The efficient compression and classification of medical signals, particularly electroencephalography (EEG) and electrocardiography (ECG) signals in wireless body area network (WBAN) systems, are crucial for real-time monitoring and diagnosis. This paper addresses the challenges of compressive sensing and classification in WBAN systems for EEG and ECG signals. To tackle these challenges, a sequential approach is proposed. The first step involves compressing the EEG and ECG signals using the optimized Walsh-Hadamard transform (OWHT). This transform allows for efficient representation of the signals while preserving their essential characteristics. However, the presence of noise can impact the quality of the compressed signals. To mitigate this effect, the signals are subsequently recovered using the Sparse Group Lasso 1 (SPGL1) algorithm and OWHT, which take into account the noise characteristics during the recovery process. To evaluate the performance of the proposed compressive sensing algorithm, two metrics are employed: mean squared error (MSE) and maximum correntropy criterion (MCC). These metrics provide insights into the accuracy and reliability of the recovered signals at different signal-to-sample ratio (SSR) ratios. The results of the evaluation demonstrate the effectiveness of the proposed algorithm in accurately reconstructing the EEG and ECG signals while effectively managing the noise interference. Furthermore, to enhance the classification capabilities of the compressed signals, a local binary pattern (LBP) approach is applied. This technique extracts discriminative features from the compressed signals, which are then fed into a classification algorithm based on residual learning. This classification algorithm is trained from scratch and specifically designed to work with the compressed signals. The experimental results showcase the high accuracy achieved by the proposed algorithm in classifying the compressed EEG and ECG signals without the need for signal recovery. The findings of this study highlight the potential of the proposed approach in achieving efficient and accurate medical signal analysis in WBAN systems. By eliminating the computational burden of signal recovery and leveraging the advantages of compressive sensing, the proposed algorithm offers a promising solution for real-time monitoring and diagnosis, ultimately improving the overall efficiency and effectiveness of healthcare systems.