A Fourier Transform of a piecewise function

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Here is the Problem Statement : Find Fourier Transform of the piecewise function

upload_2016-7-24_16-56-58.png


Can someone sheds some lights on how to start solving this?

Thanks
 
The Fourier transform of your function f(t) is given as:

$$ F\left[f(t)\right] = \int_{-\infty}^{\infty} dt e^{i\omega t}f(t) = \int_{-\tau}^{0} -e^{i\omega t}dt + \int_{0}^{\tau} e^{i\omega t}dt $$

In the last step, I made use of the fact that f(t) is 0 elsewhere. As a final step, one can perform a simple integration to solve for the Fourier transform of f(t).
 
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Thanks Absalonsen! Is it e^(iwt) or e^(-iwt)?Let me know.
 
Thanks Absalonsen! Is it e^(iwt) or e^(-iwt)?Let me know.
np. It is usually a convention to determine the sign of the exponential in Fourier transform. In physics, forward Fourier transform from time to frequency space is carried out by ##e^{-iwt}##, while forward Fourier transform from real space to momentum space contains ##e^{ikx}##.
 

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