Let x$[$n$]$ be a discrete time signal with DTFT x$($e$^($j$\backslash$omega $)).$ The real and imaginary part of the DTFT

is shown in the figure below

Now consider another signal y$[$n$]$ with DTFT Y$($e$^($j$\backslash$omega $)).$ Express y$[$n$]$ in terms of x$[$n$]$

Now let

$\backslash$alpha $=(\backslash$sum$\_($n$=-\backslash$infty $)^(\backslash$infty $)$ nx$[$n$])/(\backslash$sum$\_($n$=-\backslash$infty $)^(\backslash$infty $)$ x$[$n$])$

Determine the value of $\backslash$alpha obviously without determining the Inverse.