A normalized spectral test for assessing non-flat spectrum near a given frequency

A new statistical test is proposed for detecting isolated spectral peaks in regions with flat spectra. The need for such tests typically arises in hearing tests based on the analysis of EEG (electroencephalography) signals with auditory steady state responses. Commonly, a local F-test is used as a statistical technique in these cases. The current work proposes a modification of this method, which bounds the parameter to the range 0 to 1. The aim is to facilitate monitoring the strength of responses by keeping values bounded to facilitate their interpretation. The probability density function of the new detector was derived for both the cases of lack and presence of evoked responses, which allowed obtaining the confidence limits and the probability of detection. Simulation studies were carried out to confirm the theoretical results, and the technique was applied to the electroencephalogram during auditory stimulation by amplitude-modulated tones. The proposed technique has detection power similar to other local detectors. However, it has the advantage of making the detector time-evolution visualization easier since it is always bounded between zero and one. • A statistical test is proposed for detecting spectral peaks in flat spectra regions. • It reflects a normalization of the local F-test, which is usually used in audiology. • The probability density function of the new detector was entirely derived. • Simulation studies were carried out to confirm the theoretical results. • The results with electroencephalographic signals are consistent and seem promising.