The Fourier Transform Step Functions and Tent Functions

We define the Fourier transform of an integrable function. We prove two examples: First, we find the Fourier transform of a symmetric step function (characteristic function). The Fourier transform is related to the sinc(\xi) function. Second, we find the Fourier transform of a tent function (triangular distribution). This will be, up to constants, the square of the sinc function.

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