Properties of linear convolution

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) * [ h1 (n) +  h2 (n) ] =  [ x (n) * h1 (n) ]  + [   x (n) * h2 (n) ]

3. Associative property :

[ x (n) * h1 (n) ] *  h2 (n)  =  x (n) * [ h1 (n) *  h2 (n) ]