GATE 2017 EC – Question 43

Let $h[n]$ be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by $h[0] = \frac{1}{3}$; $h[1] = \frac{1}{3}$; $h[2] = \frac{1}{3}$; and $h[n] = 0$ for $n < 0$ and $n > 2$. Let $H(\omega)$ be the discrete-time Fourier transform (DTFT) of $h[n]$, where $\omega$ is the normalized angular frequency in radians. Given that $H(\omega_0) = 0$ and $0 < \omega_0 < \pi$, the value of $\omega_0$ (in radians) is equal to ________.