Distributed Property for Continuous time (ECE301Summer2008asan) - Rhea

Given: $ y(t)=x(t)*h(t)=\int_{k=-\infty}^{\infty}x(\tau)h(t-\tau)d\tau $

1. $ x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*(h_1(t-\tau)+h_2(t-\tau))d\tau $
2. $ x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}(x(\tau)*h_1(t-\tau)+x(\tau)*h_2(t-\tau))d\tau $
3. $ x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*h_1(t-\tau)d\tau+\int_{k=-\infty}^{\infty}x(\tau)*h_2(t-\tau)d\tau $
4. $ x(t)*(h_1(t)+h_2(t))=x(t)*h_1(t)+x(t)*h_2(t) $