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Depending on your intended use, Convolve could provide a more useable representation of the solution than Integrate. Please note this comes at some performance expense, however the main delay was the unevaluated use inside of Plot, which has been solved by @Chenminqi. Your issue with only being able to work with infinite intervals can be resolved when you ...


Way 1: As Stephen Luttrell said in comment: conv1[t_] := Evaluate@Integrate[twopulse[s]*imp[t - s], {s, 0, t}, Assumptions -> t \[Element] Reals] now conv1 is: then plot it: Plot[conv1[t], {t, 0.09, 0.18}, PlotRange -> All, PlotStyle -> Green, Exclusions -> None] Way 2: conv2[t_] := NIntegrate[twopulse[s]*imp[t - s], {s, 0, t}]; ...

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