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Consider a four-point moving average filter defined by the equation $y[n]  = \displaystyle{}\sum _{i=0}^{3}\alpha_{i}\:x[n-i].$ The condition on the filter coefficients that results in a null at zero frequency is

  1. $\alpha_{1} = \alpha_{2} = 0;\:\alpha_{0} = -\alpha_{3}$
  2. $\alpha_{1} = \alpha_{2} = 1;\:\alpha_{0} = -\alpha_{3}$
  3. $\alpha_{0} = \alpha_{3} = 0;\:\alpha_{1} = \alpha_{2}$
  4. $\alpha_{1} = \alpha_{2} = 0;\:\alpha_{0} = \alpha_{3}$
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