Changes in rhythm and characteristics in EEG signals during sleep stages is an important element in diagnosing sleep disorders. This paper has explored the benefit of the Fourier Bessel series expansion (FBSE) technique to classify EEG signals into different sleep stages. The coefficients of FBSE are investigated extensively studies to find the most important characteristics associated with sleep stages. Each EEG segment is passed through FBSE. Then, different features including frequency and entropy are extracted and the most powerful ones are selected using statistical feature selection metrics. The extracted features are sent into the least support vector machine (LS-SVM) as well as other models. One public dataset is employed to assess the proposed model. The proposed model tested with different sleep problems including 2-class, 3-class, 4-class, 5-class, and 6-class problems. The proposed model obtained an accuracy of 98% for classifying 2 class sleep stages classification problem. The proposed model can be implemented in a hardware device to support experts in monitoring patients’ state during sleep disorders.