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We have recently shown that click evoked auditory brainstem responses (ABRs) can be efficiently processed using a novelty detection paradigm. Here, ABRs as a large-scale reflection of a stimulus locked neuronal group synchronization at the brainstem level are detected as novel instance-novel as compared to the spontaneous activity which does not exhibit a regular stimulus locked synchronization. In this paper we propose for the first time Gabor frame operators as an efficient feature extraction technique for ABR single sweep sequences that is in line with this paradigm. In particular, we use this decomposition technique to derive the Gabor frame phase stability (GFPS) of sweep sequences of click and chirp evoked ABRs. We show that the GFPS of chirp evoked ABRs provides a stable discrimination of the spontaneous activity from stimulations above the hearing threshold with a small number of sweeps, even at low stimulation intensities. It is concluded that the GFPS analysis represents a robust feature extraction method for ABR single sweep sequences. Further studies are necessary to evaluate the value of the presented approach for clinical applications.