Tensor products algebra applied to time frequency analysis of auditory encephalographic signal

Abstract

Time-frequency methods (TFM) increase the dimensionality of signal spaces. In this thesis, a computational signal processing framework using tensor products algebra is developed to map Electroencephalographic (EEG) signals to time-frequency space, extract robust features and classify them. EEG signal acquisition is a modality to record brain signals using electrodes placed on the scalp of a subject. The signals are recorded with 32 electrodes while the subject listens to an auditory stimulus such as repeated tones, vowels, or words. The TFM used are cyclic short time Fourier transform (CSTFT) and continuous wavelet transform (CWT). The framework takes as input the raw EEG signals. The time-frequency sparse representations using the STFT and CWT are computed on the noise free channels at di erent time steps. The source localization using event related potentials (ERP) can be compared with time-frequency based localization. Results of multichannel EEG nonnegative matrix factorization (NMF) and reconstruction is also presented. The algorithms are implemented as part of a multichannel signal analysis toolbox (MSAT) using the Python programming language. The algorithms presented in this thesis can be extended to more general algorithms for analyzing and classifying the sources of multichannel biosensory signals.