The system is described with the following recursive differences equation:
now lets say the input is delayed by k, then:
and now the output by the same k:
here is the problem , I cannot see how same expression will be acquired . I've tried performing simple substitution of n-k=m , which leads to:
which is still not quite the same. Obviously the equation is linear differences equation with constant coefficients , therefore I suppose the system indeed TI but how to mathematically show this specific case.