Question

If all the frequency components of the input signal undergo the same time delay, then the value of the group delay of the system is

• A. Zero
• B. Unity
• C. Constant
• D. Infinity

Hint:

Linear phase systems have constant group delay and therefore do not distort the waveform shape.

Answer 1

The Correct Option is C

Concept: Group delay is defined as \[ \tau_g = -\frac{d\phi(\omega)}{d\omega}. \] It measures the delay experienced by the signal envelope.

Step 1: Consider equal delay for all frequencies.
If every frequency component is delayed by the same amount, \[ \phi(\omega) = -\omega\tau. \]

Step 2: Compute group delay.
\[ \tau_g = -\frac{d(-\omega\tau)}{d\omega} = \tau. \] Since \(\tau\) is fixed, \[ \boxed{\tau_g=\text{constant}} \]