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We address the properties of nonlinear-Fourier-transform (NFT)-based fiber-optic communications systems and, particularly, study how the presence of noise deteriorates the performance of these systems. Similarly to the case of linear Fourier modes evolving independently under the action of chromatic dispersion alone, NFT-based systems employ so-called “nonlinear modes,” forming a nonlinear spectrum, as data carriers, and these nonlinear modes evolve independently in an uncoupled manner under the joint action of nonlinearity and dispersion. However, the influence of amplified-spontaneous-emission (ASE) noise on these nonlinear modes is still relatively poorly studied. In this paper, dealing with a continuous nonlinear spectrum, we scrutinize the properties of the effective noise emerging in the nonlinear Fourier domain. We also show that in the transmission stages, where the signal peak power is …