Define a DT LTI system
$ y[n] = x[n+1] + x[n]\, $
Obtain the Unit Impulse Response h[n]
By definition, to obtain the unit impulse response from a system defined by $ y[n] = x[n]\, $, simply replace the $ x[n]\, $ by $ \delta[n]\, $.
$ h[n] = \delta[n+1] + \delta[n]\, $
Obtain the System Function $ F(z)\, $ of the System
$ F(z) = \sum^{\infty}_{m=-\infty} h[n] * x[n] dn\, $ where $ x[n] = e^{jwn} \, $
