Is this piecewise-defined system time-invariant?

1. Is a piecewise function time invariant?
2. How do you know if a system is time invariant?
3. How do you know if a discrete time system is time invariant?
4. What is the example of time-invariant system?

Is a piecewise function time invariant?

I found this question in web: Whether or not is this time-invariant. The short answer is no.

How do you know if a system is 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).

How do you know if a discrete time system is time invariant?

◦ The system is time invariant. This means that if the input signal x(t) generates the output signal y(t), then, for each real number s, the time shifted input signal ˜x(t) = x(t − s) generates the time shifted output signal ˜y(t) = y(t − s).

What is the example of time-invariant system?

b) y(T)=sin[x(T)]

Similarly, if the system is passed through the time delay first then through the system then output will be sinx(T−t). We can see clearly that both the outputs are same. Hence, the system is time invariant.