Time Invariance? or Time Variance?

System: $ Y_k[n] = (k+1)^2 d[n - (k+1)] \, $

Input: $ X_k[n] = d[n-k] \, $

Prob: Which variable represent time ?

1st Assumption: n represents time

$ d[n-k] --> [system] --> (k+1)^2 d[n - (k+1)] --> [timedelay -1] --> (k+1)^2 d[(n-1) -( k+1)] ,\ $

yields the same result as:

$ d[n-k] --> [timedelay -1] --> d[(n-1) - k] --> [system] --> (k+1)^2 d[(n-1) - (k+1)] ,\ $

2st Assumption: k represents time

$ d[n-k] --> [system] --> (k+1)^2 d[n - (k+1)] --> [timedelay -1] --> (k+1)^2 d[n-k] ,\ $

yields not the same result as:

$ d[n-k] --> [timedelay -1] --> d[n - (k-1)] --> [system] --> k^2 d[n-k] ,\ $

Remember: Time delay only occurs on function, not variable on equations.

Concluded, it is time invariant if we say n represents time,

      and it is time   variant if we say k represents time.