Fourier Transform of Heaviside Function

Question

I'm trying to find the Fourier transform of $H(k - |x|)$, where $H$ is the Heaviside step function. I've solved a few Fourier transforms recently, but this one is giving me a bit of trouble. I'd appreciate any help.

Answer 1

As you said, there is a sinus behind:

$$\int_{-k}^ke^{−i2\pi\omega x}dx=\frac{e^{−i2\pi\omega k}-e^{i2\pi\omega k}}{-i2\pi\omega}=\frac{\sin 2\pi \omega k}{2\pi\omega}$$