Question

What are the conditions for distortion less transmission through a system?

• A. Gain is linear and phase is constant
• B. Gain and phase should be linear
• C. Gain and phase must be constant
• D. Gain must be constant and phase should be linear

Hint:

Distortionless transmission requires: \[ |H(\omega)|=\text{constant} \] and \[ \phi(\omega)=-\omega t_0 \] (Constant magnitude + Linear phase)

Answer 1

The Correct Option is D

Concept: For distortionless transmission, the output should be an attenuated and delayed version of the input. Mathematically, \[ y(t)=Kx(t-t_0) \] where \(K\) is a constant and \(t_0\) is delay.

Step 1: Determine magnitude condition.
The magnitude response must be independent of frequency. \[ |H(\omega)|=K \] Thus gain must be constant.

Step 2: Determine phase condition.
The phase response must be linear. \[ \phi(\omega)=-\omega t_0 \] A linear phase ensures equal delay for all frequency components.

Step 3: Final Answer.
Therefore, \[ \boxed{\text{Gain constant and phase linear}} \] Hence, \[ \boxed{\text{Correct Option (D)}} \]