Discrete wavelet transform: a tool in smoothing kinematic data.

Area of Science:

• Biomechanics
• Signal Processing
• Motion Analysis

Background:

• Motion analysis systems often introduce noise into displacement data.
• Traditional Butterworth digital filters struggle with complex kinematic motions across low and high frequencies.
• Smoothing is crucial for obtaining accurate velocity and acceleration from displacement data.

Purpose of the Study:

• To present the discrete wavelet transform (DWT) as an alternative to digital filters for smoothing noisy displacement data.
• To evaluate the effectiveness of DWT in processing complex kinematic data.
• To compare DWT performance against traditional filtering methods.

Main Methods:

• The discrete wavelet transform (DWT) was applied to noisy displacement data.
• The DWT decomposes signals into approximation and detail functions using FIR filters.
• Signal reconstruction was performed using the inverse DWT.
• Daubechies wavelet of the fourth order (Db4) at the second decomposition level was optimized using Percentage of Retained Energy (PRE) and Root Mean Square Error (RMSE).

Main Results:

• The Daubechies wavelet (Db4) at the second decomposition level achieved 97.5% PRE and 4.7 rad s-2 RMSE.
• DWT demonstrated superior performance in smoothing complex, noisy displacement data compared to traditional filters.
• The optimized Db4 wavelet effectively compressed and smoothed complex displacement data from a noisy mathematical function.

Conclusions:

• The discrete wavelet transform offers a more effective approach for smoothing noisy displacement data in motion analysis.
• DWT provides a robust method for calculating accurate velocities and accelerations, especially for complex kinematic motions.
• This technique shows significant potential for improving the accuracy and reliability of motion analysis systems.