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 system does not alter the shape of the input signal, apart from a possible overall scale and a pure time shift. This happens when the output is a scaled and delayed version of the input: y(t) = K x(t - t0). In transform terms, the impulse response is h(t) = K δ(t - t0), and the frequency response is H(jω) = K e^{-jω t0}. This has constant magnitude across all frequencies and a linear phase, so every frequency component is scaled by the same amount and delayed by the same amount, preserving the waveform. That’s why this option is the best: it captures the general idea of distortionless behavior. The other statements fail for different reasons: requiring no gain or delay is too restrictive (a distortionless system can include scaling and delay); using a non-flat frequency response would distort different frequencies differently; and adding noise changes the signal content, which is not distortionless.

Distortionless means the system does not alter the shape of the input signal, apart from a possible overall scale and a pure time shift. This happens when the output is a scaled and delayed version of the input: y(t) = K x(t - t0). In transform terms, the impulse response is h(t) = K δ(t - t0), and the frequency response is H(jω) = K e^{-jω t0}. This has constant magnitude across all frequencies and a linear phase, so every frequency component is scaled by the same amount and delayed by the same amount, preserving the waveform.

That’s why this option is the best: it captures the general idea of distortionless behavior. The other statements fail for different reasons: requiring no gain or delay is too restrictive (a distortionless system can include scaling and delay); using a non-flat frequency response would distort different frequencies differently; and adding noise changes the signal content, which is not distortionless.