2
$\begingroup$

Is the system $y[n]=x[n]+2=T\{x[n]\}$ an LTI-System?

Linearity: $ \alpha \cdot T\{x_1[n] \} + \beta \cdot T\{x_2[n] \} = T\{\alpha \cdot x_1[n]\ + \beta \cdot x_2[n] \} \\\alpha \cdot (x_1[n]+2) + \beta \cdot(x_2[n]+2)= \alpha \cdot (x_1[n]+2) + \beta \cdot(x_2[n]+2)$

Time-Invariance: $y_1[n] = y[n-n_0] = x[n-n_0]+2 \\ x_2[n]= x_1[n-n_0]\\ y_2 [n]=T\{x_2[n ]\}= x[n-n_0]+2 \\y_1[n]=y_2[n]$

So I would say it is an LTI-System, is that right?

$\endgroup$
0
$\begingroup$

A system that adds a constant is rarely linear. If you have two inputs $x_1$ and $x_2$, each one gets the constant, so their combination get the constant two times. While the input $x_1+x_2$ gets the constant only once.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.