With the increasing application of composite components in various industries, the assessment of their structural integrity, the analysis of damage processes, and the identification of damage patterns are becoming increasingly important. The accuracy of the analysis relies heavily on the selection of features. This paper presents a new idea to extract effective damage features from acoustic emission (AE) signals and accurately identify different damages in the failure process of carbon fiber reinforced polymer specimens. The method combines Hilbert–Huang transform (HHT) and Linear Discriminant Analysis (LDA) to analyze the AE signals generated during the damage process of composite specimens. Specifically, the Hilbert marginal energy spectrum of the signals was regarded as frequency domain descriptors. The frequency domain descriptors were subsequently associated with the parametric features after dimensionality reduction by LDA to construct the classification framework named HHT-LDA. The results show that the frequency domain descriptors of the AE signals associated with each damage mode characterized distinctly. The frequency band of energy distribution in the raw waveform for matrix cracking, delamination, and fiber breakage are (100–150 kHz), (150–300 kHz), and (300–350 kHz), respectively. In addition, the three damage patterns mentioned above were successfully detected and recognized from the complex AE waveforms using HHT-LDA with 85% overall classification rate. This research idea will serve as a potential method for future composite damage pattern recognition and provide supporting knowledge for practical applications of AE monitoring.