Deep Learning (DL) techniques has shown promising results in various Artificial Intelligence applications viz. image recognition, large language models, intrusion detection system, neural machine translation, natural language processing, anti-malware, etc. Hence, Gravitational Waves (GW) data analysis community also started proposing various techniques based on DL for the detection, parameter estimation, and characterization of gravitational wave signals. In this, most of the models are binary or multi-class based classification using white noise. However, one-step multi-class classification has an over-training issue and favors those classes that are most represented in the dataset and are easier to separate. Also, as the number of classes increases then it’s more difficult for the feature set to provide a clear separation between the classes. Therefore, we propose a novel two-step cascaded classification to detect BBH and BNS GW signals buried in the noisy time series data using a Convolutional Neural Network. We did an exhaustive empirical analysis using various combinations of white and colored noise. The models has been tested with both generated datasets and the real GW events. The analysis shows that colored noise models outperform the white noise models and the generated datasets which contain BBH and BNS GW signals have been classified with 100% accuracy with high probability. Hence, as the model’s accuracy is 100% with generated datasets, therefore we again tested the models with the real GW (BBH/BNS) events for its robustness and we achieved the accuracy of 100% and 97.29% in the first and second step respectively i.e. in the first step the model perfectly differentiated the GW signals (BBH/BNS) from the noise. Nevertheless, with randomly generated data in both steps our model results are 100% accurate with high probability, which shows the robustness of our proposed models.