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An elegant method of nonlinear Fourier transform (NFT) has attracted worldwide research interests and such NFT methodology provides a new viewpoint on the physics of laser dynamics. Recently, the use of the NFT has been proposed for the investigation of laser radiation, indicating the capability to characterize the ultrashort pulse in the nonlinear frequency domain. Here, pure solitons are numerically separated from the resonant continuous wave (CW) background in a fiber laser by utilizing NFT. It is identified that the soliton and the resonant CW background have different eigenvalue distributions in the nonlinear frequency domain. Similar to water distillation, we propose the approach of soliton distillation, by making NFT on a steady pulse generated from a fiber laser, then filtering out the eigenvalues of the resonant CW background in the nonlinear frequency domain, and finally recovering the soliton by inverse …