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Injurious falls are a prevalent and serious problem faced by a growing elderly population. Accurate assessment and long-term monitoring of falls-risk could prove useful in the prevention of falls, by identifying those at risk of falling early so targeted intervention may be prescribed. Previous studies have demonstrated the feasibility of using triaxial accelerometry to estimate the risk of a person falling in the near future, by characterizing their movement as they execute a restricted sequence of predefined movements in an unsupervised environment, termed a directed routine. This study presents an improvement on this previously published system, which relied explicitly on time-domain features extracted from the accelerometry signals. The proposed improvement incorporates features derived from spectral analysis of the same accelerometry signals; in particular the harmonic ratios between signal harmonics and the fundamental frequency component are used. Employing these additional frequency-domain features, in combination with the previously reported time-domain features, an increase in the observed correlation with the clinical gold-standard risk of falling, from ρ = 0.81 to ρ = 0.96, was achieved when using manually annotated event segmentation markers; using an automated algorithm to segment the signals gave corresponding results of ρ = 0.73 and ρ = 0.99, before and after the inclusion of spectral features. The strong correlation with falls-risk observed in this preliminary study further supports the feasibility of using an unsupervised assessment of falls-risk in the home environment.