Baseline drift is an endemic problem in matrix-assisted laser desorption ionization time of flight mass spectrometry (MALDI-TOF), a device frequently used in proteomics investigations and in selected genomics work. Following an explanation of the origin of this baseline drift that sheds light on the inherent difficulty of its removal by chemical means, the stochastic Bernstein function approximation (SB), a new signal processing method, is developed into a procedure to obtain a numerically straightforward baseline shift removal. This is successfully applied to proteomics and genmomics MALDI-TOF spectra. Evolutionary computation (EC) can discover (optimize, tune) aspects of the algorithm, for example, the free parameter σ(x) of the SB method...