$($b$)$ Consider a casual LTI system with below frequency response

$H(e^j)=\frac{1}{1-\frac{1}{2}{e}^{-j}+\frac{1}{4}{e}^{-j2}}$

i$)$ Determine the LCCDE of the system; $(4\text{'})$

ii$)$ Find the response of the system to the input with the following Fourier transform: $(8\text{'})$

$x(e^j)=\frac{2-e^{-j}}{1+\frac{1}{2}{e}^{-j}}$