Question

Find the convolution of x(t) = exp(3t)u(-t), and h(t) = u(t-3)

(a) 0.33exp(2t-6) u(-t+3) + 0.5u(t-3)

(b) 0.5exp(4t-3) u(-t+3) + 0.8u(t-3)

(c) 0.33exp(2t-6) u(-t+3) + 0.5u(t-6)

(d) 0.33exp(3t-6) u(-t+3) + 0.33u(t-3)

The question was asked in quiz.

This intriguing question comes from Continuous Time Convolution in chapter Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

Right option is (d) 0.33exp(3t-6) u(-t+3) + 0.33u(t-3)

The best I can explain: Divide it into 2 sectors and apply the convolution formula.