It is desired to find a three-tap causal filter that gives zero signal as an output to an input of the form \(x\left[ n \right] = {c_1}\exp \left( { - \frac{{j\pi n}}{2}} \right) + {c_2}\exp \left( {\frac{{j\pi n}}{2}} \right)\), where c1 and c2 are arbitrary real numbers. The desired three-tap filter is given by h[0] = 1, h[1] = a, h[2] = b and h[n] = 0 for n < 0 or n > 2. What are the values of the filter taps a and b if the output is y[n] = 0 for all n when x[n] is as given above?

• A. a = 1, b = 1
• B. a = 0, b = −1
• C. a = −1, b = 1
• D. a = 0, b = 1