This paper introduces a novel electroencephalogram (EEG) data classification scheme together with its implementation in hardware using an innovative approach. The proposed scheme integrates into a single, end-to-end trainable model a spatial filtering technique and a neural network based classifier. The spatial filters, as well as, the coefficients of the neural network classifier are simultaneously estimated during training. By using different time-locked spatial filters, we introduce for the first time the notion of "attention" in EEG processing, which allows for the efficient capturing of the temporal dependencies and/or variability of the EEG sequential data. One of the most important benefits of our approach is that the proposed classifier is able to construct highly discriminative features directly from raw EEG data and, at the same time, to exploit the function approximation properties of neural networks, in order to produce highly accurate classification results. The evaluation of the proposed methodology, using public available EEG datasets, indicates that it outperforms the standard EEG classification approach based on filtering and classification as two separated steps. Moreover, we present a prototype implementation of the proposed scheme in state-of-the-art reconfigurable hardware; our novel implementation outperforms by more than one order of magnitude, in terms of power efficiency, the conventional CPU-based approaches.