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In a discrete-time Low pass Filter, the frequency response is

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  1. Aperiodic
  2. Aperiodic with response restricted to (-ω0 + ω0)
  3. Periodic with period 2π 
  4. Quasi-periodic with response extending to infinity

Answer (Detailed Solution Below)

Option 3 : Periodic with period 2π 
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Detailed Solution

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Explanation:

D.T.F.T

Discrete-time Fourier transform is defined by

 

It is periodic with 2π

Periodicity of DTFT

For any integer k,

 

 

Discrete LPF

Discrete-time LPF is shown below

From the response itself, it is clear that the LPF is periodic with 2π as a period.

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