# Time-Frequency Analysis of Daily Activities for Fall Detection
## 1 Introduction  
Fall detection, especially in older populations, has been receiving increasing attention in recent years. Falls are a significant cause of injury for elderly individuals resulting in disabling fractures that can potentially lead to death due to complications, such as infection or pneumonia or lasting disability. More than one-third of elderly individuals over 75 years old fall each year, 24% of whom experience serious injuries [1]. Accurate and reliable fall detection is necessary for protecting health and mitigating long-term disability. Automated recognition of a fall event can provide round-the-clock surveillance for elders living at home or in nursing homes. Robust, timely alerts to caregivers and family members may mitigate the lasting, long-term damage resulting from a fall. Prior research on fall detection has utilized accelerometers for detecting fall events. Key algorithms monitor changes in body kinematics and critical peak amplitudes to detect falls and characterize daily activities [2; 3; 4; 5]. These systems successfully detect fall events with sensitivities greater than 85% and specificities between 88-94%. However, focusing only on large acceleration can result in many false positives from other activities where large impacts occur, such as running and jumping. To address these complexities, prior studies have implemented sophisticated machine learning techniques [6] such as neural networks [7; 8; 9; 10; 11], support vector machines(SVM) [12; 13], Markov models [14], or k-Nearest Neighbors (k-NN) [13; 15] to detect the falls and classify daily activities. However, fall detection accuracy is not substantially improved over simpler thresholding methods. Additional drawbacks of machine learning techniques include the excessive computational resources required, lack of real-time response, and, perhaps most limiting, the need for training with large datasets. In falls research, ecologically accurate datasets collected in the target population (i.e., elderly) and in real-world, in-home settings are scarce for safety reasons and, as such, a barrier to a machine learning approach. Some fall detection algorithms rely upon detection of the final posture, assuming the faller ends up lying prone after a fall event [4; 16; 17]. These strategies are less effective when a person's fall posture is not horizontal, e.g., fall happen on stairs. In our previous study [18], we proposed a multisensor combination of accelerometer and gyroscope to improve fall detection accuracy (i.e., sensitivity, specificity). Whereas the accelerometer detects impacts, the gyroscope adds complementary information related to biomechanical movement. The addition of angular velocity information reduces false positives resulting from rigorous activity such as running. However, the angular velocity of jumping occasionally overlaps with fall events slightly reducing system specificity. The disadvantages of a multisensor approach include increased sensor cost, but more importantly additional computational, storage, and data communication costs. Energy consumption and battery requirements are key drawbacks of gyroscope inclusion in a fall detection strategy that is implemented on a wearable device. Power requirements for a gyroscope can be several hundred times greater than that for an accelerometer [19]  
Several studies have studied frequency domain characteristics of daily activities. [PERSON] et al. [20] demonstrated the usefulness of the power spectral density (PSD) to recognize activities such as walking, cycling, running and driving. Critical frequency corresponding to the highest computed PSD values have been used in several studies for activity recognition [21; 22; 23]. [PERSON] et al. used frequency information of the accelerometer signal to distinguish falls from low-rigor activities such as walking and sitting; however, the accuracy of their algorithm was not reported [24]. [PERSON] et al. developed a fall detection algorithm using Short Time Fourier Transform (STFT) [25].