Output of stage-1:

$S_1 (0)=x(0)+x(4)=1+1=2$

$S_1 (1)=x(1)+x(5)=2+0=2$

$S_1 (2)=x(2)+x(6)=2+0=2$

$S_1 (3)=x(3)+x(7)=2+0=2$

$S_1 (4)=[x(0)-x(4) ] W_8^0=(1-1) W_8^0=0$

$S_1 (5)=[x(1)-x(5) ] W_8^1=(2-0)(0.707-0.707j)=1.414-1.414j$

$S_1 (6)=[x(2)-x(6) ] W_8^2=(2-0)(-j)=-2j$

$S_1 (7)=[x(3)-x(7) ]=(2-0)(-0.707-j0.707)=-1.414-1.414j$

Output of stage- 2

$S_2 (0)=S_1 (0)+S_1 (2)=2+2=4$

$S_2 (1)=S_1 (1)+S_1 (3)=2+2=4$

$S_2 (2)=[S_1 (0)-S_1 (2) ] W_8^0=(2-2)(1)=0$

$S_2 (3)=[S_1 (1)-S_1 (3) ] …