# Time-Frequency Analysis of Daily Activities for Fall Detection
## 3 Results
### Fall Detection Algorithm Development  
From the results of the daily activity analysis in both the time and frequency domain, we propose a hierarchical strategy to identify fall events. Following the protocol described in Section 2.1, a total of 1227 activities were collected across 36 subjects. Half the experi  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Activities** & **Peak Acceleration (g)** & **Frequency Range (Hz)** \\ \hline \multirow{6}{*}{Low-rigor Activities} & Standing & 1 & - \\ \cline{2-4}  & Walking & 1.5–1.8 & 2.5–3.5 \\ \cline{2-4}  & Sitting down/Standing up & 1.6–2.0 & 1–2 \\ \cline{2-4}  & Lying down/sitting up & 1.4–1.8 & 0.5–3 \\ \cline{2-4}  & Stepping & 1.8–2.1 & 1.5–2.5 \\ \hline \multirow{6}{*}{High-rigor Activities} & Running & 2.2–2.8 & 3.5–5.5 \\ \cline{2-4}  & Jumping forward & 2.0–4.0 & 1–2 \\ \cline{1-1} \cline{2-4}  & Jumping up/down & 2.0–4.0 & 2.5–3.5 \\ \cline{1-1} \cline{2-4}  & Falling & 2.5–5.4 & 2-3.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of acceleration data for various activities in the time and frequency domains.  
mental dataset was used to develop and optimize the algorithm, while the other half was used for validation and accuracy testing.  
Figure 5 summarizes the proposed fall detection algorithm. Using the two-stage schema proposed in Figure 2, we differentiate between low- and high-rigor activities in the time domain (Stage A). The acceleration signal is collected and analyzed in real-time in 500 ms intervals, a period referred to as fall window [27; 28]. In this window, we look to see if Acc surpasses a critical threshold, upper fall threshold (UFT), representing the fall impact. From our previous work in time-domain analyses of acceleration data, the UFT is used for TH1 in our algorithm (e.g., 2.5 g) [29].  
Using only TH1 results in high fall detection, but also identification of many false positives from rigorous activities such as running and jumping (sensitivity = 97.9%; specificity = 58.6%).  
As evidenced by the data in Table 1, fall events have distinct peak energy levels between 2-3.5 Hz that are distinct from other rigorous activities. To improve accuracy, we further analyze the acceleration signal in frequency domain. In Stage B, we calculate and identify the peak PSD for each activity. If the peak PSD value is not between 2-3.5 Hz, we rule out a fall occurrence. Otherwise, a potential fall may have occurred. Using this algorithm, we achieved sensitivity and specificity of 97.8% and 85.8%, respectively. Clearly, Stage B had the added benefit of improving specificity by decreasing false positive detection resulting from rigorous activities.  
Further analysis of the remaining false positives show jumping (up/down) results in the same peak energy spectra as fall events. To further improve specificity, a check for sensor axes reorientation is conducted using Acc\({}_{yz}\) with threshold TH2 set at 1.7 g. After fall confirmation using Acc\({}_{yz}\), sensitivity and specificity were 97.3% and 98.3%, respectively. Specificity is further improved with this additional step.