Topic: Signals and Systems
Phase function of a filter is $\phi(f)=kf^{2}$, $k>0$. The group delay of the filter has the shape
- A. Straight line with negative slope
- B. Straight line with positive slope
- C. Horizontal line
- D. Parabola
Answer: A. Straight line with negative slope
Explanation: Group delay is defined as $\tau_{g} = -\frac{d\phi(f)}{df}$ (or with respect to $\omega$). Taking the derivative of the phase function, $\tau_{g} = -\frac{d(kf^{2})}{df} = -2kf$. This represents a straight line with a negative slope passing through the origin.