Suppose we have a continuous time-interval $I=[a,b]$, and a signal $x \colon I \to \mathbb{R}$.
A procedure that is sometimes carried out (e.g. when doing bispectral analysis) is to partition $I$ into $k$ small sub-intervals $[a\!=\!a_0,a_1],[a_1,a_2],\ldots,[a_{k-2},a_{k-1}],[a_{k-1},a_k\!=\!b]$ and take the Fourier transform of $x$ over each of these intervals, $$ \hat{x}(n,\xi) \ := \ \int_{a_{n-1}}^{a_n} x(t)e^{-2\pi i \xi t} \, dt \, , \hspace{8mm} n \in \{1,\ldots,k\}. $$
Is there a name for $\hat{x}(n,\xi)$ (e.g. something like "time-segmented Fourier transform")?