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In this paper, a text-independent automatic speaker recognition (ASkR) system is proposed-the SRHurst-which employs a new speech feature and a new classifier. The statistical feature pH is a vector of Hurst (H) parameters obtained by applying a wavelet-based multidimensional estimator (M_dim_wavelets ) to the windowed short-time segments of speech. The proposed classifier for the speaker identification and verification tasks is based on the multidimensional fBm (fractional Brownian motion) model, denoted by M_dim_fBm. For a given sequence of input speech features, the speaker model is obtained from the sequence of vectors of H parameters, means, and variances of these features. The performance of the SRHurst was compared to those achieved with the Gaussian mixture models (GMMs), autoregressive vector (AR), and Bhattacharyya distance (dB) classifiers. The speech database-recorded from fixed and cellular phone channels-was uttered by 75 different speakers. The results have shown the superior performance of the M_dim_fBm classifier and that the pH feature aggregates new information on the speaker identity. In addition, the proposed classifier employs a much simpler modeling structure as compared to the GMM.