Given a system with a time-dependent output function
Example: Is
time invariant? The system is time invariant.
- If we apply delay
onto the input , then and . - If we apply delay
onto the output , then .
We find that applying delay to the input or output gives us the same output, so the system is time invariant.
Example: Is
time invariant? The system is not time invariant.
- If we apply delay
onto the input , then and - If we apply delay
onto the input , then We get different results, so the system is not time invariant.
If a time-invariant system is also linear, it is called a linear time-invariant system.