Module 1 : Signals in natural domain
Lecture 10 : Properties of LTI Systems

3) Associative property

a) Discrete time :

  

Proof : We know that  

Making the substitutions: p = k ; q = (l - k) and comparing the two equations makes our proof complete. 

Note: As k and l go from  to + independently of each other, so do p and q, however p depends on k, and q depends on l and k.