Nonlinear Fourier transform (NFT) is a powerful tool for characterizing optical soliton dynamics, which, however, suffers from fundamental limitations that ultra-wide bandwidth photodetectors and ultra-high sampling rate analog-to-digital converters should be used when accessing the full-field information of an ultrafast optical pulse. Herein, we report on the experimental demonstration of the linear optical sampling (LOS) enabled nonlinear frequency spectrum classification of ultrashort optical pulses, which could break this limitation. Instead of traditional coherent detection, the LOS overcomes the ultra-wide bandwidth constraint of commercially available optoelectrical devices. By finely adjusting the repetition rate difference between the soliton to be characterized and the sampling pulsed source, a 55.56-TSa/s equivalent sampling rate arising in the LOS can be secured, where only 400-MHz balanced photodetectors and 5-GSa/s analog-to-digital converter are used. Meanwhile, according to the nonlinear frequency spectrum calculated from the accurate full-field information, the promising concept of soliton distillation has been experimentally verified for the first time. The LOS-enabled NFT technique provides an alternative and efficient characterization tool for ultrafast fiber lasers, which facilities comprehensive insight into soliton dynamics.