Consider the system yn 025 y n2 y n2 delta n with initial

Consider the system y(n) - 0.25 y (n-2) y (n-2) = delta (n) with initial conditions y(-1) = 0 and y(-2) = 2, (1) Find the total output y(n) (2) Is the system stable?

Solution

Y(n)= (n)+0.25y(n-2)         where y(-1) = 0 and y(-2) =2;

For n=0;

Y(0) = (0)+0.25y(0-2)

Y(0)= 1 + 0.25*2;

Y(0)=1.5;

The present out put depents on present input,past output so the system is stable