Edge computing aims to integrate computing into everyday settings, enabling the system to be context-aware and private to the user. With the increasing success and popularity of deep learning methods, there is an increased demand to leverage these techniques in mobile and wearable computing scenarios. In this paper, we present an assessment of a deep human activity recognition system's memory and execution time requirements, when implemented on a mid-range smartphone class hardware and the memory implications for embedded hardware. This paper presents the design of a convolutional neural network (CNN) in the context of human activity recognition scenario. Here, layers of CNN automate the feature learning and the influence of various hyper-parameters such as the number of filters and filter size on the performance of CNN. The proposed CNN showed increased robustness with better capability of detecting activities with temporal dependence compared to models using statistical machine learning techniques. The model obtained an accuracy of 96.4% in a five-class static and dynamic activity recognition scenario. We calculated the proposed model memory consumption and execution time requirements needed for using it on a mid-range smartphone. Per-channel quantization of weights and per-layer quantization of activation to 8-bits of precision post-training produces classification accuracy within 2% of floating-point networks for dense, convolutional neural network architecture. Almost all the size and execution time reduction in the optimized model was achieved due to weight quantization. We achieved more than four times reduction in model size when optimized to 8-bit, which ensured a feasible model capable of fast on-device inference.