IS THIS SYSTEM TIME INVARIANT?
$ X_k[n] = d[n-k] \Rightarrow Y_k[n]=(k+1)2 d[n-(k+1)] $
TEST
$ d[n-k] \Rightarrow (k+1)2 d[n-(k+1)] \rightarrow [time delay] \rightarrow Z(t) = (k+1)^2 d[n -(k+1) - t_o] $
$ d[n-k] \rightarrow [time delay] \rightarrow d[(n-k) - t_o] \Rightarrow W(t) = (k+1)^2 d[n -(k+1) - t_o] $
since $ Z(t) = W(t) $ the system is time invariant.
PART B
Assuming that this system is linear, what input $ X[n] $ would yield the output $ Y[n]=u[n-1] $?
The input would have to be $ u[n] $
