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GATE EC 2019 Set 1 — Question 39

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MCQ+2 / -0.67MediumFrequency ResponseLTI SystemsSignals & Systems

Signals & Systems → LTI Systems → Frequency Response

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It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the formx[n]=c1exp⁡(−jπn2)+c2exp⁡(jπn2),x[n] = c_1 \exp\left(-\frac{j\pi n}{2}\right) + c_2 \exp\left(\frac{j\pi n}{2}\right),where c1c_1 and c2c_2 are arbitrary real numbers. The desired three-tap filter is given by h[0]=1,h[1]=a,h[2]=bh[0] = 1, h[1] = a, h[2] = b and h[n]=0h[n] = 0 for n<0n < 0 or n>2n > 2. What are the values of the filter taps aa and bb if the output is y[n]=0y[n] = 0 for all nn, when x[n]x[n] is as given above?
Block diagram of the filter
  1. A.
    a=1,b=1a = 1, b = 1
  2. B.
    a=0,b=−1a = 0, b = -1
  3. C.
    a=−1,b=1a = -1, b = 1
  4. id.
    a=0,b=1a = 0, b = 1

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