  Recent studies have revealed that multi-soliton solutions of the nonlinear
Schr\"odinger equation, as carriers of information, offer a promising solution
to the problem of nonlinear signal distortions in fiber optic channels. In any
nonlinear Fourier transform based transmission methodology seeking to modulate
the discrete spectrum of the multi-solitons, choice of an appropriate windowing
function is an important design issue on account of the unbounded support of
such signals. Here, we consider the rectangle function as the windowing
function for the multi-solitonic signal and provide the exact solution of the
associated Zakharov-Shabat scattering problem for the windowed/doubly-truncated
multi-soliton potential. This method further allows us to avoid prohibitive
numerical computations normally required in order to accurately quantify the
effect of time-domain windowing on the nonlinear Fourier spectrum of the
multi-solitonic signals. The method devised in this work also applies to
general type of signals and may prove to be a useful tool in the theoretical
analysis of such systems.
