PERCH's Spectral Analysis is based on quantum mechanical spin system calculation and iterative optimization of the spectral parameters (chemical shifts, coupling, baseline, line-shape) to match the experimental data. The algorithm is using integral transforms and is described in following publication:

Laatikainen, R.; Niemitz, M.; Weber, U.; Sundelin, J.; Hassinen, T.; Vepsäläinen, J. J. Magn. Reson. 1996, 120, 1–10. doi:10.1006/jmra.1996.0094