I want to evaluate a convolution for a stripe function and a Gaussian:

stripe[x_, d_] := If[EvenQ[Quotient[x, d]], 1, 0] gaussian[x_, \[Mu]_, \[Sigma]_] =      1/(Sqrt[2 \[Pi]] \[Sigma]) Exp[-((x - \[Mu])^2/(2 \[Sigma]^2))]; Plot[{stripe[\[Tau], 1], gaussian[\[Tau], 0, 0.5]}, {\[Tau], -10, +10}] 

Then, the convolution I want to evaluate is:

Convolve[UnitStep[\[Tau] + 5] stripe[\[Tau], 1] UnitStep[5 - \[Tau]],      gaussian[\[Tau], 0, 0.5], \[Tau], x] 

the result was 0, although it should not be 0.

I also tried to evaluate it via Integrate:

Integrate[stripe[\[Tau], 1] gaussian[x - \[Tau], 0, 0.5], {\[Tau], -5, +5}] 

the result was 0 again.

I don’t know why the results were zero. How can I evaluate it correctly?

Any advice is appreciated.