Linear convolution or proof of LTI system is completely characterized by unit impulse response h(n).

These properties are :

- Commutative property
- Associative property
- Distributive property

**1. Commutative property :**

x (n) * h (n) = h (n) * x (n)

**2. Distributive property :**

x (n) * [ h

_{1}(n) + h_{2}(n) ] = [ x (n) * h_{1}(n) ] + [ x (n) * h_{2}(n) ]**3. Associative property :**

[ x (n) * h

_{1}(n) ] * h_{2}(n) = x (n) * [ h_{1}(n) * h_{2}(n) ]
Linear convolution or proof of LTI system is completely characterized by unit impulse response h(n).

These properties are :

- Commutative property
- Associative property
- Distributive property

**1. Commutative property :**

x (n) * h (n) = h (n) * x (n)

**2. Distributive property :**

x (n) * [ h

_{1}(n) + h_{2}(n) ] = [ x (n) * h_{1}(n) ] + [ x (n) * h_{2}(n) ]**3. Associative property :**

[ x (n) * h

_{1}(n) ] * h_{2}(n) = x (n) * [ h_{1}(n) * h_{2}(n) ]