the output keeps the same waveform shape as the input, allowing only a proportional change in amplitude and a pure time shift. In a linear time-invariant system, this happens when the impulse response is a scaled delta function at a delay: h(t) = K δ(t − t0). The resulting output is y(t) = x(t) * h(t) = K x(t − t0), which matches the statement that the input is preserved in shape, scaled by K, and delayed by t0. This is exactly the behavior described, so it best defines a distortionless system. The idea that the output must be identical with no gain or delay is too restrictive, even though it is a special case of distortionless. A non-flat frequency response would change the relative magnitudes of different frequency components and distort the signal. Adding noise alters the signal content, which also breaks the distortionless condition.