Having difficulty checking for time invariance of discrete system

1. How do you find the time invariance of a discrete system?
2. How do you determine time invariant?
3. What is the property that must be satisfied by a time-invariant system?

How do you find the time invariance of a discrete system?

The discrete system is time invariant because the y'(n) output sequence is equal to the y(n) sequence shifted to the right by four samples, or y'(n) = y(n–4). We can see that y'(4) = y(0), y'(5) = y(1), y'(6) = y(2), and so on as shown in Figure 1–9(c).

How do you determine time invariant?

A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).

What is the property that must be satisfied by a time-invariant system?

The system is time-invariant if and only if y₂(t) = y₁(t – t₀) for all time t, for all real constant t₀ and for all input x₁(t).