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A system has a phase response given by $\phi(\omega)$, where $w$ is the angular frequency. The phase delay and group delay at $\omega=\omega_{0}$ are respectively given by
 

  1. $ – \frac{\phi\left(\omega_{n}\right)}{\omega_{n}},-\left.\frac{d \phi(\omega)}{d \omega}\right|_{\omega=\omega_{0}}$
  2. $\phi\left(\omega_{0}\right),-\left.\frac{d^{2} \phi\left(\omega_{0}\right)}{d \omega^{2}}\right|_{\omega=\omega_{0}}$
  3. $\frac{\omega_{o}}{\phi\left(\omega_{o}\right)},-\left.\frac{d \phi(\omega))}{d\omega}\right|_{\omega=\omega_{0}}$
  4. $\omega_{o} \phi\left(\omega_{o}\right)_{1} \int_{-\infty}^{\omega_{\infty}} \phi(\lambda) d \lambda$

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