Epilepsy, a form of brain disorder, can be detected by analyzing EEG signals. Although this condition commonly affects children, it can also be found in adults in certain cases. Early diagnosis of epilepsy poses a challenge for medical professionals. In this research, the authors have employed a deep learning approach to classify EEG signals as either epileptic or normal. To enhance the effectiveness of the analysis, the Dual-Tree Complex Wavelet Transform (DT-CWT) is utilized. Subsequently, the DT-CWT coefficients are disintegrated to extract cumulant features. These features undergo dimensionality reduction using spectral regression discriminant analysis (SRDA) and are then employed as input for the Radial Basis Function (RBF) hybrid kernel classifier. The proposed method demonstrates an impressive classification accuracy of approximately 99.8%, showcasing a significant improvement overpreviously proposed algorithms. Notably, this study pioneers the use of nonlinear feature extraction on DT-CWT coefficients of EEG signals for epilepsy diagnosis.