In order to calculate the continuous relative phase (CRP) between joints, the portrait method based on the joint angle and angular velocity and the Hilbert transform method based on the analytical signal have been widely used. However, there are few comparisons of these methods. Therefore, the aim of this study is to quantitatively compare these methods by calculating the CRP in the lower-limb joints of the elderly during level free walking. Eighteen elderly female adults (76.4±5.6 year-old, 150.1±2.8cm, 54.4±8.4kg) wearing a Helen Hayes full-body marker set walked 10m on level ground at a self-selected velocity. The angles of the hip, knee, and ankle were measured. To calculate the CRP using the portrait method, the angular velocities were measured. Then, the phases between the angle and the angular velocity were calculated. To calculate the CRP using the Hilbert transform method, analytical signals were acquired. Then, the phases between the real and imaginary parts were calculated. A CRP was calculated as the difference between the phase in the proximal joint and the phase in the distal joint. To evaluate the similarity in the shape between the portrait and Hilbert transform methods, the cross-correlation was calculated. Bland–Altman plot analyses were performed to assess the agreement between these methods. For the root mean squares (RMSs) and standard deviations (SDs), a paired t-test and the Pearson correlation between methods were evaluated. There were similarities in the in-phase or out-of-phase features and in the RMS and SD between the methods. Additionally, a higher cross-correlation and agreement between them were found. These results indicated the similarity between the portrait and Hilbert transform methods for the calculation of the CRP. Therefore, either method can be used to evaluate joint coordination.

中文翻译：

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评估老年人步行时下肢关节间连续相对相位的纵向和希尔伯特变换方法

为了计算关节之间的连续相对相位（CRP），基于关节角度和角速度的肖像法和基于解析信号的希尔伯特变换法得到了广泛的应用。但是，这些方法的比较很少。因此，本研究的目的是通过计算老年人在水平自由行走时下肢关节的 CRP 来定量比较这些方法。十八岁的成年女性（76.4±5.6 岁，150.1±2.8厘米，54.4±8.4kg) 穿着 Helen Hayes 全身标记套装走了 10m 在水平地面上以自选速度。测量臀部、膝盖和脚踝的角度。为了使用纵向方法计算 CRP，测量了角速度。然后，计算角度和角速度之间的相位。为了使用希尔伯特变换方法计算 CRP，获取了分析信号。然后，计算实部和虚部之间的相位。CRP 被计算为近端关节的相位与远端关节的相位之差。为了评估肖像和希尔伯特变换方法之间形状的相似性，计算了互相关。进行 Bland-Altman 图分析以评估这些方法之间的一致性。对于均方根 (RMS) 和标准差 (SD)，一对吨-test 和 Pearson 方法之间的相关性进行了评估。在同相或异相特征以及方法之间的 RMS 和 SD 方面存在相似之处。此外，还发现它们之间具有更高的互相关性和一致性。这些结果表明用于计算 CRP 的肖像和希尔伯特变换方法之间的相似性。因此，任何一种方法都可以用来评估联合协调。