Okay this could be a very silly question but I am asking it anyway.

Why do we consider in most cases of signal processing that the system is Time-invariant?

Is it because most signals are linear and time-invariant or is there a more compelling reason to consider a system as LTI while looking at problems in this field?

## Best Answer

What makes the analysis of LTI systems attractive are the following:

Linearity:Time (or shift) invariance:\$h(t - \tau)\$ is the output due to the input \$\delta(t - \tau)\$.

We then call \$h(t)\$ the

impulse responseof the system.If and only ifthe above are true of a system do we have:\$y(t) = h(t) * x(t) = \int_{-\infty}^{+\infty}h(t-\tau)x(\tau)d\tau\$

and

\$Y(s) = H(s) X(s) \$

Now, no real LTI system is truly LTI but are

effectivelyso and thus we may use the above "tricks" to analyze them.