  We derive exact analytical expressions for the spatial Fourier spectrum of
the fundamental bright soliton solution for the $(1 + 1)$-dimensional nonlinear
Schr\"odinger equation. Similar to a Gaussian profile, the Fourier transform
for the hyperbolic secant shape is also shape-preserving. We further confirm
that the fundamental soliton indeed satisfies essential characteristics such as
Parseval's relation and the stretch-bandwidth reciprocity relationship. The
fundamental bright solitons find rich applications in nonlinear fiber optics
and optical telecommunication systems.
