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 $\omega=\frac{\pi}{2}$ is $\left|H\left(\frac{\pi}{2}\right)\right|=0.5$, the value of $a$ is (rounded off to two decimal places).