How is this method of proving shift invariance correct

1. How do you prove shift invariant?
2. What is shift invariance in image processing?
3. How do you calculate time invariance?
4. Is shift invariant and time-invariant same?

How do you prove shift invariant?

If g(x + x0) = H[f(x + x0)] then the system is shift invariant, otherwise it is not.

What is shift invariance in image processing?

A shift-invariant system is one where a shift in the independent variable of the input signal causes a corresponding shift in the output signal. So if the response of a system to an input is , then the response to an input is .

How do you calculate time invariance?

Time-Invariant Systems

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).

Is shift invariant and time-invariant same?

Discrete time-invariant systems are known as shift-invariant systems. Systems which lack the time-invariant property are studied as time-variant systems.