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In predicting subjective quality of speech signal degraded by telecommunication networks, conventional objective models require a reference source speech signal, which is applied as an input to the network, as well as the degraded speech. Non-intrusive estimation of speech quality is a challenging problem in that only the degraded speech signal is available. Non-intrusive estimation can be used in many real applications when source speech signal is not available. In this paper, we propose a new approach for non-intrusive speech quality estimation utilizing the temporal envelope representation of speech. The proposed auditory non-intrusive quality estimation (ANIQUE) model is based on the functional roles of human auditory systems and the characteristics of human articulation systems. Experimental evaluations on 35 different tests demonstrated the effectiveness of the proposed model.