Given the nature of the second spatial derivative, the calculation of the surface Laplacian is not directly affected by temporal signal properties (i.e., the SL estimate at time point t is not impacted by the SL estimates at t - 1 or t + 1), in contrast to temporal filters. However, because EEG time series data are highly intercorrelated, SL estimates for consecutive time points will also be similar (i.e., the surface Laplacian does not impose independence on time-correlated data). Furthermore, because the transformation itself is a linear operation, it will not interfere with other linear data transformations, including averaging the EEG across epochs (trials) or subjects, baseline correction, and applying a temporal filter (i.e., these transformations may be applied to the EEG data either before or after the surface Laplacian transform without altering the final result). Importantly, this rule does not hold for any nonlinear transformation, including the computation of spectral estimates (power) that involves rectifying (squaring) the data (cf. Fig. 1 in Tenke and Kayser, 2005). For this reason, all nonlinear operations have to be performed on the CSD-transformed data (i.e., after the surface Laplacian transform).
