$3\mathrm{.}14.$ When the impulse train

$x[n]={\displaystyle \underset{k=-}{\overset{}{}}}[n-4k]$

is the input to a particular LTI system with frequency response $H(e^j),$ the output of the system is found to be

$H(e^{(j\frac{}{2})})e^{j\frac{3}{2}}+\frac{1}{4}H(e^j)e^{jn},y[n]=cos(\frac{5}{2}n+\frac{}{4})$

Determine the values of $H(e^{jk\frac{}{2}})$ for $k=0,1,2,$ and $3.$