GATE 2019 Electronics & Communication Q29

Question

It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form $x[n] = c_1 \exp\left(-\frac{j\pi n}{2}\right) + c_2 \exp\left(\frac{j\pi n}{2}\right)$, where $c_1$ and $c_2$ 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?

Answer

$a = 1, b = 1$

Answer

$a = 0, b = -1$

Answer

$a = -1, b = 1$

Answer

$a = 0, b = 1$