Question

For an LTI system______________.

• A. group delay is twice phase delay
• B. group delay is always greater than phase delay
• C. group delay is always less than phase delay
• D. group delay is equal to phase delay

Hint:

In LTI systems with linear phase, group and phase delays are equal. This helps avoid signal distortion.

Answer 1

The Correct Option is D

For a Linear Time-Invariant (LTI) system with phase response \( \theta(\omega) \), the:
Group delay (\(\tau_g\)) is defined as: \( \tau_g = -\frac{d\theta(\omega)}{d\omega} \)
Phase delay (\(\tau_p\)) is defined as: \( \tau_p = -\frac{\theta(\omega)}{\omega} \)
When the phase response is linear (\( \theta(\omega) = -\omega\tau \)), then:
\( \tau_g = \tau \)
\( \tau_p = \tau \)
Thus, group delay equals phase delay for systems with linear phase, which is typical in ideal LTI systems.