A new multi-harmonic statistic for the detection of steady-state evoked potentials

We consider the problem of detecting visual evoked potentials (VEPs) obtained at near-threshold stimulus levels. A new multi-harmonic based statistic (Generalized T_circ²) is derived. This statistic, denoted by GT_circ², is based on the same assumptions concerning the variability of a Fourier component that are made in the use of the T_circ² statistic. However, unlike the T_circ² statistic which only treats a single harmonic, the GT_circ² statistic performs a multi-harmonic analysis which is more suitable for detecting multi-harmonic VEPs. A complete theoretical analysis for the derivation of the (GT_circ²) statistic is presented as a function of the likelihood ratio criterion, and its distribution is found under the H₀ hypothesis