Question

Which of the following input - output relationship is both linear and time - invariant ?

• A. $y\left[n\right]=odd\left\{x\right(t\left)\right\}$
• B. $y\left(t\right)=t^{2}x(t-1)$
• C. $y\left[n\right]=x^2[n-2]$
• D. $y\left[n\right]=x[n+1]-x[n-1]$

Answer 1

The correct option is D $y\left[n\right]=x[n+1]-x[n-1]$

(a) As function of 't' is multiplied in input thus $t^{2}x(t-1)$ is time-variant
(b) For square of a function, function becomes non-linear
(c) Function is both linear and time -invariant
$\left(d\right)odd\left\{x\right(t\left)\right\}=\frac{x\left(t\right)-x(-t)}{2}$

Thus for time reversal, function is time - variant.