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The triangular functionhas angular-frequency Fourier transform $4{\sin }^2(\xi /2)/{\xi }^2$.

Equivalently, this is the convolution of two unit-width rectangular functions: the overlap length is $1-|x|$ when $|x|<1$, and zero otherwise. Time rescaling and amplitude changes give triangular pulses with different widths and heights. The convolution theorem also obtains the displayed transform by squaring $\sin (\xi /2)/(\xi /2)$, with continuous value one at zero.