An LTI system is described by the difference equation y$[$n$]=$x$[$n$]$x$[$n$4]($a$)$ Determine an equation for the frequency response H$($ej $$ $)$ and express it in the form H$($ej $$ $)=$ R$($ej $$ $)$ej$/2$e$$j $$ n$0$ where R$($ej $$ $)$ is a real function and n$0$ is an integer. $($b$)$ Determine the output if the input signal is x$[$n$]=4+$ cos$(0\mathrm{.}25$n$$ $/4).($c$)$ The signal x$1[$n$]=(4+$ cos$(0\mathrm{.}25$n$$ $/4))$u$[$n$]$ is zero for n$<0,$ so it $$starts$$ at n $=0.$ If the input signal is x$1[$n$],$ for which values of n is the corresponding output equal to the output obtained in part $($b$)?$