I need to find Fourier transform of
$$\sum_{n=-\infty }^\infty e^{-|t-2n|}$$
I found the solution online. But I think the choice of limits in equation (1) of the solution is wrong.It should be probably from -infinity to 2n for the first integral and from 2n to infinity for the second integral.But I am confused about what the limits would be as the both integration and summation is involved. and I am not sure whose limits to change(Probably limits of integration must be changed only and that of summation must be kept as it is)
Given Solution:
Please tell me what the limits will be and the explanation. Also if possible please solve the problem.
Original answer:
$$ \frac{(1-e^{-2(1+jw)})}{(1-e^{-2})(1+jw)}-\frac{(e^{-2})(1-e^{-2(1+jw)})}{(1-e^{-2})(1-jw)}$$
OR
Answer:
