Overiap-save method-

$ x(n)=1,2,2,2,1,1 $

and $h(n)=1,2$

determine output response using overlap - save method

$\begin{aligned} \text { (1) } x_{1}\left(n)=0,1,2,2\right.& \text { . } \\ x_{2}(n)=& 0,2,1,1 \\ h(n)=1,2,0,0 & \text { . } \\ y_{1}(n, 0)=x_{1}(n)(N) h(n) \end{aligned}$

$\left[\begin{array}{cccc}{1} & {0} & {0} & {2} \\ {0} & {1} & {0} & {0} \\ {0} & {2} & {1} & {0} \\ {0} & {0} & {2} & {1}\end{array}\right]\left[\begin{array}{c}{0} \\ {1} \\ {2} \\ {2}\end{array}\right]=\left[\begin{array}{c}{4} \\ {1} \\ {4} \\ {6}\end{array}\right]$

$y_{2}(n)=x_{2}(n)(N) h(n)$

$\left[\begin{array}{cccc}{1} & {0} & {0} & {2} \\ {2} & {1} & {0} & {0} \\ {0} & {2} & {1} & {0} \\ {0} & {0} & {2} & {1}\end{array}\right]\left[\begin{array}{c}{0} \\ {2} \\ {1} \\ {1}\end{array}\right]=\left[\begin{array}{c}{2} \\ {2} \\ {5} \\ {3}\end{array}\right]$

$y_{1}(n)=1,4,6,4$

$y_{2}(n)=1,2,5,3,2$

$y(n)=1,4,6,6,5,3,2$

Crosscheck:-

$y(n)=1,4,6,6,5,3,2$