Human Activity Recognition (HAR) has recently become in the spotlight of scientific research due to the development and proliferation of wearable sensors. HAR has found applications in such areas as digital health, mobile medicine, sports, abnormal activity detection and fall prevention. Neural Networks have recently become a widespread method for dealing with HAR problems due to their ability automatically extract and select features from the raw sensor data. However, this approach requires extensive training datasets to perform sufficiently under diverse circumstances. This study proposes a novel Deep Learning - based model, pre-trained on the KU-HAR dataset. The raw, six-channel sensor data was preliminarily processed using the Continuous Wavelet Transform (CWT) for better performance. Nine popular Convolutional Neural Network (CNN) architectures, as well as different wavelets and scale values, were tested to choose the best-performing combination. The proposed model was tested on the whole UCI-HAPT dataset and its subset to assess how it performs on new activities and different amounts of training data. The results show that using the pre-trained model, especially with frozen layers, leads to improved performance, smoother gradient descent and faster training on small datasets. Additionally, the model performed on the KU-HAR dataset with a classification accuracy of 97.48% and F1-score of 97.52%, which is a competitive performance compared to other state-of-the-art HAR models.