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The transform is easily determined using the convolution property of Fourier transforms and the Fourier transform of the rectangular function:

F { tri ⁡ ⁡ ( t ) } = F { rect ⁡ ⁡ ( t ) ∗ ∗ rect ⁡ ⁡ ( t ) } = F { rect ⁡ ⁡ ( t ) } ⋅ ⋅ F { rect ⁡ ⁡ ( t ) } = F { rect ⁡ ⁡ ( t ) } 2 = s i n c 2 ( f ) , {\displaystyle {\begin{aligned}{\mathcal {F}}\{\operatorname {tri} (t)\}&={\mathcal {F}}\{\operatorname {rect} (t)*\operatorname {rect} (t)\}\\&={\mathcal {F}}\{\operatorname {rect} (t)\}\cdot {\mathcal {F}}\{\operatorname {rect} (t)\}\\&={\mathcal {F}}\{\operatorname {rect} (t)\}^{2}\\&=\mathrm {sinc} ^{2}(f),\end{aligned}}}

where sinc ⁡ ⁡ ( x ) = sin ⁡ ⁡ ( π π x ) / ( π π x ) {\displaystyle \operatorname {sinc} (x)=\sin(\pi x)/(\pi x)} is the normalized sinc function.

For the general form, we have:

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