Countour Integ & Fourier Transform

[Swapnil]

Why is it that we don't use contour integration when we take the integral of a complex function to find the Fourier transform:

$$X(j\omega) = \int_{-\infty}^\infty x(t) e^{- j\omega t} dt$$

 

[HallsofIvy]

Here, t is obviously a real number, not a complex number. You can use contour integration- there are a number of techniques for using contour integration to find a real integral- you include the portion of the real line you are integrating on in the contour- but the integral you show is NOT itself a contour integral.

 

[Swapnil]

Oh, I see. Thanks!