<P> Let ∥ x ∥ ∞ (\ displaystyle \ x \ _ (\ infty)) be the maximum value of x (n) (\ displaystyle \ x (n)), i.e., the L ∞ (\ displaystyle L_ (\ infty)) - norm . </P> <Dl> <Dd> y (n) = ∑ k = − ∞ ∞ h (n − k) x (k) (\ displaystyle \ left y (n) \ right = \ left \ sum _ (k = - \ infty) ^ (\ infty) h (n-k) x (k) \ right) </Dd> </Dl> <Dd> y (n) = ∑ k = − ∞ ∞ h (n − k) x (k) (\ displaystyle \ left y (n) \ right = \ left \ sum _ (k = - \ infty) ^ (\ infty) h (n-k) x (k) \ right) </Dd> <Dl> <Dd> <Dl> <Dd> ≤ ∑ k = − ∞ ∞ h (n − k) x (k) (\ displaystyle \ leq \ sum _ (k = - \ infty) ^ (\ infty) \ left h (n-k) \ right \ left x (k) \ right) (by the triangle inequality) </Dd> </Dl> </Dd> </Dl>

Why does the frequency response not exist for bibo unstable systems