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GATE EC 2017 Set 1 — Question 33

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NAT+1 / -0MediumDTFT & PropertiesDiscrete-Time SignalsSignals & Systems

Signals & Systems → Discrete-Time Signals → DTFT & Properties

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Question

Let h[n]h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by
h[0]=13;h[1]=13;h[2]=13;h[0] = \frac{1}{3}; h[1] = \frac{1}{3}; h[2] = \frac{1}{3}; and h[n]=0h[n] = 0 for n<0n < 0 and n>2n > 2.
Let H(ω)H(\omega) be the discrete-time Fourier transform (DTFT) of h[n]h[n], where ω\omega is the normalized angular frequency in radians. Given that H(ω0)=0H(\omega_0) = 0 and 0<ω0<π0 < \omega_0 < \pi, the value of ω0\omega_0 (in radians) is equal to ________.
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