**5. Mathematical Methods**

Once the sensor data are obtained, how to make use of it is also a challenging task. As presented in the common methodology given in Figure 2, the key steps include pre-processing, segmentation, feature extraction, and classification/model application. In this section, we focus on the mathematical methods for the two key steps: feature extraction and classification.

### *5.1. Features and Feature Extraction*

The feature extraction methods can be categorized into four types according to their outputs: heuristic, time-domain, time–frequency, or frequency-domain features [85,100], which are as shown in Table 4. Heuristic features are those derived and characterized by an intuitive understanding of how activities produce signal changes. Time-domain features are typically statistical measures obtained from a windowed signal that are not directly related to specific aspects of individual movements or postures. Time–frequency features, such as wavelet coe fficients, are competitive for detecting the transitions between human activities [65]. Then, frequency-domain features are usually the preferred option for human activity recognition. Mathematical tools such as FFT, short-time Fourier transform (STFT), and discrete cosine transform (DCT) are the commonly used methods.


**Table 4.** Types of features for HAR [60,71,80,95].
