It is desired to find a three-tap casual filter which gives zero signal as an output to an input of the form

$x[n]= c_{1}exp(-\frac{j\pi n}{2})+c_{2}(\frac{j\pi n}{2}),$

where $c_{1}$ and $c_{2}$ are arbitrary real numbers. The desired three-tap filter is given by

$h[0]=1,\quad h[1]=a,\quad h[2]=b$

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 ?

1. $a=1,b=1$
2. $a=0,b=-1$
3. $a=-1,b=1$
4. $a=0,b=1$
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