We saw before that an arbitrary input sequence x(n) can be represented by a sum of weighted delayed unit impulse functions :
If we knew the response h(n) of the system to 
, it is straightforward for an LTI system
to write a corresponding expression for y(n) , the output from the system.
Linearity = homogeneity + additivity
The Convolution Sum
Thus the forced output of an LTI discrete system with unit sample response h(n) is given by the
convolution sum :
The MATLAB function conv produces a convolution sum.
However the problem remains to calculate h(n). Calculating h(n) from the DE in the time
domain is not easy in general. It is better done using transform methods yet to come.