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Previously, we introduced a windowless linear-prediction method known as circular linear prediction (CLP) modeling for pitch-synchronous analysis of the speech spectrum and presented its spectral modeling properties using synthetic speech signals. In this paper, we discuss how the CLP method and its multicycle generalization can be used with real speech signals. We also present the CLP methods' spectral estimation performance using real speech. As was the case for synthetic speech, these experiments proved that the CLP method has superior spectral estimation accuracy at onsets and has similar estimation performance to the autocorrelation method in stationary regions. We also observed that the multicycle generalization of the CLP method is required for partially-voiced regions.