Question

So I'm very confused about the concept of time invariance in terms of what it actually is and if someone could please explain it to me by applying it the following example.

y(t) = t^2*x(t-1). How would check this function for time invariance. Thanks.

Answer 1

As already mentioned time invariant systems are those systems whose input output characteristics do not change with time shifting. Let us consider x(n) be the input to the system which produces output y(n). Now delay input by k samples, it means our new input will become x(n-k). Now apply this delayed input x(n-k) to the same system. Now if the output of this system also delayed by k samples (i.e. if output is equal to y(n-k)) then this system is said to be Time invariant (or shift invariant) system.