It is desired to find three-tap causal filter which gives zero signal as an output to and 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?
\[\xrightarrow{{x\left[ n \right]}}\boxed{\begin{array}{*{20}{c}} {n = 0} \\ \downarrow \\ {h\left[ n \right] = \left\{ {1,a,b} \right\}} \end{array}}\xrightarrow{{y\left[ n \right] = 0}}\]

A. a = -1, b = 1

B. a = 0, b = 1

C. a = 1, b = 1

D. a = 0, b = -1

Answer: Option B