A causal LTI system has system function (i.e., transfer function)
H(z) = 1-z^-1/(l-0.5z^-1)(l+ 0.5z^-1)
Determine the output of the system when the input is x[n] = u[n]. Determine the input x[n] so that the corresponding output of the above system is y[n] = delta[n] - delta[n - 1] Determine the output y[n] when the input is x[n] = cos(0.5pin) for - infinity < n < infinity.