There is this following question.
Consider the transformation H {x}[n] = n x [n]. Does H define an LTI system?
What I understood from the question is:
x[n] -> H -> y[n] or according to the question, x[n] -> H -> n x[n]
to prove the time invariance, if I put n-no instead of n, it should be,
x[n-no] -> H -> y[n-no] = n x[n-no] but it turns out to be, x[n-no] -> H -> n x[n - no] - no x[n-no] which means the output depends on extra term no x[n-n0] and is not time invariant.
Incase, the trasformation was any constant * x[n] the it would have conserve the time invariance property, if I am not wrong.
But the proof mentioned in the notes is,
I have difficulty understanding the proof. If anyone could explain it to me or if I understood the question wrong, I'd appreciate it.