Estimation of Magnitude-Squared Coherence Using Least Square Method and Phase Compensation: A New Objective Response Detector

Abstract

Auditory Steady-State Responses (ASSR) are bioelectric potential evoked in the brain due to periodic auditory stimulation. An example of stimulus used to evoke an ASSR is the amplitude modulated tones, wherein the ASSR is characterized by an increase of energy at the modulation frequency of the electroencephalogram power spectrum. The presence or absence of an ASSR can be statistically determined by objective response detectors, usually implemented in the frequency domain through the Discrete Fourier Transform (DFT). To avoid spectral leakage in the DFT analysis, coherent sampling is often used. This technique consists of adjusting the stimulus modulation frequency so that an entire number of cycles occurs in an epoch of analysis. Thus, once the modulation frequency has been defined, other epoch lengths cannot be analyzed. This work proposes an objective response detector using the magnitude-squared coherence with least square and phase compensation to estimate spectral content, which does not require coherent sampling. This detector was analyzed in different epoch lengths and different type of windowing. For a small epoch, the new detector did not work because the false positive was not controlled. For large epochs, the new detector has lower detection rates. The best epoch lengths to use are the smallest possible ones before losing control of the false positive. For the data used in this work, the best epoch lengths were ranging from 256 to 512 samples. The tukey windowing was the most robust in terms of spectral leakage and presented the higher detection rate with false positive close to the significance level.