To address the challenge of online recognition of multi-class waste textiles in their sorting process, the Fabric-ModernTCN, a CNN architecture with strong fabric recognition performance and real-time inference capability, is proposed in this paper. The design of Fabric-ModernTCN is inspired by the state-of-the-art ModernTCN in the field of time series analysis. Using the Fabric-NIR-Dataset, a raw near-infrared spectral dataset including the spectra of 18 categories of fabrics, and its four preprocessed versions generated by applying the standard normal variate transformation, SG smoothing, min-max normalization, and arPLS baseline correction to Fabric-NIR-Dataset, respectively, five categories of Fabric-ModernTCN models are trained, and their recognition performances are evaluated. The most effective preprocessing method, SG smoothing, and its corresponding Fabric-ModernTCN model are selected. Further performance evaluation experiments of this model are conducted, demonstrating its classification accuracy of 93.28 % and F1-score of 94.47 %. The comparative experiments are conducted against two baseline models, InceptionTime and MiniRocket + MLP (MiniRocket coupled with a linear classifier). The results reveal that the Fabric-ModernTCN model outperforms both baseline models across five performance metrics: classification accuracy, precision, recall, F1-score, and inference time per sample. Specifically, the Fabric-ModernTCN model achieves improvements of 2.97 % and 1.82 % in classification accuracy, and 2.52 % and 1.31 % in F1-score, respectively, compared to the baseline models. Regarding computational efficiency, the inference time per sample of the Fabric-ModernTCN model is only 0.0025612 s, corresponding to an FPS of 390.4448, which highlights its strong real-time performance. The ablation experiment results further validate the rationality of the structural design and parameter selection of Fabric-ModernTCN.