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Real-time fall detection using a wearable sensor remains a challenging problem due to high gait variability. Furthermore, finding the type of sensor to use and the optimal location of the sensors are also essential factors for real-time fall-detection systems. This work presents real-time fall-detection methods using deep learning models. Early detection of falls, followed by pneumatic protection, is one of the most effective means of ensuring the safety of the elderly. First, we developed and compared different data-segmentation techniques for sliding windows. Next, we implemented various techniques to balance the datasets because collecting fall datasets in the real-time setting has an imbalanced nature. Moreover, we designed a deep learning model that combines a convolution-based feature extractor and deep neural network blocks, the LSTM block, and the transformer encoder block, followed by a position-wise feedforward layer. We found that combining the input sequence with the convolution-learned features of different kernels tends to increase the performance of the fall-detection model. Last, we analyzed that the sensor signals collected by both accelerometer and gyroscope sensors can be leveraged to develop an effective classifier that can accurately detect falls, especially differentiating falls from near-falls. Furthermore, we also used data from sixteen different body parts and compared them to determine the better sensor position for fall-detection methods. We found that the shank is the optimal position for placing our sensors, with an F1 score of 0.97, and this could help other researchers collect high-quality fall datasets.