textbooks give abstract examples of time invariant and non-time invariant (time sensitive) systems. can you please give an intuitive example of a time invariant system and one which is not? obviously in real world all systems are a bit time-sensitive, but i'm looking for an example that can be reasonably assumed to not be.
also what is the relationship between memoryless property and time invariance? it seems to me that there is no relationship, that a system can be memoryless or not and be time invariant or not (all four options are possible). eg this system is memoryless but not time invariant – is this right?
memoryless system (depends only on current time $n$):
$y[n] = n(x[n] – 5)^{2}$
then time shifting the output gives:
$y[n-1] = (n-1)(x[n-1] – 5)^2$
time shifting the input gives:
$y[n] = n(x[n-1] – 5)^2 = n(x[n-1] – 5)^2$ which is different from $y[n-1]$, hence the system is memoryless but time-sensitive. is that correct?
Best Answer
You are using a time-invariant system right now and it is called a computer! At least, in most cases, a computer is designed to be a time-invariant system.
A system $y(t) = \cdots$ can be memoryless and time-varying (e.g. $y(t) = tx(t)$), with memory and time-varying (e.g. $y(t) = t+x(t-1)$), memoryless and time-invariant (e.g. $y(t) = x(t)$), and with memory and time-invariant (e.g. $y(t) = x(t)+x(t-1)$).
Also, all you have said about your particular system and your calculations in that context are correct.