The increasing popularity of wearable devices in recent years means that a diverse range of physiological and functional data can now be captured continuously for applications in sports, wellbeing, and healthcare. This wealth of information requires efficient methods of classification and analysis where deep learning is a promising technique for large-scale data analytics. Whilst deep learning has been successful in implementations that utilize high performance computing platforms, its use on low-power wearable devices is limited by resource constraints. In this paper, we propose a deep learning methodology, which combines features learnt from inertial sensor data together with complementary information from a set of shallow features to enable accurate and real-time activity classification. The design of this combined method aims to overcome some of the limitations present in a typical deep learning framework where on-node computation is required. To optimize the proposed method for real-time on-node computation, spectral domain pre-processing is used before the data is passed onto the deep learning framework. The classification accuracy of our proposed deep learning approach is evaluated against state-of-the-art methods using both laboratory and real world activity datasets. Our results show the validity of the approach on different human activity datasets, outperforming other methods, including the two methods used within our combined pipeline. We also demonstrate that the computation times for the proposed method are consistent with the constraints of real-time on-node processing on smartphones and a wearable sensor platform.