1. The problem statement, all variables and given/known data I am supposed to determine wether or not the discrete time system [itex] x[n] \rightarrow y[n] = x[-n] [/itex] is time invariant or not. 3. The attempt at a solution Let [itex] x_d[n] = x[n-n_0][/itex] [itex]y_d[n] = x_d[-n] = x[-(n-n_0)] = x[-n+n_0][/itex] [itex]y[n-n_0] = x[-(n-n_0)] = x[-n+n_0][/itex] Since [itex]y_d[n] = y[n-n_0][/itex], shouldn't this prove time invariance? The book says the answer is that it is not time invariant... From the more qualitative definition, a time invariant system is one for which the behavior does not change depending on when it is evaluated... Now, I see that for -ve values of n, the system looks ahead, and for +ve values of n the system looks behind. Would this be considered time variant because of this? If so, how do I go about showing that mathematically?