Question

The difference equation representation for a system is,

$y\left[n\right]-2y[n-1]+y[n-2]=x\left[n\right]-x[n-1]$

If $y\left[n\right]=0,for,n<0,and,x\left[n\right]=\delta \left[n\right],theny\left[2\right]$ will be ___

• A. 1

Answer 1

The correct option is A 1
$H\left(z\right)=\frac{1-z^{-1}}{1-2z^{-1}+z^{-2}}=\frac{1-z^{-1}}{(1-z^{-1}{)}^2}$

$H\left(z\right)=\frac{1}{(1-z^{-1})}$

$Y\left(z\right)=H\left(z\right)X\left(z\right)$

$=\frac{1}{1-z^{-1}}.1$

$y\left[n\right]=u\left[n\right]$

$y\left[2\right]=1$