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Distributed Denial of Service (DDoS) attacks are one of the most harmful threats in today's Internet, disrupting the availability of essential services. The challenge of DDoS detection is the combination of attack approaches coupled with the volume of live traffic to be analysed. In this paper, we present a practical, lightweight deep learning DDoS detection system called LUCID, which exploits the properties of Convolutional Neural Networks (CNNs) to classify traffic flows as either malicious or benign. We make four main contributions; (1) an innovative application of a CNN to detect DDoS traffic with low processing overhead, (2) a dataset-agnostic preprocessing mechanism to produce traffic observations for online attack detection, (3) an activation analysis to explain LUCID's DDoS classification, and (4) an empirical validation of the solution on a resource-constrained hardware platform. Using the latest datasets, LUCID matches existing state-of-the-art detection accuracy whilst presenting a 40x reduction in processing time, as compared to the state-of-the-art. With our evaluation results, we prove that the proposed approach is suitable for effective DDoS detection in resource-constrained operational environments.