Falls are a significant health concern leading to increased morbidity and healthcare costs, especially for the elderly. Early and accurate detection of fall events is critical for timely intervention and preventing severe complications. This study presents a novel approach to triaxial accelerometer signals by employing data-adaptive Gaussian average filtering (DAGAF) decomposition in conjunction with machine learning techniques for fall detection. The triaxial accelerometer signals from the FallAllD dataset were decomposed into intrinsic mode functions (IMFs) and a residual component, from which feature vectors were extracted to train support vector machine (SVM) and k-nearest neighbor (kNN) classifiers. Experimental results demonstrate that the combination of the first and the third IMFs with the residual component yields the highest classification accuracy of 96.34%, with SVM outperforming kNN across all performance metrics. This approach significantly improves fall detection accuracy compared to using raw accelerometer signals, highlighting its potential in enhancing wearable fall detection systems. The proposed DAGAF decomposition method not only enhances feature extraction but also provides a promising advancement in the field, suggesting its potential to increase the reliability and accuracy of fall detection in practical applications.