Which option correctly describes the distortionless system in terms of waveform preservation?

Which option correctly describes the distortionless system in terms of waveform preservation?

• A. It preserves the waveform shape of the input, with no gain or delay.
• B. It preserves the waveform shape of the input, except for a constant gain and a time shift.
• C. It alters the waveform but preserves energy.
• D. It adds noise to the signal.

Answer: (B)

Distortionless means the system does not change the shape of the waveform; it only scales it and/or shifts it in time. In other words, the output is a constant multiple of the input with a possible time delay, so y(t) = a x(t − t0). This is achieved when the system's impulse response is a scaled delta function, h(t) = a δ(t − t0), and the output becomes a x(t − t0). Therefore, the description that the waveform is preserved except for a constant gain and a time shift is the correct interpretation. The other ideas don’t fit: keeping the shape with no gain or delay is too restrictive since distortionless systems can include those effects; changing the waveform while preserving energy implies alteration of the shape, which is not distortionless; adding noise certainly distorts the waveform.

Distortionless means the system does not change the shape of the waveform; it only scales it and/or shifts it in time. In other words, the output is a constant multiple of the input with a possible time delay, so y(t) = a x(t − t0). This is achieved when the system's impulse response is a scaled delta function, h(t) = a δ(t − t0), and the output becomes a x(t − t0). Therefore, the description that the waveform is preserved except for a constant gain and a time shift is the correct interpretation.

The other ideas don’t fit: keeping the shape with no gain or delay is too restrictive since distortionless systems can include those effects; changing the waveform while preserving energy implies alteration of the shape, which is not distortionless; adding noise certainly distorts the waveform.