Distributed Property for Discrete Time (ECE301Summer2008asan) - Rhea

Given: $ y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k]) $

1. $ x[n]*(h_1[n]+h_1[n])=\sum_{k=-\infty}^{\infty}x[k](h_1[n-k]+h_2[n-k]) $
2. $ x[n]*(h_1[n]+h_1[n])=\sum_{k=-\infty}^{\infty}(x[k]h_1[n-k]+x[k]h_2[n-k]) $
3. $ x[n]*(h_1[n]+h_1[n])=\sum_{k=-\infty}^{\infty}x[k]h_1[n-k]+\sum_{k=-\infty}^{\infty}x[k]h_2[n-k] $
4. $ x[n]*(h_1[n]+h_1[n])=x[n]*h_1[n]+x[n]*h_2[n] $