Analysis of non-stationary signals in a noisy environment is a challenging research topic in many fields often requiring simultaneous signal decomposition in the time and frequency domain. This paper proposes a method for the classification of noisy non-stationary time-series signals based on Cohen’s class of their time-frequency representations (TFRs) and deep learning algorithms. We demonstrated the proposed approach on the example of detecting gravitational-wave (GW) signals in intensive real-life, non-stationary, non-white, and non-Gaussian noise. For this purpose, we prepared a dataset based on the actual data from the Laser Interferometer Gravitational-Wave Observatory (LIGO) detector and the synthetic GW signals obtained by realistic simulations. Next, 12 different TFRs from Cohen’s class were calculated from the original noisy time-series data and used to train three state-of-the-art convolutional neural network (CNN) architectures: ResNet-101, Xception, and EfficientNet. The obtained classification results are compared to those achieved by the base model trained on the original time series. Analysis of the results suggests that the proposed approach combining deep CNN architectures with Cohen’s class TFRs yields high values of performance metrics and significantly improves the classification performance compared to the base model. The TFR-CNN models achieve the values of the classification accuracy of up to 97.10%, the area under the receiver operating characteristic curve (ROC AUC) of up to 0.9885, the recall of up to 95.87%, the precision of up to 99.51%, the F1 score of up to 97.03%, and the area under the precision-recall curve (PR AUC) of up to 0.9920. This classification performance is obtained on the dataset in which the signal-to-noise ratio (SNR) values of the raw, noisy time-series signals range from -123.46 to -2.27 dB. Therefore, this study suggests that using alternative TFRs of Cohen’s class can improve the deep learning-based detection of non-stationary GW signals in an intensive noise environment. Moreover, the proposed approach can also be a viable solution for deep learning-based analysis of numerous other noisy non-stationary signals in different practical applications.