Time Invariance
If a system is time invariant then its input signal x(t) can be shifted by (t-to) and its output will be the same signal, yet it will be shifted the same throughout the system.
Ex: Time Variant
x(t) ->
[sys] -> y(t) = x*(t-1)
x(t) ->
[sys] -> y(t) = x*(t-1) -> [Time Delay]-> = z(t) = y*(t-1) = [y*(t-1-to)]
These two outputs are not the same. According to this change, the time does get varied based on the shift in the subscript. This proves that the system is Time-Variant.
Ex: Time Invariant
x(t) ->
[sys] -> y(t) = 2*x^2(t)
x(t) ->
[sys] -> y(t) = 2*x^2(t) -> [Time Delay]-> = z(t) = y*(t-to) = 2*x^2(t-to)
These outputs are the same which thus shows that the system is in fact Time Invariant.
