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Water demand scenarios are defined assuming that the samples are complete. On the other hand, consumption measurements are often affected by a considerable number of missing data. This paper explores the problem of missing data and proposes an example of a data pre-processing technique. Afterwards, a deconstruction of the time series, without being influenced by the presence of gaps, is presented. For this purpose, the fast Fourier transform for nonuniform sampling is developed. This analysis allows us to generate ergodic and stationary samples, useful for pursuing the generation of water demand scenarios. An application is provided on a water consumption time series recorded in a suburban area of Naples, Italy.