Question

The Convolution of the continuous functions f(t)=e-t2 and g(t)=3t2 is 5.312t2.

(a) True

(b) False

I have been asked this question by my school teacher while I was bunking the class.

My question is based upon Continuous Time Convolution in portion Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

The correct option is (b) False

The best explanation: f(t)=e-t2 and g(t)=3t2

f(t)*g(t)= ∫f(α)g(t-α)dα

=∫e-α2-3(t-α)2 dα

=3t2√π-0+3√π/2

=5.31t2+2.659.