**6.3 Swing variables**

*Wavelet Transform and Complexity*

**6.1 Methodology and data**

**6.2 Noise reduction using wavelet**

**6. Arm swing analysis with wavelet**

differentiate PD and non-PD people. The parameters that can be considered as the most appropriate to discriminate patients are stance time, duration time, and test speed.

In gait analysis with wavelet was important to detect the gait phases; in this case, we were interested in obtaining a measure that allows quantifying the minimum and the maximum displacement of each wrist. For this reason, to generate spatiotemporal variables, we use multiple denoising methods that allow us to obtain a signal without big fluctuations; according to this, we use methods like Savitzky-Golay filter and wavelet decomposition [43]. In this chapter, we present the results

For this study, 25 patients (aged 45–87 years) and 25 controls (aged 46–88 years)

Since the original signals had fluctuations that could affect the analysis and processing, it was necessary to apply wavelet techniques to remove alterations and clean the signal. As showed in **Figure 5**, we apply three-level wavelet decomposition using Daubechies wavelet with eight vanishing moments. From this step, the

As a result of the wavelet decomposition, we obtain a clean signal to determine the relative displacement of the wrist, which allows to observe conditions such as rigidity and asymmetry in upper limbs. For the next step, we use the *a*3 signal.

*Approximation coefficient and detail coefficient for wrist signal, the sum of these coefficient level generates* 

approximation coefficients at level 3 were used as clean signal.

were selected, and like in the gait analysis, PD patients were in an early stage of the disease. All participants with PD were under a dopaminergic agonist and were evaluated while in the "on" state. The absence of dementia and any other related to neurological conditions that affect gait was confirmed by an expert neurologist. All PD subjects were completely independent mobility and did not require a walking aid.

obtained of applied wavelet decomposition using db8 to wrist signals.

**12**

**Figure 5.**

*original signals (s = a 3 + d 1 + d 2 + d 3).*

The arm swing variables calculated using the signal provided by eMotion were arm swing magnitude, arm swing time, arm swing speed, and arm swing asymmetry; these variables are defined as follows:


$$\text{et al.} \,\,\text{[44]}, \,\text{is the outcome of the next equal}$$

$$\text{\textbullet} \qquad \text{ASA} = \frac{\begin{bmatrix} \text{45}^{\text{\textdegree}} - \text{arct} \left( \frac{ArmSwing\_{\text{mwing}}}{ArmSwing\_{\text{lm}}} \right) \end{bmatrix}}{90^{\text{\textdegree}}} \text{\textbullet } \textbf{100}\%$$
