Cough detection has recently been identified as of paramount importance to fully exploit the potential of telemedicine in respiratory conditions and release some of the economic burden of respiratory care in national health systems. Current audio-based cough detection systems are either uncomfortable or not suitable for continuous patient monitoring, since the audio processing methods implemented therein fail to cope with noisy environments such as those where the acquiring device is carried in the pocket (e.g. smartphone). Moment theory has been widely applied in a number of complex problems involving image processing, computer vision, and pattern recognition. Their invariance properties and noise robustness make them especially suitable as “signature” features enabling character recognition or texture analysis. A natural extension of moment theory to one-dimensional signals is the identification of meaningful patterns in audio signals. However, to the best of our knowledge only marginal attempts have been made in this direction. This paper applies moment theory to perform cough detection in noisy audio signals. Our proposal adopts the first steps used to extract Mel frequency cepstral coefficients (time-frequency decomposition and application of a filter bank defined in the Mel scale) while the innovation is introduced in the second step, where energy patterns defined for specific temporal frames and frequency bands are characterised using moment theory. Our results show the feasibility of using moment theory to solve such a problem in a variety of noise conditions, with sensitivity and specificity values around 90%, significantly outperforming popular state-of-the-art feature sets.