Consider a filter defined by the difference equation
$$ y[n]-0.5 y[n-2]=a x[n-4] $$
where $x[n]$ and $y[n]$ represent the input and output, respectively. If the magnitude response of the filter at $\omega=\dfrac{\pi}{2}$ is $\mid H\left(\frac{\pi}{2}\right)\mid=0.5$, the value of $a$ is $\_\_\_\_\_\_$ (rounded off to two decimal places).
